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./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/structinternal_1_1FEEvaluationImplSelector-members.html │ │ │ -rw-r--r-- 0 root (0) root (0) 23679 2026-05-02 15:42:10.000000 ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/structinternal_1_1FEEvaluationImplSelector.html │ │ │ -rw-r--r-- 0 root (0) root (0) 530 2026-05-02 15:42:10.000000 ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/structinternal_1_1FEEvaluationImplSelector.js │ │ │ @@ -13777,15 +13777,15 @@ │ │ │ -rw-r--r-- 0 root (0) root (0) 9091 2026-05-02 15:42:10.000000 ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/structinternal_1_1FEFaceEvaluationFactory-members.html │ │ │ -rw-r--r-- 0 root (0) root (0) 24673 2026-05-02 15:42:10.000000 ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/structinternal_1_1FEFaceEvaluationFactory.html │ │ │ -rw-r--r-- 0 root (0) root (0) 872 2026-05-02 15:42:10.000000 ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/structinternal_1_1FEFaceEvaluationFactory.js │ │ │ 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./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/structinternal_1_1FEFaceEvaluationImplEvaluateInFaceSelector-members.html │ │ │ -rw-r--r-- 0 root (0) root (0) 10196 2026-05-02 15:42:10.000000 ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/structinternal_1_1FEFaceEvaluationImplEvaluateInFaceSelector.html │ │ │ -rw-r--r-- 0 root (0) root (0) 194 2026-05-02 15:42:10.000000 ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/structinternal_1_1FEFaceEvaluationImplEvaluateInFaceSelector.js │ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/DEALGlossary.html │ │ │ @@ -157,15 +157,15 @@ │ │ │
FE_Q
Definition fe_q.h:554
│ │ │

On the other hand, we could have produced a similar object with dim+1 blocks using

FESystem<dim> (FE_Q<dim>(2), dim,
│ │ │
FE_Q<dim>(1), 1);
│ │ │

With the exception of the number of blocks, the two objects are the same for all practical purposes, however.

│ │ │

Global degrees of freedom: While we have defined blocks above in terms of the vector components of a vector-valued solution function (or, equivalently, in terms of the vector-valued finite element space), every shape function of a finite element is part of one block or another. Consequently, we can partition all degrees of freedom defined on a DoFHandler into individual blocks. Since by default the DoFHandler class enumerates degrees of freedom in a more or less random way, you will first want to call the DoFRenumbering::component_wise function to make sure that all degrees of freedom that correspond to a single block are enumerated consecutively.

│ │ │

If you do this, you naturally partition matrices and vectors into blocks as well (see block (linear algebra)). In most cases, when you subdivide a matrix or vector into blocks, you do so by creating one block for each block defined by the finite element (i.e. in most practical cases the FESystem object). However, this needs not be so: the DoFRenumbering::component_wise function allows to group several vector components or finite element blocks into the same logical block (see, for example, the @ref step_22 step-22" or @ref step_31 "step-31" tutorial programs, as │ │ │ opposed to @ref step_20 "step-20"). As a consequence, using this feature, we can achieve │ │ │ - the same result, i.e. subdividing matrices into \_form#147 blocks and │ │ │ + the same result, i.e. subdividing matrices into \_form#122 blocks and │ │ │ vectors into 2 blocks, for the second way of creating a Stokes element │ │ │ outlined above using an extra argument as we would have using the first way │ │ │ of creating the Stokes element with two blocks right away. │ │ │ │ │ │ More information on this topic can be found in the documentation of │ │ │ FESystem, the @ref vector_valued topic and the tutorial programs │ │ │ referenced therein. │ │ │ @@ -251,23 +251,23 @@ │ │ │ product of the image of coordinate vectors on the surface of the │ │ │ unit cell. It is a vector normal to the surface, pointing outwards │ │ │ and having the length of the surface element. │ │ │ │ │ │ A more general definition would be that (at least up to the length │ │ │ of this vector) it is exactly that vector that is necessary when │ │ │ considering integration by parts, i.e. equalities of the form │ │ │ - \iline 294 \_form#148@_fakenl. Using this definition then also explains what │ │ │ + \iline 294 \_form#123@_fakenl. Using this definition then also explains what │ │ │ this vector should be in the case of domains (and corresponding │ │ │ triangulations) of dimension <code>dim</code> that are embedded in │ │ │ a space <code>spacedim</code>: in that case, the boundary form is │ │ │ still a vector defined on the faces of the triangulation; it is │ │ │ orthogonal to all tangent directions of the boundary and within the │ │ │ tangent plane of the domain. Note that this is compatible with case │ │ │ <code>dim==spacedim</code> since there the tangent plane is the │ │ │ - entire space \_form#149. │ │ │ + entire space \_form#124. │ │ │ │ │ │ In either case, the length of the vector equals the determinant of │ │ │ the transformation of reference face to the face of the current │ │ │ cell. │ │ │ </dd> │ │ │ │ │ │ │ │ │ @@ -284,15 +284,15 @@ │ │ │ reading from a mesh file that specifically sets them to something different, │ │ │ or unless you use one of the mesh generation functions in namespace GridGenerator │ │ │ that have a │ │ │ @ref GlossColorization "colorize" │ │ │ option. A typical piece of code that sets the boundary │ │ │ indicator on part of the boundary to something else would look like │ │ │ this, here setting the boundary indicator to 42 for all faces located at │ │ │ - \_form#150: │ │ │ + \_form#125: │ │ │ @code │ │ │ for (auto &face : triangulation.active_face_iterators()) │ │ │ if (face->at_boundary()) │ │ │ if (face->center()[0] == -1) │ │ │ face->set_boundary_id (42); │ │ │ @endcode │ │ │ This calls functions TriaAccessor::set_boundary_id. In 3d, it may │ │ │ @@ -528,21 +528,21 @@ │ │ │ │ │ │ │ │ │ <dt class="glossary">@anchor GlossComponent <b>Component</b></dt> │ │ │ │ │ │ <dd> When considering systems of equations in which the solution is not │ │ │ just a single scalar function, we say that we have a <i>vector system</i> │ │ │ with a <i>vector-valued solution</i>. For example, the vector solution in │ │ │ - the elasticity equation considered in @ref step_8 "step-8" is \_form#151 │ │ │ + the elasticity equation considered in @ref step_8 "step-8" is \_form#126 │ │ │ consisting of the displacements in each of the three coordinate │ │ │ directions. The solution then has three elements. Similarly, the 3d Stokes │ │ │ - equation considered in @ref step_22 "step-22" has four elements: \_form#152. We │ │ │ + equation considered in @ref step_22 "step-22" has four elements: \_form#127. We │ │ │ call the elements of the vector-valued solution <i>components</i> in │ │ │ - deal.II. To be well-posed, for the solution to have \_form#153 components, there │ │ │ - need to be \_form#153 partial differential equations to describe them. This │ │ │ + deal.II. To be well-posed, for the solution to have \_form#128 components, there │ │ │ + need to be \_form#128 partial differential equations to describe them. This │ │ │ concept is discussed in great detail in the @ref vector_valued topic. │ │ │ │ │ │ In finite element programs, one frequently wants to address individual │ │ │ elements (components) of this vector-valued solution, or sets of │ │ │ components. For example, we do this extensively in @ref step_8 "step-8", and a lot │ │ │ of documentation is also provided in the topic on │ │ │ @ref vector_valued "Handling vector valued problems". If you are thinking │ │ │ @@ -653,15 +653,15 @@ │ │ │ The FiniteElement class has functions that convert between the two kinds of │ │ │ objects. │ │ │ │ │ │ @note Not all component masks actually make sense. For example, if you have │ │ │ a FE_RaviartThomas object in 2d, then it doesn't make any sense to have a │ │ │ component mask of the form <code>[true, false]</code> because you try to │ │ │ select individual vector components of a finite element where each shape │ │ │ - function has both \_form#8 and \_form#9 velocities. In essence, while you can of │ │ │ + function has both \_form#9 and \_form#10 velocities. In essence, while you can of │ │ │ course create such a component mask, there is nothing you can do with it. │ │ │ </dd> │ │ │ │ │ │ │ │ │ │ │ │ <dt class="glossary">@anchor GlossCompress <b>Compressing distributed │ │ │ vectors and matrices</b></dt> │ │ │ @@ -793,34 +793,34 @@ │ │ │ │ │ │ <dt class="glossary">@anchor GlossDoF <b>Degree of freedom</b></dt> │ │ │ │ │ │ <dd> The term "degree of freedom" (often abbreviated as "DoF") is commonly │ │ │ used in the finite element community to indicate two slightly different, │ │ │ but related things. The first is that we'd like to represent the finite │ │ │ element solution as a linear combination of shape functions, in the form │ │ │ - \_form#154. Here, \_form#93 │ │ │ + \_form#129. Here, \_form#114 │ │ │ is a vector of expansion coefficients. Because we don't know their values │ │ │ yet (we will compute them as the solution of a linear or nonlinear system), │ │ │ they are called "unknowns" or "degrees of freedom". The second meaning of │ │ │ the term can be explained as follows: A mathematical description of finite │ │ │ element problem is often to say that we are looking for a finite │ │ │ - dimensional function \_form#155 that satisfies some set of equations │ │ │ - (e.g. \_form#156 for all test functions \iline 845 \_form#157@_fakenl). In other words, all we say here that the solution needs to lie in │ │ │ - some space \_form#91. However, to actually solve this problem on a computer we │ │ │ + dimensional function \_form#130 that satisfies some set of equations │ │ │ + (e.g. \_form#131 for all test functions \iline 845 \_form#132@_fakenl). In other words, all we say here that the solution needs to lie in │ │ │ + some space \_form#112. However, to actually solve this problem on a computer we │ │ │ need to choose a basis of this space; this is the set of shape functions │ │ │ - \_form#158 we have used above in the expansion of \iline 849 \_form#159@_fakenl with coefficients \_form#93. There are of course many bases of the space │ │ │ - \_form#91, but we will specifically choose the one that is described by the │ │ │ + \_form#133 we have used above in the expansion of \iline 849 \_form#134@_fakenl with coefficients \_form#114. There are of course many bases of the space │ │ │ + \_form#112, but we will specifically choose the one that is described by the │ │ │ finite element functions that are traditionally defined locally on the │ │ │ cells of the mesh. Describing "degrees of freedom" in this context requires │ │ │ - us to simply <i>enumerate</i> the basis functions of the space \_form#91. For │ │ │ - \_form#40 elements this means simply enumerating the vertices of the mesh in │ │ │ + us to simply <i>enumerate</i> the basis functions of the space \_form#112. For │ │ │ + \_form#35 elements this means simply enumerating the vertices of the mesh in │ │ │ some way, but for higher elements one also has to enumerate the shape │ │ │ functions that are associated with edges, faces, or cell interiors of the │ │ │ mesh. The class that provides this enumeration of the basis functions of │ │ │ - \_form#91 is called DoFHandler. The process of enumerating degrees of freedom │ │ │ + \_form#112 is called DoFHandler. The process of enumerating degrees of freedom │ │ │ is referred to as "distributing DoFs" in deal.II. │ │ │ </dd> │ │ │ │ │ │ <dt class="glossary">@anchor GlossDirectionFlag <b>Direction flags</b></dt> │ │ │ │ │ │ <dd>The <i>direction flag</i> is used in triangulations embedded in a │ │ │ higher dimensional space to denote the orientation of cells and make the │ │ │ @@ -882,16 +882,16 @@ │ │ │ the reference cell to real cell has a Jacobian whose determinant is │ │ │ non-positive somewhere in the cell. Typically, we only check the sign │ │ │ of this determinant at the vertices of the cell. The function │ │ │ GeometryInfo::alternating_form_at_vertices computes these │ │ │ determinants at the vertices. │ │ │ │ │ │ By way of example, if all of the determinants are of roughly equal value │ │ │ - and on the order of \_form#160 then the cell is well-shaped. For │ │ │ - example, a square cell or face has determinants equal to \_form#160 │ │ │ + and on the order of \_form#135 then the cell is well-shaped. For │ │ │ + example, a square cell or face has determinants equal to \_form#135 │ │ │ whereas a strongly sheared parallelogram has a determinant much │ │ │ smaller. Similarly, a cell with very unequal edge lengths will have widely │ │ │ varying determinants. Conversely, a pinched cell in which the location of │ │ │ two or more vertices is collapsed to a single point has a zero determinant │ │ │ at this location. Finally, an inverted or twisted cell in which the │ │ │ location of two vertices is out of order will have negative determinants. │ │ │ │ │ │ @@ -983,15 +983,15 @@ │ │ │ vertices which define a face may be, from the perspective of an arbitrary │ │ │ cell, in a different order than the order given to that face by the │ │ │ neighboring cell. To resolve this inconsistency deal.II stores, for each face │ │ │ and (in 3d) line, a value which may be used to permute the vertices on both │ │ │ faces into a matching configuration. This encoding contains both the number │ │ │ of times a face should be rotated (relative to its neighbor) as well as │ │ │ whether or not the face should be viewed in an opposite orientation (e.g., │ │ │ - for a Quadrilateral, whether or not vertices \_form#161 and \_form#162 should be swapped). │ │ │ + for a Quadrilateral, whether or not vertices \_form#136 and \_form#137 should be swapped). │ │ │ │ │ │ This value is called the <em>combined_orientation</em> since it combines both │ │ │ the orientation (as defined above) as well as rotations. In some │ │ │ circumstances, to disambiguate between faces and lines, it may alternatively │ │ │ be called either the <tt>combined_face_orientation</tt> or the │ │ │ <tt>combined_line_orientation</tt>. These orientations are represented by │ │ │ types::geometric_orientation, which encodes how the vertices of the canonical │ │ │ @@ -1015,52 +1015,52 @@ │ │ │ </dd> │ │ │ │ │ │ <dt class="glossary">@anchor GlossGeneralizedSupport <b>Generalized support points</b></dt> │ │ │ <dd>"Generalized support points" are, as the name suggests, a │ │ │ generalization of @ref GlossSupport "support points". The latter │ │ │ are used to describe that a finite element simply <i>interpolates</i> │ │ │ values at individual points (the "support points"). If we call these │ │ │ - points \_form#163 (where the hat indicates that these points │ │ │ - are defined on the reference cell \_form#164), then one typically defines │ │ │ - shape functions \_form#158 in such a way that the │ │ │ - <i>nodal functionals</i> \_form#165 simply evaluate the function │ │ │ - at the support point, i.e., that \_form#166, │ │ │ - and the basis is chosen so that \_form#167 where │ │ │ - \_form#168 is the Kronecker delta function. This leads to the common │ │ │ + points \_form#138 (where the hat indicates that these points │ │ │ + are defined on the reference cell \_form#139), then one typically defines │ │ │ + shape functions \_form#133 in such a way that the │ │ │ + <i>nodal functionals</i> \_form#140 simply evaluate the function │ │ │ + at the support point, i.e., that \_form#141, │ │ │ + and the basis is chosen so that \_form#142 where │ │ │ + \_form#143 is the Kronecker delta function. This leads to the common │ │ │ @ref GlossLagrange "Lagrange elements". │ │ │ │ │ │ (In the vector valued case, the only other piece of information │ │ │ - besides the support points \_form#163 that one needs to provide │ │ │ - is the <i>vector component</i> \_form#169 the \_form#45th node functional │ │ │ - corresponds, so that \_form#170.) │ │ │ + besides the support points \_form#138 that one needs to provide │ │ │ + is the <i>vector component</i> \_form#144 the \_form#65th node functional │ │ │ + corresponds, so that \_form#145.) │ │ │ │ │ │ On the other hand, there are other kinds of elements that are not │ │ │ defined this way. For example, for the lowest order Raviart-Thomas element │ │ │ (see the FE_RaviartThomas class), the node functional evaluates not │ │ │ individual components of a vector-valued finite element function with @p dim │ │ │ components, but the <i>normal component</i> of this vector: │ │ │ - \iline 1082 \iline 1083 \iline 1084 \_form#171@_fakenl@_fakenl@_fakenl, where the \_form#172 are the normal vectors to the face of the cell │ │ │ - on which \_form#163 is located. In other words, the node functional │ │ │ - is a <i>linear combination</i> of the components of \_form#133 when │ │ │ - evaluated at \_form#163. Similar things happen for the BDM, │ │ │ + \iline 1082 \iline 1083 \iline 1084 \_form#146@_fakenl@_fakenl@_fakenl, where the \_form#147 are the normal vectors to the face of the cell │ │ │ + on which \_form#138 is located. In other words, the node functional │ │ │ + is a <i>linear combination</i> of the components of \_form#148 when │ │ │ + evaluated at \_form#138. Similar things happen for the BDM, │ │ │ ABF, and Nedelec elements (see the FE_BDM, FE_ABF, FE_Nedelec classes). │ │ │ │ │ │ In these cases, the element does not have <i>support points</i> because │ │ │ it is not purely interpolatory; however, some kind of interpolation │ │ │ is still involved when defining shape functions as the node functionals │ │ │ - still require point evaluations at special points \_form#163. │ │ │ + still require point evaluations at special points \_form#138. │ │ │ In these cases, we call the points <i>generalized support points</i>. │ │ │ │ │ │ Finally, there are elements that still do not fit into this │ │ │ scheme. For example, some hierarchical basis functions │ │ │ (see, for example the FE_Q_Hierarchical element) are defined so │ │ │ that the node functionals are <i>moments</i> of finite element │ │ │ functions, │ │ │ - \iline 1102 \iline 1103 \iline 1104 \iline 1105 \iline 1106 \_form#173@_fakenl@_fakenl@_fakenl@_fakenl@_fakenl in 2d, and similarly for 3d, where the \_form#174 are the order │ │ │ - of the moment described by shape function \_form#45. Some other elements │ │ │ + \iline 1102 \iline 1103 \iline 1104 \iline 1105 \iline 1106 \_form#149@_fakenl@_fakenl@_fakenl@_fakenl@_fakenl in 2d, and similarly for 3d, where the \_form#150 are the order │ │ │ + of the moment described by shape function \_form#65. Some other elements │ │ │ use moments over edges or faces. In all of these cases, node functionals │ │ │ are not defined through interpolation at all, and these elements then │ │ │ have neither support points, nor generalized support points. │ │ │ </dd> │ │ │ │ │ │ │ │ │ <dt class="glossary">@anchor geometry_paper <b>geometry paper</b></dt> │ │ │ @@ -1224,15 +1224,15 @@ │ │ │ } │ │ │ @endcode │ │ │ It is available from <a href="https://www.math.colostate.edu/~bangerth/publications.html">https://www.math.colostate.edu/~bangerth/publications.html</a>, also see <a href="https://www.dealii.org/publications.html#details">deal.II publications</a> for details. │ │ │ │ │ │ The numerical examples shown in that paper are generated with a slightly │ │ │ modified version of @ref step_27 "step-27". The main difference to that │ │ │ tutorial program is that various operations in the program were timed for │ │ │ - the paper to compare different options and show that \_form#20 methods are │ │ │ + the paper to compare different options and show that \_form#0 methods are │ │ │ really not all that expensive. │ │ │ </dd> │ │ │ │ │ │ │ │ │ <dt class="glossary">@anchor GlossInterpolation <b>Interpolation with finite elements</b></dt> │ │ │ <dd>The purpose of interpolation with finite elements is computing │ │ │ a vector of coefficients representing a finite element function, │ │ │ @@ -1467,57 +1467,57 @@ │ │ │ Locally relevant DoFs are a superset of the │ │ │ @ref GlossLocallyActiveDof "locally active DoFs." │ │ │ </dd> │ │ │ │ │ │ │ │ │ <dt class="glossary">@anchor GlossLumpedMassMatrix <b>Lumped mass matrix</b></dt> │ │ │ <dd>The @ref GlossMassMatrix "mass matrix" is a matrix of the form │ │ │ - \iline 1526 \iline 1527 \_form#175@_fakenl@_fakenl │ │ │ + \iline 1526 \iline 1527 \_form#154@_fakenl@_fakenl │ │ │ It frequently appears in the solution of time dependent problems where, if │ │ │ one uses an explicit time stepping method, it then leads to the need │ │ │ to solve problems of the form │ │ │ - \iline 1532 \iline 1533 \_form#176@_fakenl@_fakenl │ │ │ - in time step \_form#153, where \_form#177 is the solution to be computed, \_form#178 is the │ │ │ - known solution from the first time step, and \_form#95 is a matrix related to the │ │ │ - differential operator in the PDE. \_form#179 is the size of the time step. A similar │ │ │ + \iline 1532 \iline 1533 \_form#155@_fakenl@_fakenl │ │ │ + in time step \_form#128, where \_form#156 is the solution to be computed, \_form#157 is the │ │ │ + known solution from the first time step, and \_form#116 is a matrix related to the │ │ │ + differential operator in the PDE. \_form#158 is the size of the time step. A similar │ │ │ linear system of equations also arises out of the discretization of second-order │ │ │ differential equations. │ │ │ │ │ │ - The presence of the matrix \_form#145 on the left side is a nuisance because, even │ │ │ + The presence of the matrix \_form#120 on the left side is a nuisance because, even │ │ │ though we have used an explicit time stepping method, we still have to solve a │ │ │ linear system in each time step. It would be much preferable if the matrix were │ │ │ - diagonal. "Lumping" the mass matrix is a strategy to replace \_form#145 by a matrix │ │ │ - \_form#180 that actually is diagonal, yet does not destroy the accuracy │ │ │ + diagonal. "Lumping" the mass matrix is a strategy to replace \_form#120 by a matrix │ │ │ + \_form#159 that actually is diagonal, yet does not destroy the accuracy │ │ │ of the resulting solution. │ │ │ │ │ │ Historically, mass lumping was performed by adding the elements of a row │ │ │ - together and setting the diagonal entries of \_form#180 to that │ │ │ - sum. This works for \_form#40 and \_form#181 elements, for example, and can be │ │ │ + together and setting the diagonal entries of \_form#159 to that │ │ │ + sum. This works for \_form#35 and \_form#160 elements, for example, and can be │ │ │ understood mechanically by replacing the continuous medium we are │ │ │ discretizating by one where the continuous mass distribution is replaced by │ │ │ one where (finite amounts of) mass are located only at the nodes. That is, │ │ │ we are "lumping together" the mass of an element at its vertices, thus │ │ │ giving rise to the name "lumped mass matrix". A more mathematical perspective │ │ │ - is to compute the integral above for \_form#182 via special quadrature rules; │ │ │ + is to compute the integral above for \_form#161 via special quadrature rules; │ │ │ in particular, we replace the computation of │ │ │ - \iline 1558 \iline 1559 \iline 1560 \_form#183@_fakenl@_fakenl@_fakenl │ │ │ + \iline 1558 \iline 1559 \iline 1560 \_form#162@_fakenl@_fakenl@_fakenl │ │ │ by quadrature │ │ │ - \iline 1563 \iline 1564 \iline 1565 \_form#184@_fakenl@_fakenl@_fakenl │ │ │ + \iline 1563 \iline 1564 \iline 1565 \_form#163@_fakenl@_fakenl@_fakenl │ │ │ where we choose the quadrature points as the <em>nodes</em> at which the │ │ │ shape functions are defined. If we order the quadrature points in the │ │ │ same way as the shape functions, then │ │ │ - \iline 1570 \iline 1571 \_form#185@_fakenl@_fakenl │ │ │ + \iline 1570 \iline 1571 \_form#164@_fakenl@_fakenl │ │ │ and consequently │ │ │ - \iline 1574 \iline 1575 \_form#186@_fakenl@_fakenl │ │ │ - where the sum extends over those cells on which \_form#187 is nonzero. │ │ │ + \iline 1574 \iline 1575 \_form#165@_fakenl@_fakenl │ │ │ + where the sum extends over those cells on which \_form#166 is nonzero. │ │ │ The so-computed mass matrix is therefore diagonal. │ │ │ │ │ │ Whether or not this particular choice of quadrature formula is │ │ │ sufficient to retain the convergence rate of the discretization is │ │ │ - a separate question. For the usual \_form#188 finite elements │ │ │ + a separate question. For the usual \_form#169 finite elements │ │ │ (implemented by FE_Q and FE_DGQ), the appropriate quadrature │ │ │ formulas are of QGaussLobatto type. Mass lumping can also be done │ │ │ with FE_SimplexP_Bubbles, for example, if appropriate quadrature rules │ │ │ are chosen. │ │ │ │ │ │ For an example of where lumped mass matrices play a role, see @ref step_69 "step-69". │ │ │ </dd> │ │ │ @@ -1534,15 +1534,15 @@ │ │ │ defining the locations of @ref GlossSupport "support points", and defining │ │ │ the locations of quadrature points. │ │ │ │ │ │ By default, all manifold indicators of a mesh are set to │ │ │ numbers::flat_manifold_id. A typical piece of code that sets the │ │ │ manifold indicator on a object to something else would look like │ │ │ this, here setting the manifold indicator to 42 for all cells whose │ │ │ - center has an \_form#8 component less than zero: │ │ │ + center has an \_form#9 component less than zero: │ │ │ │ │ │ @code │ │ │ for (auto &cell : triangulation.active_cell_iterators()) │ │ │ if (cell->center()[0] < 0) │ │ │ cell->set_manifold_id(42); │ │ │ @endcode │ │ │ │ │ │ @@ -1564,40 +1564,40 @@ │ │ │ </dd> │ │ │ │ │ │ @see @ref manifold "The topic on Manifolds" │ │ │ │ │ │ │ │ │ <dt class="glossary">@anchor GlossMassMatrix <b>Mass matrix</b></dt> │ │ │ <dd>The "mass matrix" is a matrix of the form │ │ │ - \iline 1637 \iline 1638 \_form#175@_fakenl@_fakenl │ │ │ + \iline 1637 \iline 1638 \_form#154@_fakenl@_fakenl │ │ │ possibly with a coefficient inside the integral, and │ │ │ - where \_form#189 are the shape functions of a finite element. │ │ │ + where \_form#170 are the shape functions of a finite element. │ │ │ The origin of the term refers to the fact that in structural mechanics │ │ │ (where the finite element method originated), one often starts from the │ │ │ elastodynamics (wave) equation │ │ │ - \iline 1645 \iline 1646 \iline 1647 \_form#190@_fakenl@_fakenl@_fakenl │ │ │ - If one multiplies this equation by a test function \_form#187, │ │ │ - integrates over \_form#191, and then discretizes by the substitution │ │ │ - \_form#192, │ │ │ + \iline 1645 \iline 1646 \iline 1647 \_form#171@_fakenl@_fakenl@_fakenl │ │ │ + If one multiplies this equation by a test function \_form#166, │ │ │ + integrates over \_form#172, and then discretizes by the substitution │ │ │ + \_form#173, │ │ │ then the first term above results in │ │ │ - \iline 1653 \iline 1654 \iline 1655 \_form#193@_fakenl@_fakenl@_fakenl │ │ │ + \iline 1653 \iline 1654 \iline 1655 \_form#174@_fakenl@_fakenl@_fakenl │ │ │ which can be written as │ │ │ - \iline 1658 \iline 1659 \iline 1660 \_form#194@_fakenl@_fakenl@_fakenl │ │ │ + \iline 1658 \iline 1659 \iline 1660 \_form#175@_fakenl@_fakenl@_fakenl │ │ │ where │ │ │ - \iline 1663 \iline 1664 \_form#195@_fakenl@_fakenl │ │ │ + \iline 1663 \iline 1664 \_form#176@_fakenl@_fakenl │ │ │ Since the matrix entries are a (weighted) integral over a mass density, they │ │ │ have the units of "mass", giving the "mass matrix" its name. │ │ │ │ │ │ In mathematics, where we often consider non-dimensionalized equations, we │ │ │ - end up with the case \_form#196, and as a consequence the matrix without │ │ │ + end up with the case \_form#177, and as a consequence the matrix without │ │ │ the coefficient, │ │ │ - \iline 1672 \iline 1673 \_form#175@_fakenl@_fakenl │ │ │ + \iline 1672 \iline 1673 \_form#154@_fakenl@_fakenl │ │ │ also carries the name "mass matrix". │ │ │ │ │ │ - The mass matrix is almost always written with the symbol \_form#145. See, for example, │ │ │ + The mass matrix is almost always written with the symbol \_form#120. See, for example, │ │ │ @ref step_23 "step-23", @ref step_26 "step-26", and a number of the other time dependent equations solved by │ │ │ tutorial programs. │ │ │ │ │ │ The mass matrix is occasionally approximated by a diagonal matrix, │ │ │ see the glossary entry for @ref GlossLumpedMassMatrix "lumped mass matrix". │ │ │ See also the @ref GlossStiffnessMatrix "stiffness matrix" │ │ │ for a related case. │ │ │ @@ -1742,25 +1742,25 @@ │ │ │ for the paper and <a href="https://www.dealii.org/publications.html#details">deal.II publications</a> for more details. │ │ │ </dd> │ │ │ │ │ │ │ │ │ <dt class="glossary">@anchor GlossNodes <b>Node values or node functionals</b></dt> │ │ │ │ │ │ <dd>It is customary to define a finite element as a triple │ │ │ - \_form#197 where │ │ │ - - \_form#84 is the cell, where in deal.II this is always a line segment, │ │ │ + \_form#178 where │ │ │ + - \_form#44 is the cell, where in deal.II this is always a line segment, │ │ │ quadrilateral, or hexahedron; │ │ │ - - \_form#198 is a finite-dimensional space, e.g., a polynomial space mapped │ │ │ - from the @ref GlossReferenceCell "reference cell" to \_form#84; │ │ │ - - \_form#199 is a set of "node functionals", i.e., functionals │ │ │ - \_form#200. │ │ │ - The dimension of \_form#198 must be equal to the number of node functionals. │ │ │ + - \_form#179 is a finite-dimensional space, e.g., a polynomial space mapped │ │ │ + from the @ref GlossReferenceCell "reference cell" to \_form#44; │ │ │ + - \_form#180 is a set of "node functionals", i.e., functionals │ │ │ + \_form#181. │ │ │ + The dimension of \_form#179 must be equal to the number of node functionals. │ │ │ With this definition, we can define a basis of the local function space, │ │ │ - i.e., a set of "shape functions" \_form#201, by requiring that │ │ │ - \_form#202, where \_form#203 is the Kronecker delta. │ │ │ + i.e., a set of "shape functions" \_form#182, by requiring that │ │ │ + \_form#183, where \_form#184 is the Kronecker delta. │ │ │ │ │ │ This definition of what a finite element is has several advantages, │ │ │ concerning analysis as well │ │ │ as implementation. For the analysis, it means that conformity with │ │ │ certain spaces (FiniteElementData::Conformity), e.g. continuity, is │ │ │ up to the node functionals. In deal.II, it helps simplifying the │ │ │ implementation of more complex elements like FE_RaviartThomas │ │ │ @@ -1800,142 +1800,142 @@ │ │ │ <dt class="glossary">@anchor GlossParallelScaling <b>Parallel scaling</b></dt> │ │ │ <dd>When we say that a parallel program "scales", what we mean is that the │ │ │ program does not become unduly slow (or takes unduly much memory) if we │ │ │ make the problem it solves larger, and that run time and memory consumption │ │ │ decrease proportionally if we keep the problem size the same but increase │ │ │ the number of processors (or cores) that work on it. │ │ │ │ │ │ - More specifically, think of a problem whose size is given by a number \_form#204 │ │ │ + More specifically, think of a problem whose size is given by a number \_form#185 │ │ │ (which could be the number of cells, the number of unknowns, or some other │ │ │ indicative quantity such as the number of CPU cycles necessary to solve │ │ │ - it) and for which you have \_form#198 processors available for solution. In an │ │ │ - ideal world, the program would then require a run time of \_form#205, │ │ │ + it) and for which you have \_form#179 processors available for solution. In an │ │ │ + ideal world, the program would then require a run time of \_form#186, │ │ │ and this would imply that we could reduce the run time to any desired │ │ │ value by just providing more processors. Likewise, for a program to be │ │ │ - scalable, its overall memory consumption needs to be \_form#206 and on │ │ │ - each involved process needs to be \_form#205, again │ │ │ + scalable, its overall memory consumption needs to be \_form#187 and on │ │ │ + each involved process needs to be \_form#186, again │ │ │ implying that we can fit any problem into the fixed amount of memory │ │ │ computers attach to each processor, by just providing │ │ │ sufficiently many processors. │ │ │ │ │ │ For practical assessments of scalability, we often distinguish between │ │ │ "strong" and "weak" scalability. These assess asymptotic statements │ │ │ - such as \_form#205 run time in the limits \_form#207 │ │ │ - and/or \_form#208. Specifically, when we say that a program │ │ │ + such as \_form#186 run time in the limits \_form#188 │ │ │ + and/or \_form#189. Specifically, when we say that a program │ │ │ is "strongly scalable", we mean that if we have a problem of fixed │ │ │ - size \_form#204, then we can reduce the run time and memory consumption (on │ │ │ - every processor) inversely proportional to \_form#198 by just throwing more │ │ │ + size \_form#185, then we can reduce the run time and memory consumption (on │ │ │ + every processor) inversely proportional to \_form#179 by just throwing more │ │ │ processors at the problem. In particular, strong scalability implies │ │ │ that if we provide twice as many processors, then run time and memory │ │ │ consumption on every process will be reduced by a factor of two. In │ │ │ other words, we can solve the <i>same problem</i> faster and faster │ │ │ by providing more and more processors. │ │ │ │ │ │ Conversely, "weak scalability" means that if we increase the problem │ │ │ - size \_form#204 by a fixed factor, and increase the number of processors │ │ │ - \_form#198 available to solve the problem by the same factor, then the │ │ │ + size \_form#185 by a fixed factor, and increase the number of processors │ │ │ + \_form#179 available to solve the problem by the same factor, then the │ │ │ overall run time (and the memory consumption on every processor) │ │ │ remains the same. In other words, we can solve <i>larger and larger │ │ │ problems</i> within the same amount of wallclock time by providing │ │ │ more and more processors. │ │ │ │ │ │ No program is truly scalable in this theoretical sense. Rather, all programs │ │ │ - cease to scale once either \_form#204 or \_form#198 grows larger than certain limits. │ │ │ + cease to scale once either \_form#185 or \_form#179 grows larger than certain limits. │ │ │ We therefore often say things such as "the program scales up to 4,000 cores", or "the program scales up to 100,000,000 unknowns". There are │ │ │ a number of reasons why programs cannot scale without limit; these can │ │ │ all be illustrated by just looking at the (relatively simple) @ref step_17 "step-17" │ │ │ tutorial program: │ │ │ - Sequential sections: Many programs have sections of code that │ │ │ either cannot or are not parallelized, i.e., where one processor has to do │ │ │ a certain, fixed amount of work that does not decrease just because │ │ │ - there are a total of \_form#198 processors around. In @ref step_17 "step-17", this is │ │ │ + there are a total of \_form#179 processors around. In @ref step_17 "step-17", this is │ │ │ the case when generating graphical output: one processor creates │ │ │ the graphical output for the entire problem, i.e., it needs to do │ │ │ - \_form#206 work. That means that this function has a run time │ │ │ - of \_form#206, regardless of \_form#198, and consequently the overall │ │ │ - program will not be able to achieve \_form#205 run time but │ │ │ - have a run time that can be described as \_form#209 where │ │ │ + \_form#187 work. That means that this function has a run time │ │ │ + of \_form#187, regardless of \_form#179, and consequently the overall │ │ │ + program will not be able to achieve \_form#186 run time but │ │ │ + have a run time that can be described as \_form#195 where │ │ │ the first term comes from scalable operations such as assembling │ │ │ the linear system, and the latter from generating graphical │ │ │ - output on process 0. If \_form#210 is sufficiently small, then the │ │ │ + output on process 0. If \_form#196 is sufficiently small, then the │ │ │ program might look like it scales strongly for small numbers of │ │ │ processors, but eventually strong scalability will cease. In │ │ │ addition, the program can not scale weakly either because │ │ │ - increasing the size \_form#204 of the problem while increasing the │ │ │ - number of processors \_form#198 at the same rate does not keep the │ │ │ + increasing the size \_form#185 of the problem while increasing the │ │ │ + number of processors \_form#179 at the same rate does not keep the │ │ │ run time of this one function constant. │ │ │ - Duplicated data structures: In @ref step_17 "step-17", each processor stores the entire │ │ │ mesh. That is, each processor has to store a data structure of size │ │ │ - \_form#206, regardless of \_form#198. Eventually, if we make the problem │ │ │ + \_form#187, regardless of \_form#179. Eventually, if we make the problem │ │ │ size large enough, this will overflow each processor's memory space │ │ │ even if we increase the number of processors. It is thus clear that such │ │ │ a replicated data structure prevents a program from scaling weakly. │ │ │ But it also prevents it from scaling strongly because in order to │ │ │ - create an object of size \_form#206, one has to at the very │ │ │ - least write into \_form#206 memory locations, costing │ │ │ - \_form#206 in CPU time. Consequently, there is a component of the │ │ │ - overall algorithm that does not behave as \_form#205 if we │ │ │ + create an object of size \_form#187, one has to at the very │ │ │ + least write into \_form#187 memory locations, costing │ │ │ + \_form#187 in CPU time. Consequently, there is a component of the │ │ │ + overall algorithm that does not behave as \_form#186 if we │ │ │ provide more and more processors. │ │ │ - Communication: If, to pick just one example, you want to compute │ │ │ - the \_form#211 norm of a vector of which all MPI processes store a few │ │ │ + the \_form#205 norm of a vector of which all MPI processes store a few │ │ │ entries, then every process needs to compute the sum of squares of │ │ │ - its own entries (which will require \_form#205 time, and │ │ │ + its own entries (which will require \_form#186 time, and │ │ │ consequently scale perfectly), but then every process needs to │ │ │ send their partial sum to one process that adds them all up and takes │ │ │ the square root. In the very best case, sending a message that │ │ │ contains a single number takes a constant amount of time, │ │ │ regardless of the overall number of processes. Thus, again, every │ │ │ program that does communication cannot scale strongly because │ │ │ there are parts of the program whose CPU time requirements do │ │ │ - not decrease with the number of processors \_form#198 you allocate for │ │ │ - a fixed size \_form#204. In reality, the situation is actually even │ │ │ + not decrease with the number of processors \_form#179 you allocate for │ │ │ + a fixed size \_form#185. In reality, the situation is actually even │ │ │ worse: the more processes are participating in a communication │ │ │ step, the longer it will generally take, for example because │ │ │ the one process that has to add everyone's contributions has │ │ │ - to add everything up, requiring \_form#212 time. In other words, │ │ │ + to add everything up, requiring \_form#208 time. In other words, │ │ │ CPU time <i>increases</i> with the number of processes, therefore │ │ │ not only preventing a program from scaling strongly, but also from │ │ │ - scaling weakly. (In reality, MPI libraries do not implement \_form#211 │ │ │ + scaling weakly. (In reality, MPI libraries do not implement \_form#205 │ │ │ norms by sending every message to one process that then adds everything │ │ │ up; rather, they do pairwise reductions on a tree that doesn't │ │ │ - grow the run time as \_form#212 but as \_form#213, │ │ │ + grow the run time as \_form#208 but as \_form#209, │ │ │ at the expense of more messages sent around. Be that as it may, │ │ │ the fundamental point is that as you add more processors, the │ │ │ - run time will grow with \_form#198 regardless of the way the operation │ │ │ + run time will grow with \_form#179 regardless of the way the operation │ │ │ is actually implemented, and it can therefore not scale.) │ │ │ │ │ │ These, and other reasons that prevent programs from scaling perfectly can │ │ │ be summarized in <a href="https://en.wikipedia.org/wiki/Amdahl%27s_law"> │ │ │ - <i>Amdahl's law</i></a> that states that if a fraction \_form#214 │ │ │ - of a program's overall work \_form#215 can be parallelized, i.e., it can be │ │ │ - run in \_form#216 time, and a fraction \_form#217 of the │ │ │ + <i>Amdahl's law</i></a> that states that if a fraction \_form#210 │ │ │ + of a program's overall work \_form#211 can be parallelized, i.e., it can be │ │ │ + run in \_form#212 time, and a fraction \_form#213 of the │ │ │ program's work can not be parallelized (i.e., it consists either of │ │ │ work that only one process can do, such as generating graphical output │ │ │ in @ref step_17 "step-17"; or that every process has to execute in a replicated way, │ │ │ such as sending a message with a local contribution to a dedicated │ │ │ process for accumulation), then the overall run time of the program │ │ │ will be │ │ │ - \iline 1999 \iline 2000 \_form#218@_fakenl@_fakenl │ │ │ + \iline 1999 \iline 2000 \_form#215@_fakenl@_fakenl │ │ │ Consequently, the "speedup" you get, i.e., the factor by which your │ │ │ - programs run faster on \_form#198 processors compared to running the program │ │ │ + programs run faster on \_form#179 processors compared to running the program │ │ │ on a single process (assuming this is possible) would be │ │ │ - \iline 2005 \iline 2006 \iline 2007 \_form#219@_fakenl@_fakenl@_fakenl │ │ │ - If \_form#220, which it is for all practically existing programs, │ │ │ - then \_form#221 as \_form#208, implying │ │ │ + \iline 2005 \iline 2006 \iline 2007 \_form#216@_fakenl@_fakenl@_fakenl │ │ │ + If \_form#217, which it is for all practically existing programs, │ │ │ + then \_form#218 as \_form#189, implying │ │ │ that there is a point where it does not pay off in any significant way │ │ │ any more to throw more processors at the problem. │ │ │ │ │ │ In practice, what matters is <i>up to which problem size</i> or │ │ │ <i>up to which number of processes</i> or <i>down to which size │ │ │ - of local problems \_form#222</i> a program scales. For deal.II, │ │ │ + of local problems \_form#219</i> a program scales. For deal.II, │ │ │ experience shows that on most clusters with a reasonable fast │ │ │ network, one can solve problems up to a few billion unknowns, │ │ │ up to a few thousand processors, and down to somewhere between │ │ │ 40,000 and 100,000 unknowns per process. The last number is the │ │ │ - most relevant: if you have a problem with, say, \_form#223 unknowns, │ │ │ + most relevant: if you have a problem with, say, \_form#221 unknowns, │ │ │ then it makes sense to solve it on 1000-2500 processors since the │ │ │ number of degrees of freedom each process handles remains at more │ │ │ than 40,000. Consequently, there is enough work every process │ │ │ has to do so that the \_form#224 time for communication does │ │ │ not dominate. But it doesn't make sense to solve such a problem with │ │ │ 10,000 or 100,000 processors, since each of these processor's local │ │ │ problem becomes so small that they spend most of their time waiting │ │ │ @@ -2021,55 +2021,55 @@ │ │ │ <dd>The restriction of the finite element basis functions to a single │ │ │ grid cell. │ │ │ </dd> │ │ │ │ │ │ │ │ │ <dt class="glossary">@anchor GlossStiffnessMatrix <b>Stiffness matrix</b></dt> │ │ │ <dd>The "stiffness matrix" is a matrix of the form │ │ │ - \iline 2114 \iline 2115 \iline 2116 \_form#225@_fakenl@_fakenl@_fakenl │ │ │ + \iline 2114 \iline 2115 \iline 2116 \_form#227@_fakenl@_fakenl@_fakenl │ │ │ possibly with a coefficient inside the integral, and │ │ │ - where \_form#189 are the shape functions of a finite element. │ │ │ + where \_form#170 are the shape functions of a finite element. │ │ │ The term is also used for variations of the case above, for example │ │ │ replacing the gradient by the symmetric gradient in the case where │ │ │ the solution variable is vector-valued (e.g., in elasticity, or the │ │ │ Stokes equations). The key feature is that in the integral, first │ │ │ derivatives are applied to both the test and trial functions, │ │ │ - \_form#226. │ │ │ + \_form#228. │ │ │ │ │ │ The origin of the term refers to the fact that in structural mechanics │ │ │ (where the finite element method originated), one often starts from the │ │ │ elastostatics equation │ │ │ - \iline 2130 \iline 2131 \_form#227@_fakenl@_fakenl │ │ │ - In this equation, \_form#73 is the stress-strain tensor that, informally │ │ │ + \iline 2130 \iline 2131 \_form#229@_fakenl@_fakenl │ │ │ + In this equation, \_form#50 is the stress-strain tensor that, informally │ │ │ speaking, relates how much force one has to apply to obtain a │ │ │ unit displacement. In other words, it encodes the "stiffness" of │ │ │ - the material: A large \_form#73, i.e., a large stiffness, means a large │ │ │ + the material: A large \_form#50, i.e., a large stiffness, means a large │ │ │ required force for a desired displacement and the other way around. │ │ │ │ │ │ - If one multiplies this equation by a test function \_form#187, │ │ │ - integrates over \_form#191, and then discretizes by the substitution │ │ │ - \_form#192, │ │ │ + If one multiplies this equation by a test function \_form#166, │ │ │ + integrates over \_form#172, and then discretizes by the substitution │ │ │ + \_form#173, │ │ │ then after integration by parts one ends up with │ │ │ - \iline 2143 \iline 2144 \iline 2145 \_form#228@_fakenl@_fakenl@_fakenl │ │ │ + \iline 2143 \iline 2144 \iline 2145 \_form#230@_fakenl@_fakenl@_fakenl │ │ │ which can be written as │ │ │ - \iline 2148 \iline 2149 \_form#229@_fakenl@_fakenl │ │ │ + \iline 2148 \iline 2149 \_form#231@_fakenl@_fakenl │ │ │ where │ │ │ - \iline 2152 \iline 2153 \_form#230@_fakenl@_fakenl │ │ │ + \iline 2152 \iline 2153 \_form#232@_fakenl@_fakenl │ │ │ Since the matrix entries are (weighted) integrals of the stiffness │ │ │ coefficient, the resulting matrix is called the "stiffness matrix". │ │ │ │ │ │ In mathematics, where we often consider non-dimensionalized equations, │ │ │ - we end up with the case \_form#231, and as a consequence the matrix without │ │ │ + we end up with the case \_form#233, and as a consequence the matrix without │ │ │ the coefficient, │ │ │ - \iline 2161 \iline 2162 \_form#232@_fakenl@_fakenl │ │ │ + \iline 2161 \iline 2162 \_form#234@_fakenl@_fakenl │ │ │ which corresponds to the Laplace or Poisson equation, │ │ │ - \iline 2165 \iline 2166 \_form#233@_fakenl@_fakenl │ │ │ + \iline 2165 \iline 2166 \_form#235@_fakenl@_fakenl │ │ │ also carries the name "stiffness matrix". │ │ │ │ │ │ - The stiffness matrix is almost always denotes by the symbol \_form#70. See, for example, │ │ │ + The stiffness matrix is almost always denotes by the symbol \_form#47. See, for example, │ │ │ @ref step_4 "step-4", @ref step_6 "step-6", as well as a number of the time dependent equations considered in │ │ │ programs such as @ref step_23 "step-23" or @ref step_26 "step-26". │ │ │ │ │ │ See also the @ref GlossStiffnessMatrix "stiffness matrix" │ │ │ for a related case. │ │ │ </dt> │ │ │ │ │ │ @@ -2123,16 +2123,16 @@ │ │ │ subdomain ids, but they are read and written by the │ │ │ CellAccessor::level_subdomain_id() and CellAccessor::set_level_subdomain_id() │ │ │ functions. │ │ │ </dd> │ │ │ │ │ │ │ │ │ <dt class="glossary">@anchor GlossSupport <b>Support points</b></dt> │ │ │ - <dd>Support points are by definition those points \_form#234, such that for the │ │ │ - shape functions \_form#235 holds \_form#236. Therefore, a finite │ │ │ + <dd>Support points are by definition those points \_form#236, such that for the │ │ │ + shape functions \_form#237 holds \_form#238. Therefore, a finite │ │ │ element interpolation can be defined uniquely by the values in the support │ │ │ points. │ │ │ │ │ │ Lagrangian elements fill the vector accessed by │ │ │ FiniteElement::get_unit_support_points(), such that the │ │ │ function FiniteElement::has_support_points() returns │ │ │ <tt>true</tt>. Naturally, these support points are on the │ │ │ @@ -2275,24 +2275,24 @@ │ │ │ │ │ │ │ │ │ <dt class="glossary">@anchor GlossUserProvidedCallBack <b>User provided callbacks</b></dt> │ │ │ <dd> │ │ │ Much functionality in deal.II under the hood uses external libraries that │ │ │ operate by calling back into user-provided functions. Examples are │ │ │ ODE solvers that solve differential equations of the form │ │ │ - \iline 2384 \iline 2385 \_form#237@_fakenl@_fakenl │ │ │ - where users need to provide a function that, for a given time \_form#238 and vector │ │ │ - \_form#239 returns the value of the right hand side \_form#240. │ │ │ + \iline 2384 \iline 2385 \_form#239@_fakenl@_fakenl │ │ │ + where users need to provide a function that, for a given time \_form#240 and vector │ │ │ + \_form#241 returns the value of the right hand side \_form#242. │ │ │ Other examples are solvers for nonlinear systems │ │ │ - \iline 2390 \iline 2391 \_form#241@_fakenl@_fakenl │ │ │ - where users need to provide functions that for a given vector \_form#242 returns │ │ │ - the vector \_form#243 and, in many cases, also the Jacobian │ │ │ - \_form#244 as well as possibly other information about │ │ │ + \iline 2390 \iline 2391 \_form#243@_fakenl@_fakenl │ │ │ + where users need to provide functions that for a given vector \_form#244 returns │ │ │ + the vector \_form#245 and, in many cases, also the Jacobian │ │ │ + \_form#246 as well as possibly other information about │ │ │ the problem such as the relative scaling of solution variables within the │ │ │ - vector \_form#242 that can be used to make the problem better conditioned. │ │ │ + vector \_form#244 that can be used to make the problem better conditioned. │ │ │ │ │ │ These functions are often called "callbacks" because the ODE or nonlinear │ │ │ solver libraries "call back" into user code. In code written in the C programming │ │ │ language, these callbacks would often be described by pointers to user │ │ │ functions handed to the solver library. Since deal.II is written in C++, we │ │ │ typically instead use │ │ │ <a href="https://en.cppreference.com/w/cpp/utility/functional/function" ><tt>std::function</tt></a> │ │ │ @@ -2303,16 +2303,16 @@ │ │ │ │ │ │ Many of these libraries use a convention that comes from their origin in the │ │ │ C programming language: User callbacks for the purposes of these libraries │ │ │ return the data they are asked through one of their arguments, and indicate │ │ │ success or failure by returning an <tt>int</tt> that needs to be zero if the function │ │ │ returned successfully, and a nonzero value if the function failed for whatever │ │ │ reason. (Examples of failures could include if the right hand side function │ │ │ - \_form#240 contains a square root of one of the \_form#245, but that │ │ │ - \_form#245 is negative; or perhaps if a function requires table lookup for values │ │ │ + \_form#242 contains a square root of one of the \_form#247, but that │ │ │ + \_form#247 is negative; or perhaps if a function requires table lookup for values │ │ │ that are outside the range that is tabulated.) │ │ │ │ │ │ The approach to return integer values is decidedly not in the spirit │ │ │ of C++: If a function cannot complete the work it is asked to do, the C++ way │ │ │ to deal with this is to throw an exception. As a consequence, for all of the │ │ │ places where deal.II wraps external libraries and where user codes need to │ │ │ provide callbacks, we adopt the following conventions that user callbacks │ │ │ @@ -2329,18 +2329,18 @@ │ │ │ typically lead to some clean-up operations inside that external library, │ │ │ and a return to the wrapper code. There, the originally thrown exception │ │ │ will then be re-thrown and become visible again in the place where the │ │ │ wrappers were thrown. In other words, for all practical purposes, it │ │ │ looks like the exception thrown in the callback had simply propagated │ │ │ all the way back to user code. │ │ │ - There are some libraries that allow callbacks to indicate "recoverable errors". For example, KINSOL can solve nonlinear systems │ │ │ - \_form#246 and deal with situations where a function │ │ │ - evaluation for \_form#247 is not possible &ndash; for example the case above │ │ │ + \_form#248 and deal with situations where a function │ │ │ + evaluation for \_form#249 is not possible &ndash; for example the case above │ │ │ one tries to take the square root of a negative value &ndash; but where it │ │ │ - could then try again for a modified \_form#242 for which evaluation │ │ │ + could then try again for a modified \_form#244 for which evaluation │ │ │ of the square root is possible. (This is often possible in │ │ │ <a href="https://en.wikipedia.org/wiki/Line_search" >line search algorithms</a> │ │ │ where using a shorter step length might actually succeed.) In such │ │ │ cases, a user-provided callback function should throw an exception │ │ │ of type StandardExceptions::RecoverableUserCallbackError, │ │ │ which will then internally be │ │ │ translated into an appropriate code understandable by the underlying │ │ │ ├── html2text {} │ │ │ │ @@ -135,15 +135,15 @@ │ │ │ │ _m_a_t_r_i_x_ _o_r_ _v_e_c_t_o_r_ _i_n_t_o_ _b_l_o_c_k_s_,_ _y_o_u_ _d_o_ _s_o_ _b_y_ _c_r_e_a_t_i_n_g_ _o_n_e_ _b_l_o_c_k_ _f_o_r_ _e_a_c_h │ │ │ │ _b_l_o_c_k_ _d_e_f_i_n_e_d_ _b_y_ _t_h_e_ _f_i_n_i_t_e_ _e_l_e_m_e_n_t_ _(_i_._e_._ _i_n_ _m_o_s_t_ _p_r_a_c_t_i_c_a_l_ _c_a_s_e_s_ _t_h_e │ │ │ │ _F_E_S_y_s_t_e_m_ _o_b_j_e_c_t_)_._ _H_o_w_e_v_e_r_,_ _t_h_i_s_ _n_e_e_d_s_ _n_o_t_ _b_e_ _s_o_:_ _t_h_e_ _D_o_F_R_e_n_u_m_b_e_r_i_n_g_:_: │ │ │ │ _c_o_m_p_o_n_e_n_t___w_i_s_e_ _f_u_n_c_t_i_o_n_ _a_l_l_o_w_s_ _t_o_ _g_r_o_u_p_ _s_e_v_e_r_a_l_ _v_e_c_t_o_r_ _c_o_m_p_o_n_e_n_t_s_ _o_r │ │ │ │ _f_i_n_i_t_e_ _e_l_e_m_e_n_t_ _b_l_o_c_k_s_ _i_n_t_o_ _t_h_e_ _s_a_m_e_ _l_o_g_i_c_a_l_ _b_l_o_c_k_ _(_s_e_e_,_ _f_o_r_ _e_x_a_m_p_l_e_,_ _t_h_e │ │ │ │ _@_r_e_f_ _s_t_e_p___2_2_ step-22" or @ref step_31 "step-31" tutorial programs, as │ │ │ │ opposed to @ref step_20 "step-20"). As a consequence, using this feature, │ │ │ │ - we can achieve the same result, i.e. subdividing matrices into \_form#147 │ │ │ │ + we can achieve the same result, i.e. subdividing matrices into \_form#122 │ │ │ │ blocks and vectors into 2 blocks, for the second way of creating a Stokes │ │ │ │ element outlined above using an extra argument as we would have using the │ │ │ │ first way of creating the Stokes element with two blocks right away. More │ │ │ │ information on this topic can be found in the documentation of FESystem, │ │ │ │ the @ref vector_valued topic and the tutorial programs referenced │ │ │ │ therein. Selecting blocks: Many functions allow you to restrict │ │ │ │ their operation to certain vector components or blocks. For example, this │ │ │ │ @@ -197,37 +197,37 @@ │ │ │ │ triangulation in dim-dimensional space, the boundary form is a vector │ │ │ │ defined on faces. It is the vector product of the image of coordinate │ │ │ │ vectors on the surface of the unit cell. It is a vector normal to the │ │ │ │ surface, pointing outwards and having the length of the surface element. │ │ │ │ A more general definition would be that (at least up to the length of │ │ │ │ this vector) it is exactly that vector that is necessary when considering │ │ │ │ integration by parts, i.e. equalities of the form \iline 294 │ │ │ │ - \_form#148@_fakenl. Using this definition then also explains what this │ │ │ │ + \_form#123@_fakenl. Using this definition then also explains what this │ │ │ │ vector should be in the case of domains (and corresponding │ │ │ │ triangulations) of dimension dim that are embedded in a │ │ │ │ space spacedim: in that case, the boundary form is still a │ │ │ │ vector defined on the faces of the triangulation; it is orthogonal to all │ │ │ │ tangent directions of the boundary and within the tangent plane of the │ │ │ │ domain. Note that this is compatible with case dim==spacedim │ │ │ │ - since there the tangent plane is the entire space \_form#149. In either │ │ │ │ + since there the tangent plane is the entire space \_form#124. In either │ │ │ │ case, the length of the vector equals the determinant of the │ │ │ │ transformation of reference face to the face of the current cell. │ │ │ │

@anchor GlossBoundaryIndicator Boundary │ │ │ │ indicator
In a Triangulation object, every part of the │ │ │ │ boundary may be associated with a unique number (of type types:: │ │ │ │ boundary_id) that is used to determine what kinds of boundary conditions │ │ │ │ are to be applied to a particular part of a boundary. The boundary is │ │ │ │ composed of the faces of the cells and, in 3d, the edges of these faces. │ │ │ │ By default, all boundary indicators of a mesh are zero, unless you are │ │ │ │ reading from a mesh file that specifically sets them to something │ │ │ │ different, or unless you use one of the mesh generation functions in │ │ │ │ namespace GridGenerator that have a @ref GlossColorization "colorize" │ │ │ │ option. A typical piece of code that sets the boundary indicator on part │ │ │ │ of the boundary to something else would look like this, here setting the │ │ │ │ - boundary indicator to 42 for all faces located at \_form#150: @code for │ │ │ │ + boundary indicator to 42 for all faces located at \_form#125: @code for │ │ │ │ (auto &face : triangulation.active_face_iterators()) if (face- │ │ │ │ >at_boundary()) if (face->center()[0] == -1) face->set_boundary_id (42); │ │ │ │ @endcode This calls functions TriaAccessor::set_boundary_id. In 3d, it │ │ │ │ may also be appropriate to call TriaAccessor::set_all_boundary_ids │ │ │ │ instead on each of the selected faces. To query the boundary indicator of │ │ │ │ a particular face or edge, use TriaAccessor::boundary_id. Many of the │ │ │ │ functions in namespaces DoFTools and VectorTools take arguments that │ │ │ │ @@ -395,20 +395,20 @@ │ │ │ │ make_graph_coloring() computes a decomposition of a Triangulation (more │ │ │ │ exactly, a range of iterators). No two adjacent cells are given the same │ │ │ │ color.
@anchor GlossComponent │ │ │ │ Component
When considering systems of equations in which │ │ │ │ the solution is not just a single scalar function, we say that we have a │ │ │ │ vector system with a vector-valued solution. For example, │ │ │ │ the vector solution in the elasticity equation considered in @ref step_8 │ │ │ │ - "step-8" is \_form#151 consisting of the displacements in each of the │ │ │ │ + "step-8" is \_form#126 consisting of the displacements in each of the │ │ │ │ three coordinate directions. The solution then has three elements. │ │ │ │ Similarly, the 3d Stokes equation considered in @ref step_22 "step-22" │ │ │ │ - has four elements: \_form#152. We call the elements of the vector-valued │ │ │ │ + has four elements: \_form#127. We call the elements of the vector-valued │ │ │ │ solution components in deal.II. To be well-posed, for the solution │ │ │ │ - to have \_form#153 components, there need to be \_form#153 partial │ │ │ │ + to have \_form#128 components, there need to be \_form#128 partial │ │ │ │ differential equations to describe them. This concept is discussed in │ │ │ │ great detail in the @ref vector_valued topic. In finite element programs, │ │ │ │ one frequently wants to address individual elements (components) of this │ │ │ │ vector-valued solution, or sets of components. For example, we do this │ │ │ │ extensively in @ref step_8 "step-8", and a lot of documentation is also │ │ │ │ provided in the topic on @ref vector_valued "Handling vector valued │ │ │ │ problems". If you are thinking only in terms of the partial differential │ │ │ │ @@ -495,15 +495,15 @@ │ │ │ │ class) and @ref GlossBlockMask "block masks" (represented by the │ │ │ │ BlockMask class). The FiniteElement class has functions that convert │ │ │ │ between the two kinds of objects. @note Not all component masks actually │ │ │ │ make sense. For example, if you have a FE_RaviartThomas object in 2d, │ │ │ │ then it doesn't make any sense to have a component mask of the form │ │ │ │ [true, false] because you try to select individual vector │ │ │ │ components of a finite element where each shape function has both │ │ │ │ - \_form#8 and \_form#9 velocities. In essence, while you can of course │ │ │ │ + \_form#9 and \_form#10 velocities. In essence, while you can of course │ │ │ │ create such a component mask, there is nothing you can do with it.
│ │ │ │
@anchor GlossCompress Compressing distributed │ │ │ │ vectors and matrices
For %parallel computations, deal.II │ │ │ │ uses the vector and matrix classes defined in the PETScWrappers and │ │ │ │ TrilinosWrappers namespaces. When running programs in %parallel using │ │ │ │ MPI, these classes only store a certain number of rows or elements on the │ │ │ │ current processor, whereas the rest of the vector or matrix is stored on │ │ │ │ @@ -588,36 +588,36 @@ │ │ │ │ one". Examples of uses where these two arguments are not the same are │ │ │ │ shown in @ref step_34 "step-34", @ref step_38 "step-38", @ref step_54 │ │ │ │ "step-54".
@anchor GlossDoF Degree of │ │ │ │ freedom
The term "degree of freedom" (often abbreviated as │ │ │ │ "DoF") is commonly used in the finite element community to indicate two │ │ │ │ slightly different, but related things. The first is that we'd like to │ │ │ │ represent the finite element solution as a linear combination of shape │ │ │ │ - functions, in the form \_form#154. Here, \_form#93 is a vector of │ │ │ │ + functions, in the form \_form#129. Here, \_form#114 is a vector of │ │ │ │ expansion coefficients. Because we don't know their values yet (we will │ │ │ │ compute them as the solution of a linear or nonlinear system), they are │ │ │ │ called "unknowns" or "degrees of freedom". The second meaning of the term │ │ │ │ can be explained as follows: A mathematical description of finite element │ │ │ │ problem is often to say that we are looking for a finite dimensional │ │ │ │ - function \_form#155 that satisfies some set of equations (e.g. \_form#156 │ │ │ │ - for all test functions \iline 845 \_form#157@_fakenl). In other words, │ │ │ │ - all we say here that the solution needs to lie in some space \_form#91. │ │ │ │ + function \_form#130 that satisfies some set of equations (e.g. \_form#131 │ │ │ │ + for all test functions \iline 845 \_form#132@_fakenl). In other words, │ │ │ │ + all we say here that the solution needs to lie in some space \_form#112. │ │ │ │ However, to actually solve this problem on a computer we need to choose a │ │ │ │ - basis of this space; this is the set of shape functions \_form#158 we │ │ │ │ - have used above in the expansion of \iline 849 \_form#159@_fakenl with │ │ │ │ - coefficients \_form#93. There are of course many bases of the space │ │ │ │ - \_form#91, but we will specifically choose the one that is described by │ │ │ │ + basis of this space; this is the set of shape functions \_form#133 we │ │ │ │ + have used above in the expansion of \iline 849 \_form#134@_fakenl with │ │ │ │ + coefficients \_form#114. There are of course many bases of the space │ │ │ │ + \_form#112, but we will specifically choose the one that is described by │ │ │ │ the finite element functions that are traditionally defined locally on │ │ │ │ the cells of the mesh. Describing "degrees of freedom" in this context │ │ │ │ requires us to simply enumerate the basis functions of the space │ │ │ │ - \_form#91. For \_form#40 elements this means simply enumerating the │ │ │ │ + \_form#112. For \_form#35 elements this means simply enumerating the │ │ │ │ vertices of the mesh in some way, but for higher elements one also has to │ │ │ │ enumerate the shape functions that are associated with edges, faces, or │ │ │ │ cell interiors of the mesh. The class that provides this enumeration of │ │ │ │ - the basis functions of \_form#91 is called DoFHandler. The process of │ │ │ │ + the basis functions of \_form#112 is called DoFHandler. The process of │ │ │ │ enumerating degrees of freedom is referred to as "distributing DoFs" in │ │ │ │ deal.II.
@anchor GlossDirectionFlag │ │ │ │ Direction flags
The direction flag is used in │ │ │ │ triangulations embedded in a higher dimensional space to denote the │ │ │ │ orientation of cells and make the manifold oriented. It is accessed using │ │ │ │ CellAccessor::direction_flag() and set by the Triangulation class upon │ │ │ │ creation of a triangulation. You can change all direction flags of a │ │ │ │ @@ -662,16 +662,16 @@ │ │ │ │
@anchor GlossDistorted Distorted cells
│ │ │ │
A distorted cell is a cell for which the mapping from the │ │ │ │ reference cell to real cell has a Jacobian whose determinant is non- │ │ │ │ positive somewhere in the cell. Typically, we only check the sign of this │ │ │ │ determinant at the vertices of the cell. The function GeometryInfo:: │ │ │ │ alternating_form_at_vertices computes these determinants at the vertices. │ │ │ │ By way of example, if all of the determinants are of roughly equal value │ │ │ │ - and on the order of \_form#160 then the cell is well-shaped. For example, │ │ │ │ - a square cell or face has determinants equal to \_form#160 whereas a │ │ │ │ + and on the order of \_form#135 then the cell is well-shaped. For example, │ │ │ │ + a square cell or face has determinants equal to \_form#135 whereas a │ │ │ │ strongly sheared parallelogram has a determinant much smaller. Similarly, │ │ │ │ a cell with very unequal edge lengths will have widely varying │ │ │ │ determinants. Conversely, a pinched cell in which the location of two or │ │ │ │ more vertices is collapsed to a single point has a zero determinant at │ │ │ │ this location. Finally, an inverted or twisted cell in which the location │ │ │ │ of two vertices is out of order will have negative determinants. The │ │ │ │ following two images show a well-formed, a pinched, and a twisted cell │ │ │ │ @@ -736,15 +736,15 @@ │ │ │ │ perspective of an arbitrary cell, in a different order than the order │ │ │ │ given to that face by the neighboring cell. To resolve this inconsistency │ │ │ │ deal.II stores, for each face and (in 3d) line, a value which may be used │ │ │ │ to permute the vertices on both faces into a matching configuration. This │ │ │ │ encoding contains both the number of times a face should be rotated │ │ │ │ (relative to its neighbor) as well as whether or not the face should be │ │ │ │ viewed in an opposite orientation (e.g., for a Quadrilateral, whether or │ │ │ │ - not vertices \_form#161 and \_form#162 should be swapped). This value is │ │ │ │ + not vertices \_form#136 and \_form#137 should be swapped). This value is │ │ │ │ called the combined_orientation since it combines both the │ │ │ │ orientation (as defined above) as well as rotations. In some │ │ │ │ circumstances, to disambiguate between faces and lines, it may │ │ │ │ alternatively be called either the combined_face_orientation or │ │ │ │ the combined_line_orientation. These orientations are │ │ │ │ represented by types::geometric_orientation, which encodes how the │ │ │ │ vertices of the canonical definition of a face should be permuted so that │ │ │ │ @@ -764,48 +764,48 @@ │ │ │ │ values. In practice, essentially no applications dependent on deal.II │ │ │ │ ever need to handle orientation problems.
@anchor GlossGeneralizedSupport Generalized support │ │ │ │ points
"Generalized support points" are, as the name │ │ │ │ suggests, a generalization of @ref GlossSupport "support points". The │ │ │ │ latter are used to describe that a finite element simply │ │ │ │ interpolates values at individual points (the "support points"). │ │ │ │ - If we call these points \_form#163 (where the hat indicates that these │ │ │ │ - points are defined on the reference cell \_form#164), then one typically │ │ │ │ - defines shape functions \_form#158 in such a way that the nodal │ │ │ │ - functionals \_form#165 simply evaluate the function at the support │ │ │ │ - point, i.e., that \_form#166, and the basis is chosen so that \_form#167 │ │ │ │ - where \_form#168 is the Kronecker delta function. This leads to the │ │ │ │ + If we call these points \_form#138 (where the hat indicates that these │ │ │ │ + points are defined on the reference cell \_form#139), then one typically │ │ │ │ + defines shape functions \_form#133 in such a way that the nodal │ │ │ │ + functionals \_form#140 simply evaluate the function at the support │ │ │ │ + point, i.e., that \_form#141, and the basis is chosen so that \_form#142 │ │ │ │ + where \_form#143 is the Kronecker delta function. This leads to the │ │ │ │ common @ref GlossLagrange "Lagrange elements". (In the vector valued │ │ │ │ case, the only other piece of information besides the support points │ │ │ │ - \_form#163 that one needs to provide is the vector component │ │ │ │ - \_form#169 the \_form#45th node functional corresponds, so that │ │ │ │ - \_form#170.) On the other hand, there are other kinds of elements that │ │ │ │ + \_form#138 that one needs to provide is the vector component │ │ │ │ + \_form#144 the \_form#65th node functional corresponds, so that │ │ │ │ + \_form#145.) On the other hand, there are other kinds of elements that │ │ │ │ are not defined this way. For example, for the lowest order Raviart- │ │ │ │ Thomas element (see the FE_RaviartThomas class), the node functional │ │ │ │ evaluates not individual components of a vector-valued finite element │ │ │ │ function with @p dim components, but the normal component of this │ │ │ │ vector: \iline 1082 \iline 1083 \iline 1084 │ │ │ │ - \_form#171@_fakenl@_fakenl@_fakenl, where the \_form#172 are the normal │ │ │ │ - vectors to the face of the cell on which \_form#163 is located. In other │ │ │ │ + \_form#146@_fakenl@_fakenl@_fakenl, where the \_form#147 are the normal │ │ │ │ + vectors to the face of the cell on which \_form#138 is located. In other │ │ │ │ words, the node functional is a linear combination of the │ │ │ │ - components of \_form#133 when evaluated at \_form#163. Similar things │ │ │ │ + components of \_form#148 when evaluated at \_form#138. Similar things │ │ │ │ happen for the BDM, ABF, and Nedelec elements (see the FE_BDM, FE_ABF, │ │ │ │ FE_Nedelec classes). In these cases, the element does not have support │ │ │ │ points because it is not purely interpolatory; however, some kind of │ │ │ │ interpolation is still involved when defining shape functions as the node │ │ │ │ - functionals still require point evaluations at special points \_form#163. │ │ │ │ + functionals still require point evaluations at special points \_form#138. │ │ │ │ In these cases, we call the points generalized support points. │ │ │ │ Finally, there are elements that still do not fit into this scheme. For │ │ │ │ example, some hierarchical basis functions (see, for example the │ │ │ │ FE_Q_Hierarchical element) are defined so that the node functionals are │ │ │ │ moments of finite element functions, \iline 1102 \iline 1103 │ │ │ │ \iline 1104 \iline 1105 \iline 1106 │ │ │ │ - \_form#173@_fakenl@_fakenl@_fakenl@_fakenl@_fakenl in 2d, and similarly │ │ │ │ - for 3d, where the \_form#174 are the order of the moment described by │ │ │ │ - shape function \_form#45. Some other elements use moments over edges or │ │ │ │ + \_form#149@_fakenl@_fakenl@_fakenl@_fakenl@_fakenl in 2d, and similarly │ │ │ │ + for 3d, where the \_form#150 are the order of the moment described by │ │ │ │ + shape function \_form#65. Some other elements use moments over edges or │ │ │ │ faces. In all of these cases, node functionals are not defined through │ │ │ │ interpolation at all, and these elements then have neither support │ │ │ │ points, nor generalized support points.
@anchor geometry_paper geometry paper
│ │ │ │
The "geometry paper" is a paper by L. Heltai, W. Bangerth, M. │ │ │ │ Kronbichler, and A. Mola, titled "Using exact geometry information in │ │ │ │ finite element computations", that describes how deal.II describes the │ │ │ │ @@ -918,16 +918,16 @@ │ │ │ │ } @endcode It is available from https://www.math.colostate.edu/~bangerth/ │ │ │ │ publications.html, also see deal.II publications for details. The │ │ │ │ numerical examples shown in that paper are generated with a slightly │ │ │ │ modified version of @ref step_27 "step-27". The main difference to that │ │ │ │ tutorial program is that various operations in the program were timed for │ │ │ │ - the paper to compare different options and show that \_form#20 methods │ │ │ │ - are really not all that expensive.
@anchor │ │ │ │ + the paper to compare different options and show that \_form#0 methods are │ │ │ │ + really not all that expensive.
@anchor │ │ │ │ GlossInterpolation Interpolation with finite elements
The │ │ │ │ purpose of interpolation with finite elements is computing a vector of │ │ │ │ coefficients representing a finite element function, such that the @ref │ │ │ │ GlossNodes "node values" of the original function and the finite element │ │ │ │ function coincide. Therefore, the interpolation process consists of │ │ │ │ evaluating all @ref GlossNodes "node functionals" Ni │ │ │ │ for the given function f and store the result as entry i in │ │ │ │ @@ -1105,50 +1105,50 @@ │ │ │ │ degrees of freedom when using distributed meshes, see the @ref │ │ │ │ distributed topic. Locally relevant degrees of freedom are those that │ │ │ │ live on locally owned or ghost cells. Consequently, they may be owned by │ │ │ │ different processors. Locally relevant DoFs are a superset of the @ref │ │ │ │ GlossLocallyActiveDof "locally active DoFs."
@anchor GlossLumpedMassMatrix Lumped mass matrix
The @ref GlossMassMatrix "mass matrix" is a matrix of the │ │ │ │ - form \iline 1526 \iline 1527 \_form#175@_fakenl@_fakenl It frequently │ │ │ │ + form \iline 1526 \iline 1527 \_form#154@_fakenl@_fakenl It frequently │ │ │ │ appears in the solution of time dependent problems where, if one uses an │ │ │ │ explicit time stepping method, it then leads to the need to solve │ │ │ │ - problems of the form \iline 1532 \iline 1533 \_form#176@_fakenl@_fakenl │ │ │ │ - in time step \_form#153, where \_form#177 is the solution to be computed, │ │ │ │ - \_form#178 is the known solution from the first time step, and \_form#95 │ │ │ │ - is a matrix related to the differential operator in the PDE. \_form#179 │ │ │ │ + problems of the form \iline 1532 \iline 1533 \_form#155@_fakenl@_fakenl │ │ │ │ + in time step \_form#128, where \_form#156 is the solution to be computed, │ │ │ │ + \_form#157 is the known solution from the first time step, and \_form#116 │ │ │ │ + is a matrix related to the differential operator in the PDE. \_form#158 │ │ │ │ is the size of the time step. A similar linear system of equations also │ │ │ │ arises out of the discretization of second-order differential equations. │ │ │ │ - The presence of the matrix \_form#145 on the left side is a nuisance │ │ │ │ + The presence of the matrix \_form#120 on the left side is a nuisance │ │ │ │ because, even though we have used an explicit time stepping method, we │ │ │ │ still have to solve a linear system in each time step. It would be much │ │ │ │ preferable if the matrix were diagonal. "Lumping" the mass matrix is a │ │ │ │ - strategy to replace \_form#145 by a matrix \_form#180 that actually is │ │ │ │ + strategy to replace \_form#120 by a matrix \_form#159 that actually is │ │ │ │ diagonal, yet does not destroy the accuracy of the resulting solution. │ │ │ │ Historically, mass lumping was performed by adding the elements of a row │ │ │ │ - together and setting the diagonal entries of \_form#180 to that sum. This │ │ │ │ - works for \_form#40 and \_form#181 elements, for example, and can be │ │ │ │ + together and setting the diagonal entries of \_form#159 to that sum. This │ │ │ │ + works for \_form#35 and \_form#160 elements, for example, and can be │ │ │ │ understood mechanically by replacing the continuous medium we are │ │ │ │ discretizating by one where the continuous mass distribution is replaced │ │ │ │ by one where (finite amounts of) mass are located only at the nodes. That │ │ │ │ is, we are "lumping together" the mass of an element at its vertices, │ │ │ │ thus giving rise to the name "lumped mass matrix". A more mathematical │ │ │ │ - perspective is to compute the integral above for \_form#182 via special │ │ │ │ + perspective is to compute the integral above for \_form#161 via special │ │ │ │ quadrature rules; in particular, we replace the computation of \iline │ │ │ │ - 1558 \iline 1559 \iline 1560 \_form#183@_fakenl@_fakenl@_fakenl by │ │ │ │ + 1558 \iline 1559 \iline 1560 \_form#162@_fakenl@_fakenl@_fakenl by │ │ │ │ quadrature \iline 1563 \iline 1564 \iline 1565 │ │ │ │ - \_form#184@_fakenl@_fakenl@_fakenl where we choose the quadrature points │ │ │ │ + \_form#163@_fakenl@_fakenl@_fakenl where we choose the quadrature points │ │ │ │ as the nodes at which the shape functions are defined. If we │ │ │ │ order the quadrature points in the same way as the shape functions, then │ │ │ │ - \iline 1570 \iline 1571 \_form#185@_fakenl@_fakenl and consequently │ │ │ │ - \iline 1574 \iline 1575 \_form#186@_fakenl@_fakenl where the sum extends │ │ │ │ - over those cells on which \_form#187 is nonzero. The so-computed mass │ │ │ │ + \iline 1570 \iline 1571 \_form#164@_fakenl@_fakenl and consequently │ │ │ │ + \iline 1574 \iline 1575 \_form#165@_fakenl@_fakenl where the sum extends │ │ │ │ + over those cells on which \_form#166 is nonzero. The so-computed mass │ │ │ │ matrix is therefore diagonal. Whether or not this particular choice of │ │ │ │ quadrature formula is sufficient to retain the convergence rate of the │ │ │ │ - discretization is a separate question. For the usual \_form#188 finite │ │ │ │ + discretization is a separate question. For the usual \_form#169 finite │ │ │ │ elements (implemented by FE_Q and FE_DGQ), the appropriate quadrature │ │ │ │ formulas are of QGaussLobatto type. Mass lumping can also be done with │ │ │ │ FE_SimplexP_Bubbles, for example, if appropriate quadrature rules are │ │ │ │ chosen. For an example of where lumped mass matrices play a role, see │ │ │ │ @ref step_69 "step-69".
@anchor │ │ │ │ GlossManifoldIndicator %Manifold indicator
Every object │ │ │ │ that makes up a Triangulation (cells, faces, edges, etc.), is associated │ │ │ │ @@ -1158,15 +1158,15 @@ │ │ │ │ coordinates. For example, Manifold objects are responsible for generating │ │ │ │ new points when a Triangulation is refined, defining the locations of │ │ │ │ @ref GlossSupport "support points", and defining the locations of │ │ │ │ quadrature points. By default, all manifold indicators of a mesh are set │ │ │ │ to numbers::flat_manifold_id. A typical piece of code that sets the │ │ │ │ manifold indicator on a object to something else would look like this, │ │ │ │ here setting the manifold indicator to 42 for all cells whose center has │ │ │ │ - an \_form#8 component less than zero: @code for (auto &cell : │ │ │ │ + an \_form#9 component less than zero: @code for (auto &cell : │ │ │ │ triangulation.active_cell_iterators()) if (cell->center()[0] < 0) cell- │ │ │ │ >set_manifold_id(42); @endcode Here we call the function TriaAccessor:: │ │ │ │ set_manifold_id(). It may also be appropriate to call TriaAccessor:: │ │ │ │ set_all_manifold_ids() instead, to set recursively the manifold id on │ │ │ │ each face (and edge, if in 3d). To query the manifold indicator of a │ │ │ │ particular object edge, use TriaAccessor::manifold_id(). Every manifold │ │ │ │ id set on a Triangulation must have an associated Manifold object. This │ │ │ │ @@ -1174,33 +1174,33 @@ │ │ │ │ are inherited from parents to their children upon mesh refinement. Some │ │ │ │ more information about manifold indicators is also presented in a section │ │ │ │ of the documentation of the Triangulation class as well as in the @ref │ │ │ │ manifold "_M_a_n_i_f_o_l_d documentation topic". Manifold indicators are used in │ │ │ │ @ref step_53 "step-53" and @ref step_54 "step-54".
@see @ref │ │ │ │ manifold "The topic on _M_a_n_i_f_o_l_d_s"
@anchor │ │ │ │ GlossMassMatrix Mass matrix
The "mass matrix" is a matrix │ │ │ │ - of the form \iline 1637 \iline 1638 \_form#175@_fakenl@_fakenl possibly │ │ │ │ - with a coefficient inside the integral, and where \_form#189 are the │ │ │ │ + of the form \iline 1637 \iline 1638 \_form#154@_fakenl@_fakenl possibly │ │ │ │ + with a coefficient inside the integral, and where \_form#170 are the │ │ │ │ shape functions of a finite element. The origin of the term refers to the │ │ │ │ fact that in structural mechanics (where the finite element method │ │ │ │ originated), one often starts from the elastodynamics (wave) equation │ │ │ │ - \iline 1645 \iline 1646 \iline 1647 \_form#190@_fakenl@_fakenl@_fakenl If │ │ │ │ - one multiplies this equation by a test function \_form#187, integrates │ │ │ │ - over \_form#191, and then discretizes by the substitution \_form#192, │ │ │ │ + \iline 1645 \iline 1646 \iline 1647 \_form#171@_fakenl@_fakenl@_fakenl If │ │ │ │ + one multiplies this equation by a test function \_form#166, integrates │ │ │ │ + over \_form#172, and then discretizes by the substitution \_form#173, │ │ │ │ then the first term above results in \iline 1653 \iline 1654 \iline 1655 │ │ │ │ - \_form#193@_fakenl@_fakenl@_fakenl which can be written as \iline 1658 │ │ │ │ - \iline 1659 \iline 1660 \_form#194@_fakenl@_fakenl@_fakenl where \iline │ │ │ │ - 1663 \iline 1664 \_form#195@_fakenl@_fakenl Since the matrix entries are │ │ │ │ + \_form#174@_fakenl@_fakenl@_fakenl which can be written as \iline 1658 │ │ │ │ + \iline 1659 \iline 1660 \_form#175@_fakenl@_fakenl@_fakenl where \iline │ │ │ │ + 1663 \iline 1664 \_form#176@_fakenl@_fakenl Since the matrix entries are │ │ │ │ a (weighted) integral over a mass density, they have the units of "mass", │ │ │ │ giving the "mass matrix" its name. In mathematics, where we often │ │ │ │ consider non-dimensionalized equations, we end up with the case │ │ │ │ - \_form#196, and as a consequence the matrix without the coefficient, │ │ │ │ - \iline 1672 \iline 1673 \_form#175@_fakenl@_fakenl also carries the name │ │ │ │ + \_form#177, and as a consequence the matrix without the coefficient, │ │ │ │ + \iline 1672 \iline 1673 \_form#154@_fakenl@_fakenl also carries the name │ │ │ │ "mass matrix". The mass matrix is almost always written with the symbol │ │ │ │ - \_form#145. See, for example, @ref step_23 "step-23", @ref step_26 "step- │ │ │ │ + \_form#120. See, for example, @ref step_23 "step-23", @ref step_26 "step- │ │ │ │ 26", and a number of the other time dependent equations solved by │ │ │ │ tutorial programs. The mass matrix is occasionally approximated by a │ │ │ │ diagonal matrix, see the glossary entry for @ref GlossLumpedMassMatrix │ │ │ │ "lumped mass matrix". See also the @ref GlossStiffnessMatrix "stiffness │ │ │ │ matrix" for a related case.
@anchor │ │ │ │ GlossMaterialId Material id
Each cell of a triangulation │ │ │ │ has associated with it a property called "material id". It is commonly │ │ │ │ @@ -1298,23 +1298,23 @@ │ │ │ │ {SIAM Journal on Scientific Computing}, volume= {33}, number= {4}, pages= │ │ │ │ {2095--2114}, year= {2011}, publisher={SIAM}} @endcode See DOI:10.1137/090778523 for │ │ │ │ the paper and deal.II publications for more details.
@anchor GlossNodes Node values or node │ │ │ │ functionals
It is customary to define a finite element as a │ │ │ │ - triple \_form#197 where - \_form#84 is the cell, where in deal.II this is │ │ │ │ - always a line segment, quadrilateral, or hexahedron; - \_form#198 is a │ │ │ │ + triple \_form#178 where - \_form#44 is the cell, where in deal.II this is │ │ │ │ + always a line segment, quadrilateral, or hexahedron; - \_form#179 is a │ │ │ │ finite-dimensional space, e.g., a polynomial space mapped from the @ref │ │ │ │ - GlossReferenceCell "reference cell" to \_form#84; - \_form#199 is a set │ │ │ │ - of "node functionals", i.e., functionals \_form#200. The dimension of │ │ │ │ - \_form#198 must be equal to the number of node functionals. With this │ │ │ │ + GlossReferenceCell "reference cell" to \_form#44; - \_form#180 is a set │ │ │ │ + of "node functionals", i.e., functionals \_form#181. The dimension of │ │ │ │ + \_form#179 must be equal to the number of node functionals. With this │ │ │ │ definition, we can define a basis of the local function space, i.e., a │ │ │ │ - set of "shape functions" \_form#201, by requiring that \_form#202, where │ │ │ │ - \_form#203 is the Kronecker delta. This definition of what a finite │ │ │ │ + set of "shape functions" \_form#182, by requiring that \_form#183, where │ │ │ │ + \_form#184 is the Kronecker delta. This definition of what a finite │ │ │ │ element is has several advantages, concerning analysis as well as │ │ │ │ implementation. For the analysis, it means that conformity with certain │ │ │ │ spaces (FiniteElementData::Conformity), e.g. continuity, is up to the │ │ │ │ node functionals. In deal.II, it helps simplifying the implementation of │ │ │ │ more complex elements like FE_RaviartThomas considerably. Examples for │ │ │ │ node functionals are values in @ref GlossSupport "support points" and │ │ │ │ moments with respect to Legendre polynomials. Examples: │ │ │ │ @@ -1336,127 +1336,127 @@ │ │ │ │
@anchor GlossParallelScaling Parallel scaling
When we say that a parallel program "scales", what we mean is │ │ │ │ that the program does not become unduly slow (or takes unduly much │ │ │ │ memory) if we make the problem it solves larger, and that run time and │ │ │ │ memory consumption decrease proportionally if we keep the problem size │ │ │ │ the same but increase the number of processors (or cores) that work on │ │ │ │ it. More specifically, think of a problem whose size is given by a number │ │ │ │ - \_form#204 (which could be the number of cells, the number of unknowns, │ │ │ │ + \_form#185 (which could be the number of cells, the number of unknowns, │ │ │ │ or some other indicative quantity such as the number of CPU cycles │ │ │ │ - necessary to solve it) and for which you have \_form#198 processors │ │ │ │ + necessary to solve it) and for which you have \_form#179 processors │ │ │ │ available for solution. In an ideal world, the program would then require │ │ │ │ - a run time of \_form#205, and this would imply that we could reduce the │ │ │ │ + a run time of \_form#186, and this would imply that we could reduce the │ │ │ │ run time to any desired value by just providing more processors. │ │ │ │ Likewise, for a program to be scalable, its overall memory consumption │ │ │ │ - needs to be \_form#206 and on each involved process needs to be │ │ │ │ - \_form#205, again implying that we can fit any problem into the fixed │ │ │ │ + needs to be \_form#187 and on each involved process needs to be │ │ │ │ + \_form#186, again implying that we can fit any problem into the fixed │ │ │ │ amount of memory computers attach to each processor, by just providing │ │ │ │ sufficiently many processors. For practical assessments of scalability, │ │ │ │ we often distinguish between "strong" and "weak" scalability. These │ │ │ │ - assess asymptotic statements such as \_form#205 run time in the limits │ │ │ │ - \_form#207 and/or \_form#208. Specifically, when we say that a program is │ │ │ │ + assess asymptotic statements such as \_form#186 run time in the limits │ │ │ │ + \_form#188 and/or \_form#189. Specifically, when we say that a program is │ │ │ │ "strongly scalable", we mean that if we have a problem of fixed size │ │ │ │ - \_form#204, then we can reduce the run time and memory consumption (on │ │ │ │ - every processor) inversely proportional to \_form#198 by just throwing │ │ │ │ + \_form#185, then we can reduce the run time and memory consumption (on │ │ │ │ + every processor) inversely proportional to \_form#179 by just throwing │ │ │ │ more processors at the problem. In particular, strong scalability implies │ │ │ │ that if we provide twice as many processors, then run time and memory │ │ │ │ consumption on every process will be reduced by a factor of two. In other │ │ │ │ words, we can solve the same problem faster and faster by │ │ │ │ providing more and more processors. Conversely, "weak scalability" means │ │ │ │ - that if we increase the problem size \_form#204 by a fixed factor, and │ │ │ │ - increase the number of processors \_form#198 available to solve the │ │ │ │ + that if we increase the problem size \_form#185 by a fixed factor, and │ │ │ │ + increase the number of processors \_form#179 available to solve the │ │ │ │ problem by the same factor, then the overall run time (and the memory │ │ │ │ consumption on every processor) remains the same. In other words, we can │ │ │ │ solve larger and larger problems within the same amount of │ │ │ │ wallclock time by providing more and more processors. No program is truly │ │ │ │ scalable in this theoretical sense. Rather, all programs cease to scale │ │ │ │ - once either \_form#204 or \_form#198 grows larger than certain limits. We │ │ │ │ + once either \_form#185 or \_form#179 grows larger than certain limits. We │ │ │ │ therefore often say things such as "the program scales up to 4,000 │ │ │ │ cores", or "the program scales up to 100,000,000 unknowns". There are a │ │ │ │ number of reasons why programs cannot scale without limit; these can all │ │ │ │ be illustrated by just looking at the (relatively simple) @ref step_17 │ │ │ │ "step-17" tutorial program: - Sequential sections: Many programs have │ │ │ │ sections of code that either cannot or are not parallelized, i.e., where │ │ │ │ one processor has to do a certain, fixed amount of work that does not │ │ │ │ - decrease just because there are a total of \_form#198 processors around. │ │ │ │ + decrease just because there are a total of \_form#179 processors around. │ │ │ │ In @ref step_17 "step-17", this is the case when generating graphical │ │ │ │ output: one processor creates the graphical output for the entire │ │ │ │ - problem, i.e., it needs to do \_form#206 work. That means that this │ │ │ │ - function has a run time of \_form#206, regardless of \_form#198, and │ │ │ │ - consequently the overall program will not be able to achieve \_form#205 │ │ │ │ - run time but have a run time that can be described as \_form#209 where │ │ │ │ + problem, i.e., it needs to do \_form#187 work. That means that this │ │ │ │ + function has a run time of \_form#187, regardless of \_form#179, and │ │ │ │ + consequently the overall program will not be able to achieve \_form#186 │ │ │ │ + run time but have a run time that can be described as \_form#195 where │ │ │ │ the first term comes from scalable operations such as assembling the │ │ │ │ linear system, and the latter from generating graphical output on process │ │ │ │ - 0. If \_form#210 is sufficiently small, then the program might look like │ │ │ │ + 0. If \_form#196 is sufficiently small, then the program might look like │ │ │ │ it scales strongly for small numbers of processors, but eventually strong │ │ │ │ scalability will cease. In addition, the program can not scale weakly │ │ │ │ - either because increasing the size \_form#204 of the problem while │ │ │ │ - increasing the number of processors \_form#198 at the same rate does not │ │ │ │ + either because increasing the size \_form#185 of the problem while │ │ │ │ + increasing the number of processors \_form#179 at the same rate does not │ │ │ │ keep the run time of this one function constant. - Duplicated data │ │ │ │ structures: In @ref step_17 "step-17", each processor stores the entire │ │ │ │ mesh. That is, each processor has to store a data structure of size │ │ │ │ - \_form#206, regardless of \_form#198. Eventually, if we make the problem │ │ │ │ + \_form#187, regardless of \_form#179. Eventually, if we make the problem │ │ │ │ size large enough, this will overflow each processor's memory space even │ │ │ │ if we increase the number of processors. It is thus clear that such a │ │ │ │ replicated data structure prevents a program from scaling weakly. But it │ │ │ │ also prevents it from scaling strongly because in order to create an │ │ │ │ - object of size \_form#206, one has to at the very least write into │ │ │ │ - \_form#206 memory locations, costing \_form#206 in CPU time. │ │ │ │ + object of size \_form#187, one has to at the very least write into │ │ │ │ + \_form#187 memory locations, costing \_form#187 in CPU time. │ │ │ │ Consequently, there is a component of the overall algorithm that does not │ │ │ │ - behave as \_form#205 if we provide more and more processors. - │ │ │ │ + behave as \_form#186 if we provide more and more processors. - │ │ │ │ Communication: If, to pick just one example, you want to compute the │ │ │ │ - \_form#211 norm of a vector of which all MPI processes store a few │ │ │ │ + \_form#205 norm of a vector of which all MPI processes store a few │ │ │ │ entries, then every process needs to compute the sum of squares of its │ │ │ │ - own entries (which will require \_form#205 time, and consequently scale │ │ │ │ + own entries (which will require \_form#186 time, and consequently scale │ │ │ │ perfectly), but then every process needs to send their partial sum to one │ │ │ │ process that adds them all up and takes the square root. In the very best │ │ │ │ case, sending a message that contains a single number takes a constant │ │ │ │ amount of time, regardless of the overall number of processes. Thus, │ │ │ │ again, every program that does communication cannot scale strongly │ │ │ │ because there are parts of the program whose CPU time requirements do not │ │ │ │ - decrease with the number of processors \_form#198 you allocate for a │ │ │ │ - fixed size \_form#204. In reality, the situation is actually even worse: │ │ │ │ + decrease with the number of processors \_form#179 you allocate for a │ │ │ │ + fixed size \_form#185. In reality, the situation is actually even worse: │ │ │ │ the more processes are participating in a communication step, the longer │ │ │ │ it will generally take, for example because the one process that has to │ │ │ │ add everyone's contributions has to add everything up, requiring │ │ │ │ - \_form#212 time. In other words, CPU time increases with the │ │ │ │ + \_form#208 time. In other words, CPU time increases with the │ │ │ │ number of processes, therefore not only preventing a program from scaling │ │ │ │ strongly, but also from scaling weakly. (In reality, MPI libraries do not │ │ │ │ - implement \_form#211 norms by sending every message to one process that │ │ │ │ + implement \_form#205 norms by sending every message to one process that │ │ │ │ then adds everything up; rather, they do pairwise reductions on a tree │ │ │ │ - that doesn't grow the run time as \_form#212 but as \_form#213, at the │ │ │ │ + that doesn't grow the run time as \_form#208 but as \_form#209, at the │ │ │ │ expense of more messages sent around. Be that as it may, the fundamental │ │ │ │ point is that as you add more processors, the run time will grow with │ │ │ │ - \_form#198 regardless of the way the operation is actually implemented, │ │ │ │ + \_form#179 regardless of the way the operation is actually implemented, │ │ │ │ and it can therefore not scale.) These, and other reasons that prevent │ │ │ │ programs from scaling perfectly can be summarized in Amdahl's law that │ │ │ │ - states that if a fraction \_form#214 of a program's overall work │ │ │ │ - \_form#215 can be parallelized, i.e., it can be run in \_form#216 time, │ │ │ │ - and a fraction \_form#217 of the program's work can not be parallelized │ │ │ │ + states that if a fraction \_form#210 of a program's overall work │ │ │ │ + \_form#211 can be parallelized, i.e., it can be run in \_form#212 time, │ │ │ │ + and a fraction \_form#213 of the program's work can not be parallelized │ │ │ │ (i.e., it consists either of work that only one process can do, such as │ │ │ │ generating graphical output in @ref step_17 "step-17"; or that every │ │ │ │ process has to execute in a replicated way, such as sending a message │ │ │ │ with a local contribution to a dedicated process for accumulation), then │ │ │ │ the overall run time of the program will be \iline 1999 \iline 2000 │ │ │ │ - \_form#218@_fakenl@_fakenl Consequently, the "speedup" you get, i.e., the │ │ │ │ - factor by which your programs run faster on \_form#198 processors │ │ │ │ + \_form#215@_fakenl@_fakenl Consequently, the "speedup" you get, i.e., the │ │ │ │ + factor by which your programs run faster on \_form#179 processors │ │ │ │ compared to running the program on a single process (assuming this is │ │ │ │ possible) would be \iline 2005 \iline 2006 \iline 2007 │ │ │ │ - \_form#219@_fakenl@_fakenl@_fakenl If \_form#220, which it is for all │ │ │ │ - practically existing programs, then \_form#221 as \_form#208, implying │ │ │ │ + \_form#216@_fakenl@_fakenl@_fakenl If \_form#217, which it is for all │ │ │ │ + practically existing programs, then \_form#218 as \_form#189, implying │ │ │ │ that there is a point where it does not pay off in any significant way │ │ │ │ any more to throw more processors at the problem. In practice, what │ │ │ │ matters is up to which problem size or up to which number of │ │ │ │ - processes or down to which size of local problems \_form#222 a │ │ │ │ + processes or down to which size of local problems \_form#219 a │ │ │ │ program scales. For deal.II, experience shows that on most clusters with │ │ │ │ a reasonable fast network, one can solve problems up to a few billion │ │ │ │ unknowns, up to a few thousand processors, and down to somewhere between │ │ │ │ 40,000 and 100,000 unknowns per process. The last number is the most │ │ │ │ - relevant: if you have a problem with, say, \_form#223 unknowns, then it │ │ │ │ + relevant: if you have a problem with, say, \_form#221 unknowns, then it │ │ │ │ makes sense to solve it on 1000-2500 processors since the number of │ │ │ │ degrees of freedom each process handles remains at more than 40,000. │ │ │ │ Consequently, there is enough work every process has to do so that the │ │ │ │ \_form#224 time for communication does not dominate. But it doesn't make │ │ │ │ sense to solve such a problem with 10,000 or 100,000 processors, since │ │ │ │ each of these processor's local problem becomes so small that they spend │ │ │ │ most of their time waiting for communication, rather than doing work on │ │ │ │ @@ -1518,43 +1518,43 @@ │ │ │ │ BOOST serialization library. See there for │ │ │ │ examples on how to save and restore objects.
@anchor GlossShape Shape functions
The │ │ │ │ restriction of the finite element basis functions to a single grid cell. │ │ │ │
@anchor GlossStiffnessMatrix Stiffness │ │ │ │ matrix
The "stiffness matrix" is a matrix of the form \iline │ │ │ │ - 2114 \iline 2115 \iline 2116 \_form#225@_fakenl@_fakenl@_fakenl possibly │ │ │ │ - with a coefficient inside the integral, and where \_form#189 are the │ │ │ │ + 2114 \iline 2115 \iline 2116 \_form#227@_fakenl@_fakenl@_fakenl possibly │ │ │ │ + with a coefficient inside the integral, and where \_form#170 are the │ │ │ │ shape functions of a finite element. The term is also used for variations │ │ │ │ of the case above, for example replacing the gradient by the symmetric │ │ │ │ gradient in the case where the solution variable is vector-valued (e.g., │ │ │ │ in elasticity, or the Stokes equations). The key feature is that in the │ │ │ │ integral, first derivatives are applied to both the test and trial │ │ │ │ - functions, \_form#226. The origin of the term refers to the fact that in │ │ │ │ + functions, \_form#228. The origin of the term refers to the fact that in │ │ │ │ structural mechanics (where the finite element method originated), one │ │ │ │ often starts from the elastostatics equation \iline 2130 \iline 2131 │ │ │ │ - \_form#227@_fakenl@_fakenl In this equation, \_form#73 is the stress- │ │ │ │ + \_form#229@_fakenl@_fakenl In this equation, \_form#50 is the stress- │ │ │ │ strain tensor that, informally speaking, relates how much force one has │ │ │ │ to apply to obtain a unit displacement. In other words, it encodes the │ │ │ │ - "stiffness" of the material: A large \_form#73, i.e., a large stiffness, │ │ │ │ + "stiffness" of the material: A large \_form#50, i.e., a large stiffness, │ │ │ │ means a large required force for a desired displacement and the other way │ │ │ │ - around. If one multiplies this equation by a test function \_form#187, │ │ │ │ - integrates over \_form#191, and then discretizes by the substitution │ │ │ │ - \_form#192, then after integration by parts one ends up with \iline 2143 │ │ │ │ - \iline 2144 \iline 2145 \_form#228@_fakenl@_fakenl@_fakenl which can be │ │ │ │ - written as \iline 2148 \iline 2149 \_form#229@_fakenl@_fakenl where │ │ │ │ - \iline 2152 \iline 2153 \_form#230@_fakenl@_fakenl Since the matrix │ │ │ │ + around. If one multiplies this equation by a test function \_form#166, │ │ │ │ + integrates over \_form#172, and then discretizes by the substitution │ │ │ │ + \_form#173, then after integration by parts one ends up with \iline 2143 │ │ │ │ + \iline 2144 \iline 2145 \_form#230@_fakenl@_fakenl@_fakenl which can be │ │ │ │ + written as \iline 2148 \iline 2149 \_form#231@_fakenl@_fakenl where │ │ │ │ + \iline 2152 \iline 2153 \_form#232@_fakenl@_fakenl Since the matrix │ │ │ │ entries are (weighted) integrals of the stiffness coefficient, the │ │ │ │ resulting matrix is called the "stiffness matrix". In mathematics, where │ │ │ │ we often consider non-dimensionalized equations, we end up with the case │ │ │ │ - \_form#231, and as a consequence the matrix without the coefficient, │ │ │ │ - \iline 2161 \iline 2162 \_form#232@_fakenl@_fakenl which corresponds to │ │ │ │ + \_form#233, and as a consequence the matrix without the coefficient, │ │ │ │ + \iline 2161 \iline 2162 \_form#234@_fakenl@_fakenl which corresponds to │ │ │ │ the Laplace or Poisson equation, \iline 2165 \iline 2166 │ │ │ │ - \_form#233@_fakenl@_fakenl also carries the name "stiffness matrix". The │ │ │ │ - stiffness matrix is almost always denotes by the symbol \_form#70. See, │ │ │ │ + \_form#235@_fakenl@_fakenl also carries the name "stiffness matrix". The │ │ │ │ + stiffness matrix is almost always denotes by the symbol \_form#47. See, │ │ │ │ for example, @ref step_4 "step-4", @ref step_6 "step-6", as well as a │ │ │ │ number of the time dependent equations considered in programs such as │ │ │ │ @ref step_23 "step-23" or @ref step_26 "step-26". See also the @ref │ │ │ │ GlossStiffnessMatrix "stiffness matrix" for a related case.
@anchor GlossSubdomainId Subdomain id
│ │ │ │
Each cell of a triangulation has associated with it a property called │ │ │ │ the "subdomain id" that can be queried using a call like cell- │ │ │ │ @@ -1596,16 +1596,16 @@ │ │ │ │ there is a second, closely related set of flags that are associated with │ │ │ │ each cell: "level subdomain ids." These exist not only for active cells │ │ │ │ but, in fact, for every cell in a mesh hierarchy. Their meaning is │ │ │ │ entirely analogous to the regular subdomain ids, but they are read and │ │ │ │ written by the CellAccessor::level_subdomain_id() and CellAccessor:: │ │ │ │ set_level_subdomain_id() functions.
@anchor │ │ │ │ GlossSupport Support points
Support points are by │ │ │ │ - definition those points \_form#234, such that for the shape functions │ │ │ │ - \_form#235 holds \_form#236. Therefore, a finite element interpolation │ │ │ │ + definition those points \_form#236, such that for the shape functions │ │ │ │ + \_form#237 holds \_form#238. Therefore, a finite element interpolation │ │ │ │ can be defined uniquely by the values in the support points. Lagrangian │ │ │ │ elements fill the vector accessed by FiniteElement:: │ │ │ │ get_unit_support_points(), such that the function FiniteElement:: │ │ │ │ has_support_points() returns true. Naturally, these support │ │ │ │ points are on the @ref GlossReferenceCell "reference cell". Then, │ │ │ │ FEValues can be used (in conjunction with a Mapping) to access support │ │ │ │ points on the actual grid cells. @note The concept of @ref GlossSupport │ │ │ │ @@ -1691,23 +1691,23 @@ │ │ │ │ has been called. @note The usual warning about the missing type safety of │ │ │ │ @p void pointers are obviously in place here; responsibility for │ │ │ │ correctness of types etc lies entirely with the user of the pointer.
@anchor GlossUserProvidedCallBack User │ │ │ │ provided callbacks
Much functionality in deal.II under the │ │ │ │ hood uses external libraries that operate by calling back into user- │ │ │ │ provided functions. Examples are ODE solvers that solve differential │ │ │ │ - equations of the form \iline 2384 \iline 2385 \_form#237@_fakenl@_fakenl │ │ │ │ - where users need to provide a function that, for a given time \_form#238 │ │ │ │ - and vector \_form#239 returns the value of the right hand side │ │ │ │ - \_form#240. Other examples are solvers for nonlinear systems \iline 2390 │ │ │ │ - \iline 2391 \_form#241@_fakenl@_fakenl where users need to provide │ │ │ │ - functions that for a given vector \_form#242 returns the vector │ │ │ │ - \_form#243 and, in many cases, also the Jacobian \_form#244 as well as │ │ │ │ + equations of the form \iline 2384 \iline 2385 \_form#239@_fakenl@_fakenl │ │ │ │ + where users need to provide a function that, for a given time \_form#240 │ │ │ │ + and vector \_form#241 returns the value of the right hand side │ │ │ │ + \_form#242. Other examples are solvers for nonlinear systems \iline 2390 │ │ │ │ + \iline 2391 \_form#243@_fakenl@_fakenl where users need to provide │ │ │ │ + functions that for a given vector \_form#244 returns the vector │ │ │ │ + \_form#245 and, in many cases, also the Jacobian \_form#246 as well as │ │ │ │ possibly other information about the problem such as the relative scaling │ │ │ │ - of solution variables within the vector \_form#242 that can be used to │ │ │ │ + of solution variables within the vector \_form#244 that can be used to │ │ │ │ make the problem better conditioned. These functions are often called │ │ │ │ "callbacks" because the ODE or nonlinear solver libraries "call back" │ │ │ │ into user code. In code written in the C programming language, these │ │ │ │ callbacks would often be described by pointers to user functions handed │ │ │ │ to the solver library. Since deal.II is written in C++, we typically │ │ │ │ instead use std::function objects. Examples of │ │ │ │ @@ -1716,16 +1716,16 @@ │ │ │ │ @ref step_77 "step-77" illustrates how this can be used with SUNDIALS:: │ │ │ │ KINSOL. Many of these libraries use a convention that comes from their │ │ │ │ origin in the C programming language: User callbacks for the purposes of │ │ │ │ these libraries return the data they are asked through one of their │ │ │ │ arguments, and indicate success or failure by returning an int │ │ │ │ that needs to be zero if the function returned successfully, and a │ │ │ │ nonzero value if the function failed for whatever reason. (Examples of │ │ │ │ - failures could include if the right hand side function \_form#240 │ │ │ │ - contains a square root of one of the \_form#245, but that \_form#245 is │ │ │ │ + failures could include if the right hand side function \_form#242 │ │ │ │ + contains a square root of one of the \_form#247, but that \_form#247 is │ │ │ │ negative; or perhaps if a function requires table lookup for values that │ │ │ │ are outside the range that is tabulated.) The approach to return integer │ │ │ │ values is decidedly not in the spirit of C++: If a function cannot │ │ │ │ complete the work it is asked to do, the C++ way to deal with this is to │ │ │ │ throw an exception. As a consequence, for all of the places where deal.II │ │ │ │ wraps external libraries and where user codes need to provide callbacks, │ │ │ │ we adopt the following conventions that user callbacks should follow: - │ │ │ │ @@ -1741,18 +1741,18 @@ │ │ │ │ lead to some clean-up operations inside that external library, and a │ │ │ │ return to the wrapper code. There, the originally thrown exception will │ │ │ │ then be re-thrown and become visible again in the place where the │ │ │ │ wrappers were thrown. In other words, for all practical purposes, it │ │ │ │ looks like the exception thrown in the callback had simply propagated all │ │ │ │ the way back to user code. - There are some libraries that allow │ │ │ │ callbacks to indicate "recoverable errors". For example, KINSOL can solve │ │ │ │ - nonlinear systems \_form#246 and deal with situations where a function │ │ │ │ - evaluation for \_form#247 is not possible – for example the case │ │ │ │ + nonlinear systems \_form#248 and deal with situations where a function │ │ │ │ + evaluation for \_form#249 is not possible – for example the case │ │ │ │ above one tries to take the square root of a negative value – but │ │ │ │ - where it could then try again for a modified \_form#242 for which │ │ │ │ + where it could then try again for a modified \_form#244 for which │ │ │ │ evaluation of the square root is possible. (This is often possible in line search │ │ │ │ algorithms where using a shorter step length might actually succeed.) │ │ │ │ In such cases, a user-provided callback function should throw an │ │ │ │ exception of type StandardExceptions::RecoverableUserCallbackError, which │ │ │ │ will then internally be translated into an appropriate code │ │ │ │ understandable by the underlying library. It is worthwhile pointing out │ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/cell__status_8h.html │ │ │ @@ -160,21 +160,21 @@ │ │ │
│ │ │ │ │ │ │ │ │ │ │ │ - │ │ │ - │ │ │ - │ │ │ - │ │ │
cell_will_be_refined 

The cell will be or was refined.

│ │ │
children_will_be_coarsened 

The children of this cell will be or were coarsened into this cell.

│ │ │
cell_invalid 

Invalid status. Will not occur for the user.

│ │ │
CELL_PERSIST 
Deprecated
Use CellStatus::cell_will_persist instead
│ │ │ +
CELL_PERSIST 
Deprecated
Use CellStatus::cell_will_persist instead
│ │ │
CELL_REFINE 
Deprecated
Use CellStatus::cell_will_be_refined instead
│ │ │ +
CELL_REFINE 
Deprecated
Use CellStatus::cell_will_be_refined instead
│ │ │
CELL_COARSEN 
Deprecated
Use CellStatus::cell_will_be_coarsened instead
│ │ │ +
CELL_COARSEN 
Deprecated
Use CellStatus::cell_will_be_coarsened instead
│ │ │
CELL_INVALID 
Deprecated
Use CellStatus::cell_invalid instead
│ │ │ +
CELL_INVALID 
Deprecated
Use CellStatus::cell_invalid instead
│ │ │
│ │ │ │ │ │

Definition at line 30 of file cell_status.h.

│ │ │ │ │ │ │ │ │ │ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classAffineConstraints.html │ │ │ @@ -525,15 +525,15 @@ │ │ │ │ │ │ inlineexplicit │ │ │ │ │ │ │ │ │
│ │ │

Constructor. The supplied IndexSet defines for which indices this object will store constraints. In a calculation with a DoFHandler object based on parallel::distributed::Triangulation or parallel::shared::Triangulation, one should use the set of locally relevant DoFs (see GlossLocallyRelevantDof).

│ │ │

The given IndexSet allows the AffineConstraints container to save memory by just not caring about degrees of freedom that are not of importance to the current processor. In contrast, in parallel computations, if you do not provide such an index set (here, or using the reinit() function that takes such an argument), the current object will allocate memory proportional to the total number of degrees of freedom (accumulated over all processes), which is clearly wasteful and not efficient – and should be considered a bug.

│ │ │ -
Deprecated
This constructor is equivalent to calling the following one with both of its arguments equal to the index set provided here. This is not wrong, but inefficient. Use the following constructor instead.
│ │ │ +
Deprecated
This constructor is equivalent to calling the following one with both of its arguments equal to the index set provided here. This is not wrong, but inefficient. Use the following constructor instead.
│ │ │ │ │ │

Definition at line 2343 of file affine_constraints.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ AffineConstraints() [3/5]

│ │ │ @@ -753,15 +753,15 @@ │ │ │ ( │ │ │ const IndexSet & locally_stored_constraints) │ │ │ │ │ │ │ │ │ │ │ │
│ │ │

clear() the AffineConstraints object and supply an IndexSet that describes for which degrees of freedom this object can store constraints. See the discussion in the documentation of the constructor of this class that takes a single index set as argument.

│ │ │ -
Deprecated
Use the reinit() function with two index set arguments instead.
│ │ │ +
Deprecated
Use the reinit() function with two index set arguments instead.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ reinit() [3/3]

│ │ │ │ │ │
│ │ │ @@ -894,15 +894,15 @@ │ │ │ const IndexSet & filter ) │ │ │ │ │ │ │ │ │
│ │ │

This function copies the content of constraints_in with DoFs that are element of the IndexSet filter. Elements that are not present in the IndexSet are ignored. All DoFs will be transformed to local index space of the filter, both the constrained DoFs and the other DoFs these entries are constrained to. The local index space of the filter is a contiguous numbering of all (global) DoFs that are elements in the filter.

│ │ │

If, for example, the filter represents the range [10,20), and the constraints object constraints_in includes the global indices {7,13,14}, the indices {3,4} are added to the calling constraints object (since 13 and 14 are elements in the filter and element 13 is the fourth element in the index, and 14 is the fifth).

│ │ │

This function provides an easy way to create a AffineConstraints for certain vector components in a vector-valued problem from a full AffineConstraints, i.e. extracting a diagonal subblock from a larger AffineConstraints. The block is specified by the IndexSet argument.

│ │ │ -
Deprecated
This function is a combination of the get_view() function and merge() in that it selects a subset of constraints from another constraints object that is then merged into the current one. But the current function does not deal well with index sets. Furthermore, it simply discards parts of constraints that constrain one degree of freedom against ones that are not selected in the filter – something that should probably be considered a bug. Use get_view() and merge() instead.
│ │ │ +
Deprecated
This function is a combination of the get_view() function and merge() in that it selects a subset of constraints from another constraints object that is then merged into the current one. But the current function does not deal well with index sets. Furthermore, it simply discards parts of constraints that constrain one degree of freedom against ones that are not selected in the filter – something that should probably be considered a bug. Use get_view() and merge() instead.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ add_constraint()

│ │ │ │ │ │
│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classBlockSparsityPatternBase.html │ │ │ @@ -119,15 +119,15 @@ │ │ │

#include <deal.II/lac/block_sparsity_pattern.h>

│ │ │

Detailed Description

│ │ │
template<typename SparsityPatternType>
│ │ │ class BlockSparsityPatternBase< SparsityPatternType >

This is the base class for block versions of the sparsity pattern and dynamic sparsity pattern classes. It has not much functionality, but only administrates an array of sparsity pattern objects and delegates work to them. It has mostly the same interface as has the SparsityPattern, and DynamicSparsityPattern, and simply transforms calls to its member functions to calls to the respective member functions of the member sparsity patterns.

│ │ │

The largest difference between the SparsityPattern and DynamicSparsityPattern classes and this class is that mostly, the matrices have different properties and you will want to work on the blocks making up the matrix rather than the whole matrix. You can access the different blocks using the block(row,col) function.

│ │ │

Attention: this object is not automatically notified if the size of one of its subobjects' size is changed. After you initialize the sizes of the subobjects, you will therefore have to call the collect_sizes() function of this class! Note that, of course, all sub-matrices in a (block-)row have to have the same number of rows, and that all sub-matrices in a (block-)column have to have the same number of columns.

│ │ │

You will in general not want to use this class, but one of the derived classes.

│ │ │ -
Todo
Handle optimization of diagonal elements of the underlying SparsityPattern correctly.
│ │ │ +
Todo
Handle optimization of diagonal elements of the underlying SparsityPattern correctly.
│ │ │
See also
Block (linear algebra)
│ │ │ │ │ │

Definition at line 79 of file block_sparsity_pattern.h.

│ │ │
│ │ │ Inheritance diagram for BlockSparsityPatternBase< SparsityPatternType >:
│ │ │
│ │ │
Inheritance graph
│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classFEFaceEvaluation.html │ │ │ @@ -1122,15 +1122,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ VectorType & output_vector ) │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
Please use the integrate_scatter() function with the EvaluationFlags argument.
│ │ │ +
Deprecated
Please use the integrate_scatter() function with the EvaluationFlags argument.
│ │ │ │ │ │
│ │ │
│ │ │ │ │ │

◆ dof_indices()

│ │ │ │ │ │
│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classFEFacePointEvaluation.html │ │ │ @@ -8086,15 +8086,15 @@ │ │ │ 0001f950: 6665 3933 6261 3664 3763 3239 3031 3633 fe93ba6d7c290163 │ │ │ 0001f960: 3934 6362 3922 3e72 6569 6e69 7428 293c 94cb9">reinit()< │ │ │ 0001f970: 2f61 3e2e 3c2f 703e 0a3c 646c 2063 6c61 /a>.

.
│ │ │ 0001f990: 3c64 743e 3c62 3e3c 6120 636c 6173 733d
De │ │ │ +0001f9c0: 6563 6174 6564 3030 3031 3035 223e 4465 ecated000105">De │ │ │ 0001f9d0: 7072 6563 6174 6564 3c2f 613e 3c2f 623e precated │ │ │ 0001f9e0: 3c2f 6474 3e3c 6464 3e55 7365 2074 6865
Use the │ │ │ 0001f9f0: 2066 756e 6374 696f 6e20 3c61 2063 6c61 function const unsigned int q_point_index) │ │ │ const │ │ │ │ │ │ │ │ │
│ │ │

Return the normal in a given quadrature point.

│ │ │

The normal points in outwards direction as seen from the first cell of this interface.

│ │ │ -
Deprecated
Use the function normal_vector().
│ │ │ +
Deprecated
Use the function normal_vector().
│ │ │
Note
For this function to work properly, the underlying FEValues, FEFaceValues, or FESubfaceValues object on which you call it must have computed the information you are requesting. To do so, the update_normal_vectors flag must be an element of the list of UpdateFlags that you passed to the constructor of this object. See The interplay of UpdateFlags, Mapping, and FiniteElement in FEValues for more information.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ normal_vector()

│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classFEInterfaceViews_1_1Vector.html │ │ │ @@ -525,15 +525,15 @@ │ │ │ │ │ │ │ │ │ const unsigned int q_point ) const │ │ │ │ │ │ │ │ │
│ │ │

The same as above.

│ │ │ -
Deprecated
Use the average_of_gradients() function instead.
│ │ │ +
Deprecated
Use the average_of_gradients() function instead.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ jump_in_hessians()

│ │ │ │ │ │
│ │ │ @@ -578,15 +578,15 @@ │ │ │ │ │ │ │ │ │ const unsigned int q_point ) const │ │ │ │ │ │ │ │ │
│ │ │

The same as above.

│ │ │ -
Deprecated
Use the average_of_hessians() function instead.
│ │ │ +
Deprecated
Use the average_of_hessians() function instead.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ jump_in_third_derivatives()

│ │ │ │ │ │
│ │ │ @@ -716,15 +716,15 @@ │ │ │ │ │ │ │ │ │ const unsigned int q_point ) const │ │ │ │ │ │ │ │ │
│ │ │

The same as above.

│ │ │ -
Deprecated
Use the average_of_hessians() function instead.
│ │ │ +
Deprecated
Use the average_of_hessians() function instead.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ get_function_values()

│ │ │ │ │ │
│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classFEPointEvaluation.html │ │ │ @@ -9795,15 +9795,15 @@ │ │ │ 00026420: 3364 6435 3364 3036 3331 3332 3538 3930 3dd53d0631325890 │ │ │ 00026430: 3963 3731 3861 3338 3222 3e72 6569 6e69 9c718a382">reini │ │ │ 00026440: 7428 293c 2f61 3e2e 3c2f 703e 0a3c 646c t().

.
Deprecated │ │ │ 000264b0: 3c2f 623e 3c2f 6474 3e3c 6464 3e55 7365
Use │ │ │ 000264c0: 2074 6865 2066 756e 6374 696f 6e20 3c61 the function reinit()..
Deprecat │ │ │ +00014450: 3030 3031 3035 223e 4465 7072 6563 6174 000105">Deprecat │ │ │ 00014460: 6564 3c2f 613e 3c2f 623e 3c2f 6474 3e3c ed
< │ │ │ 00014470: 6464 3e55 7365 2074 6865 2066 756e 6374 dd>Use the funct │ │ │ 00014480: 696f 6e20 3c61 2063 6c61 7373 3d22 656c ion quad │ │ │ 000144c0: 7261 7475 7265 5f70 6f69 6e74 2829 3c2f rature_point()

Detailed Description

│ │ │
template<int dim>
│ │ │ class FE_ABF< dim >

Implementation of Arnold-Boffi-Falk (ABF) elements, conforming with the space Hdiv. These elements generate vector fields with normal components continuous between mesh cells.

│ │ │

These elements are based on an article from Arnold, Boffi and Falk: Quadrilateral H(div) finite elements, SIAM J. Numer. Anal. Vol.42, No.6, pp.2429-2451

│ │ │

In this article, the authors demonstrate that the usual RT elements and also BDM and other proposed finite dimensional subspaces of H(div) do not work properly on arbitrary FE grids. I.e. the convergence rates deteriorate on these meshes. As a solution the authors propose the ABF elements, which are implemented in this class.

│ │ │

This class is not implemented for the codimension one case (spacedim != │ │ │ dim).

│ │ │ -
Todo
Even if this element is implemented for two and three space dimensions, the definition of the node values relies on consistently oriented faces in 3d. Therefore, care should be taken on complicated meshes.
│ │ │ +
Todo
Even if this element is implemented for two and three space dimensions, the definition of the node values relies on consistently oriented faces in 3d. Therefore, care should be taken on complicated meshes.
│ │ │

Interpolation

│ │ │

The interpolation operators associated with the RT element are constructed such that interpolation and computing the divergence are commuting operations. We require this from interpolating arbitrary functions as well as the restriction matrices. It can be achieved by two interpolation schemes, the simplified one in FE_RaviartThomasNodal and the original one here:

│ │ │

Node values on edges/faces

│ │ │

On edges or faces, the node values are the moments of the normal component of the interpolated function with respect to the traces of the RT polynomials. Since the normal trace of the RT space of degree k on an edge/face is the space Qk, the moments are taken with respect to this space.

│ │ │

Interior node values

│ │ │

Higher order RT spaces have interior nodes. These are moments taken with respect to the gradient of functions in Qk on the cell (this space is the matching space for RTk in a mixed formulation).

│ │ │

Generalized support points

│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classFE__BDM.html │ │ │ @@ -117,16 +117,16 @@ │ │ │
│ │ │ │ │ │

#include <deal.II/fe/fe_bdm.h>

│ │ │

Detailed Description

│ │ │
template<int dim>
│ │ │ class FE_BDM< dim >

The Brezzi-Douglas-Marini element.

│ │ │

Degrees of freedom

│ │ │ -
Todo
The 3d version exhibits some numerical instabilities, in particular for higher order
│ │ │ -
Todo
Restriction matrices are missing.
│ │ │ +
Todo
The 3d version exhibits some numerical instabilities, in particular for higher order
│ │ │ +
Todo
Restriction matrices are missing.
│ │ │

The matching pressure space for FE_BDM of order k is the element FE_DGP of order k-1.

│ │ │

The BDM element of order p has p+1 degrees of freedom on each face. These are implemented as the function values in the p+1 Gauss points on each face.

│ │ │

Additionally, for order greater or equal 2, we have additional p(p-1), the number of vector valued polynomials in Pp, interior degrees of freedom. These are the vector function values in the first p(p-1)/2 of the p2 Gauss points in the cell.

│ │ │ │ │ │

Definition at line 58 of file fe_bdm.h.

│ │ │
│ │ │ Inheritance diagram for FE_BDM< dim >:
│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classFE__FaceP_3_011_00_01spacedim_01_4.html │ │ │ @@ -4085,15 +4085,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ protectedvirtualinherited │ │ │ │ │ │ │ │ │
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Deprecated
Use the version taking a hp::QCollection argument.
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Deprecated
Use the version taking a hp::QCollection argument.
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│ │ │
│ │ │ │ │ │

◆ fill_fe_values() [3/6]

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Deprecated
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Deprecated
Use the version taking a hp::QCollection argument.
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│ │ │
│ │ │ │ │ │

◆ fill_fe_subface_values() [3/6]

│ │ │ │ │ │
│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classFE__FaceQ.html │ │ │ @@ -1183,15 +1183,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ protectedvirtualinherited │ │ │ │ │ │ │ │ │
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Use the version taking a hp::QCollection argument.
│ │ │ +
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ get_subface_data()

│ │ │ │ │ │
│ │ │ @@ -1643,15 +1643,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ protectedvirtualinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ +
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ fill_fe_face_values() [4/4]

│ │ │ │ │ │
│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classFE__FaceQ_3_011_00_01spacedim_01_4.html │ │ │ @@ -2008,15 +2008,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ protectedvirtualinherited │ │ │ │ │ │ │ │ │
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Deprecated
Use the version taking a hp::QCollection argument.
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Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ │ │ │
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◆ get_subface_data() [2/4]

│ │ │ │ │ │
│ │ │ @@ -2403,15 +2403,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ protectedvirtualinherited │ │ │ │ │ │ │ │ │
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Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ +
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ fill_fe_subface_values() [2/7]

│ │ │ │ │ │
│ │ │ @@ -9549,15 +9549,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ protectedvirtual │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ +
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ get_subface_data() [4/4]

│ │ │ │ │ │
│ │ │ @@ -10007,15 +10007,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ protectedvirtual │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ +
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ fill_fe_face_values() [9/9]

│ │ │ │ │ │
│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classFE__Nedelec.html │ │ │ @@ -552,15 +552,15 @@ │ │ │ 00002270: 6361 7365 2028 3c73 7061 6e20 636c 6173 case (spacedim │ │ │ 00002290: 213d 0a64 696d 3c2f 7370 616e 3e29 2e3c !=.dim).< │ │ │ 000022a0: 2f70 3e0a 3c64 6c20 636c 6173 733d 2274 /p>.
Todo< │ │ │ +000022e0: 3030 3030 3922 3e54 6f64 6f3c 2f61 3e3c 00009">Todo< │ │ │ 000022f0: 2f62 3e3c 2f64 743e 3c64 643e 4576 656e /b>
Even │ │ │ 00002300: 2069 6620 7468 6973 2065 6c65 6d65 6e74 if this element │ │ │ 00002310: 2069 7320 696d 706c 656d 656e 7465 6420 is implemented │ │ │ 00002320: 666f 7220 7477 6f20 616e 6420 7468 7265 for two and thre │ │ │ 00002330: 6520 7370 6163 6520 6469 6d65 6e73 696f e space dimensio │ │ │ 00002340: 6e73 2c20 7468 6520 6465 6669 6e69 7469 ns, the definiti │ │ │ 00002350: 6f6e 206f 6620 7468 6520 6e6f 6465 2076 on of the node v │ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classFE__Poly.html │ │ │ @@ -137,15 +137,15 @@ │ │ │
Tensor<order,dim> compute_derivative (const unsigned int i,
│ │ │
const Point<dim> &p) const;
│ │ │
FiniteElement< dim, dim >::dimension
static constexpr unsigned int dimension
Definition fe_data.h:301
│ │ │
Point
Definition point.h:113
│ │ │ │ │ │

Example classes are TensorProductPolynomials, PolynomialSpace or PolynomialsP.

│ │ │

This class is not a fully implemented FiniteElement class. Instead there are several pure virtual functions declared in the FiniteElement and FiniteElement classes which cannot be implemented by this class but are left for implementation in derived classes.

│ │ │ -
Todo
Since nearly all functions for spacedim != dim are specialized, this class needs cleaning up.
│ │ │ +
Todo
Since nearly all functions for spacedim != dim are specialized, this class needs cleaning up.
│ │ │ │ │ │

Definition at line 75 of file fe_poly.h.

│ │ │
│ │ │ Inheritance diagram for FE_Poly< dim, spacedim >:
│ │ │
│ │ │
Inheritance graph
│ │ │ │ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classFE__PolyFace.html │ │ │ @@ -3831,15 +3831,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ protectedvirtualinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ +
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ fill_fe_values() [2/2]

│ │ │ │ │ │
│ │ │ @@ -4047,15 +4047,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ protectedvirtualinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ +
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ fill_fe_subface_values() [2/2]

│ │ │ │ │ │
│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classFE__TraceQ.html │ │ │ @@ -1073,15 +1073,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ protectedvirtualinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ +
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ get_subface_data()

│ │ │ │ │ │
│ │ │ @@ -1533,15 +1533,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ protectedvirtualinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ +
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ fill_fe_face_values() [4/4]

│ │ │ │ │ │
│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classFE__TraceQ_3_011_00_01spacedim_01_4.html │ │ │ @@ -1062,15 +1062,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ protectedvirtual │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ +
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ get_subface_data() [1/2]

│ │ │ │ │ │
│ │ │ @@ -1520,15 +1520,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ protectedvirtual │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ +
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ fill_fe_face_values() [4/7]

│ │ │ │ │ │
│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classFiniteElement.html │ │ │ @@ -3555,15 +3555,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ protectedvirtual │ │ │ │ │ │ │ │ │
│ │ │ -
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Use the version taking a hp::QCollection argument.
│ │ │ +
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ get_subface_data()

│ │ │ │ │ │
│ │ │ @@ -3826,15 +3826,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ protectedvirtual │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ +
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ fill_fe_subface_values()

│ │ │ │ │ │
│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classIndexSet.html │ │ │ @@ -1189,15 +1189,15 @@ │ │ │ ( │ │ │ ) │ │ │ │ │ │ │ │ │ │ │ │
│ │ │

Remove and return the last element of the last range. This function throws an exception if the IndexSet is empty.

│ │ │ -
Deprecated
This function is deprecated. Conceptually, an index set is a set; it should not be seen as a sorted container in which it is clear what element is stored "last".
│ │ │ +
Deprecated
This function is deprecated. Conceptually, an index set is a set; it should not be seen as a sorted container in which it is clear what element is stored "last".
│ │ │ │ │ │

Definition at line 561 of file index_set.cc.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ pop_front()

│ │ │ @@ -1210,15 +1210,15 @@ │ │ │ ( │ │ │ ) │ │ │ │ │ │ │ │ │ │ │ │
│ │ │

Remove and return the first element of the first range. This function throws an exception if the IndexSet is empty.

│ │ │ -
Deprecated
This function is deprecated. Conceptually, an index set is a set; it should not be seen as a sorted container in which it is clear what element is stored "first".
│ │ │ +
Deprecated
This function is deprecated. Conceptually, an index set is a set; it should not be seen as a sorted container in which it is clear what element is stored "first".
│ │ │ │ │ │

Definition at line 579 of file index_set.cc.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ get_index_vector()

│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classLinearAlgebra_1_1distributed_1_1BlockVector.html │ │ │ @@ -1492,15 +1492,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ inline │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
Use import_elements() instead.
│ │ │ +
Deprecated
Use import_elements() instead.
│ │ │ │ │ │

Definition at line 574 of file la_parallel_block_vector.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ operator*() [1/2]

│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classLinearAlgebra_1_1distributed_1_1Vector.html │ │ │ @@ -1337,15 +1337,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ inline │ │ │ │ │ │ │ │ │
│ │ │ -
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Use import_elements() instead.
│ │ │ +
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Use import_elements() instead.
│ │ │ │ │ │

Definition at line 729 of file la_parallel_vector.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ operator*=()

│ │ │ @@ -1486,15 +1486,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ inline │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
Use import_elements() instead.
│ │ │ +
Deprecated
Use import_elements() instead.
│ │ │ │ │ │

Definition at line 788 of file la_parallel_vector.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ operator*()

│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classMGTransferBase.html │ │ │ @@ -119,15 +119,15 @@ │ │ │

#include <deal.II/multigrid/mg_base.h>

│ │ │

Detailed Description

│ │ │
template<typename VectorType>
│ │ │ class MGTransferBase< VectorType >

Base class used to declare the operations needed by a concrete class implementing prolongation and restriction of vectors in the multigrid context. This class is abstract and has no implementation of these operations.

│ │ │

There are several derived classes, reflecting the fact that vector types and numbering of the fine-grid discretization and of the multi-level implementation are independent.

│ │ │

If you use multigrid for a single PDE or for your complete system of equations, you will use MGTransferPrebuilt together with Multigrid. The vector types used on the fine grid as well as for the multilevel operations may be Vector or BlockVector. In both cases, MGTransferPrebuilt will operate on all components of the solution.

│ │ │
Note
For the following, it is important to realize the difference between a solution component and a solution block. The distinction only applies if vector valued elements are used, but is quite important then. This is reflected in the fact that it is not possible right now to use transfer classes based on MGTransferComponentBase for genuine vector valued elements, but descendants of MGTransferBlockBase would have to be applied. In the following text, we will use the term block, but remark that it might refer to components as well.
│ │ │ -
Todo
update the following documentation, since it does not reflect the latest changes in structure.
│ │ │ +
Todo
update the following documentation, since it does not reflect the latest changes in structure.
│ │ │

For mixed systems, it may be required to do multigrid only for a single component or for some components. The classes MGTransferSelect and MGTransferBlock handle these cases.

│ │ │

MGTransferSelect is used if you use multigrid (on Vector objects) for a single component, possibly grouped using mg_target_component.

│ │ │

The class MGTransferBlock handles the case where your multigrid method operates on BlockVector objects. These can contain all or a consecutive set of the blocks of the complete system. Since most smoothers cannot operate on block structures, it is not clear whether this case is really useful. Therefore, a tested implementation of this case will be supplied when needed.

│ │ │ │ │ │

Definition at line 171 of file mg_base.h.

│ │ │
│ │ │ Inheritance diagram for MGTransferBase< VectorType >:
│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classMapping.html │ │ │ @@ -959,15 +959,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ protectedvirtual │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ +
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ get_subface_data()

│ │ │ │ │ │
│ │ │ @@ -1175,15 +1175,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ protectedvirtual │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ +
Deprecated
Use the version taking a hp::QCollection argument.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ fill_fe_subface_values()

│ │ │ │ │ │
│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classMeshWorker_1_1Assembler_1_1ResidualLocalBlocksToGlobalBlocks.html │ │ │ @@ -119,15 +119,15 @@ │ │ │

#include <deal.II/meshworker/assembler.h>

│ │ │

Detailed Description

│ │ │
template<typename VectorType>
│ │ │ class MeshWorker::Assembler::ResidualLocalBlocksToGlobalBlocks< VectorType >

Assemble local residuals into global residuals.

│ │ │

The global residuals are expected as an FEVectors object. The local residuals are block vectors.

│ │ │

Depending on whether the BlockInfo object was initialize with BlockInfo::initialize_local(), the comprehensive or block data model is used locally.

│ │ │

In the block model, each of the blocks of the local vectors corresponds to the restriction of a single block of the system to this cell (see GlossBlock). Thus, the size of this local block is the number of degrees of freedom of the corresponding base element of the FESystem.

│ │ │ -
Todo
Comprehensive model currently not implemented.
│ │ │ +
Todo
Comprehensive model currently not implemented.
│ │ │ │ │ │

Definition at line 111 of file assembler.h.

│ │ │
│ │ │ │ │ │ │ │ │ │ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classMeshWorker_1_1LocalIntegrator.html │ │ │ @@ -118,15 +118,15 @@ │ │ │ │ │ │

#include <deal.II/meshworker/local_integrator.h>

│ │ │

Detailed Description

│ │ │
template<int dim, int spacedim = dim, typename number = double>
│ │ │ class MeshWorker::LocalIntegrator< dim, spacedim, number >

A local integrator object, which can be used to simplify the call of loop(). Instead of providing the three local integration functions separately, we bundle them as virtual functions in this class.

│ │ │

Additionally, since we cannot have a virtual null function, we provide flags, which allow us to indicate, whether we want to integrate on boundary and interior faces. These flags are true by default, but can be modified by applications to speed up the loop.

│ │ │

If a function is not overloaded in a derived class, but its usage flag is true, the function will cause an exception ExcPureFunction.

│ │ │ -
Deprecated
This class is deprecated. It used to be the basis for integration via the MeshWorker::integration_loop() function, but the same functionality is available via MeshWorker::loop().
│ │ │ +
Deprecated
This class is deprecated. It used to be the basis for integration via the MeshWorker::integration_loop() function, but the same functionality is available via MeshWorker::loop().
│ │ │ │ │ │

Definition at line 60 of file local_integrator.h.

│ │ │
│ │ │ Inheritance diagram for MeshWorker::LocalIntegrator< dim, spacedim, number >:
│ │ │
│ │ │
Inheritance graph
│ │ │ │ │ │ @@ -723,15 +723,15 @@ │ │ │
│ │ │ │ │ │ │ │ │

│ │ │ Public Member Functions

void initialize (const BlockInfo *block_info, AnyData &residuals)
void initialize (const AffineConstraints< typename VectorType::value_type > &constraints)
std::vector<std::string> MeshWorker::LocalIntegrator< dim, spacedim, number >::input_vector_names
│ │ │
│ │ │

The names of the input vectors. If this vector is nonempty, it can be used by application programs to automatically select and verify the input vectors used for integration.

│ │ │
Note
This variable is currently not used by the library, but it is provided to help develop application programs.
│ │ │ -
Deprecated
Because the library itself does not use this field, it is better placed in derived classes.
│ │ │ +
Deprecated
Because the library itself does not use this field, it is better placed in derived classes.
│ │ │ │ │ │

Definition at line 133 of file local_integrator.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ output_names

│ │ │ @@ -744,15 +744,15 @@ │ │ │ │ │ │ std::vector<std::string> MeshWorker::LocalIntegrator< dim, spacedim, number >::output_names │ │ │ │ │ │ │ │ │
│ │ │

The names of the results produced. If this vector is nonempty, it can be used by application programs to automatically assign names to output values and/or verify the names of vectors.

│ │ │
Note
This variable is currently not used by the library, but it is provided to help develop application programs.
│ │ │ -
Deprecated
Because the library itself does not use this field, it is better placed in derived classes.
│ │ │ +
Deprecated
Because the library itself does not use this field, it is better placed in derived classes.
│ │ │ │ │ │

Definition at line 147 of file local_integrator.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ counter

│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classObserverPointer.html │ │ │ @@ -530,15 +530,15 @@ │ │ │ │ │ │ │ │ │ inline │ │ │ │ │ │ │ │ │
│ │ │

Delete the object pointed to and set the pointer to nullptr. Note that unlike what the documentation of the class describes, this function actually deletes the object pointed to. That is, this function assumes a ObserverPointer's ownership of the object pointed to.

│ │ │ -
Deprecated
This function is deprecated. It does not use the semantics we usually use for this class, and its use is surely going to be confusing.
│ │ │ +
Deprecated
This function is deprecated. It does not use the semantics we usually use for this class, and its use is surely going to be confusing.
│ │ │ │ │ │

Definition at line 434 of file observer_pointer.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ operator T*()

│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classPathSearch.html │ │ │ @@ -134,15 +134,15 @@ │ │ │
...
│ │ │
PathSearch::PathSearch
PathSearch(const std::string &cls, const unsigned int debug=0)
Definition path_search.cc:103
│ │ │
path_search.h
│ │ │

This piece of code will first traverse all paths in the list set up for file class MESH. If it manages to open a file, it returns the istream object. If not, it will try to append the first suffix of the suffix list and do the same. And so on. If no file is found in the end, an exception is thrown.

│ │ │

If you want to restrict your search to a certain mesh format, .inp for instance, then either use "grid.inp" in the code above or use the alternative find(const std::string&,const std::string&,const char*) function

std::string full_name = search.find("grid", ".inp");
│ │ │

Path lists are by default starting with the current directory ("./"), followed optionally by a standard directory of deal.II. Use show() to find out the path list for a given class. Paths and suffixes can be added using the functions add_path() and add_suffix(), respectively.

│ │ │
Note
Directories in the path list should always end with a trailing "/", while suffixes should always start with a dot. These characters are not added automatically (allowing you to do some real file name editing).
│ │ │ -
Deprecated
Use the std::filesystem facilities instead.
│ │ │ +
Deprecated
Use the std::filesystem facilities instead.
│ │ │ │ │ │

Definition at line 82 of file path_search.h.

│ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │

│ │ │ Public Types

enum  Position { back │ │ │ , front │ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classPersistentTriangulation.html │ │ │ @@ -934,15 +934,15 @@ │ │ │ │ │ │ inherited
│ │ │
│ │ │

The elements of this enum are used to inform functions how a specific cell is going to change. This is used in the course of transferring data from one mesh to a refined or coarsened version of the mesh, for example. Note that this may me different than the refine_flag() and coarsen_flag() set on a cell, for example in parallel calculations, because of refinement constraints that an individual machine does not see.

│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2242 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ raw_cell_iterator

│ │ │ @@ -3789,15 +3789,15 @@ │ │ │ │ │ │ │ │ │ inherited │ │ │ │ │ │ │ │ │
│ │ │

Return the MPI communicator used by this triangulation. In the case of a serial Triangulation object, MPI_COMM_SELF is returned.

│ │ │ -
Deprecated
Use get_mpi_communicator() instead.
│ │ │ +
Deprecated
Use get_mpi_communicator() instead.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ global_active_cell_index_partitioner()

│ │ │ │ │ │
│ │ │ @@ -8650,15 +8650,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2248 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_REFINE

│ │ │ @@ -8675,15 +8675,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2255 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_COARSEN

│ │ │ @@ -8700,15 +8700,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2262 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_INVALID

│ │ │ @@ -8725,15 +8725,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2269 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ signals

│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classPolarManifold.html │ │ │ @@ -1324,15 +1324,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │
const Point<spacedim> PolarManifold< dim, spacedim >::center
│ │ │
│ │ │

The center of the spherical coordinate system.

│ │ │ -
Deprecated
Use get_center() instead.
│ │ │ +
Deprecated
Use get_center() instead.
│ │ │ │ │ │

Definition at line 153 of file manifold_lib.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ p_center

│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classReferenceCell.html │ │ │ @@ -1049,15 +1049,15 @@ │ │ │ │ │ │ │ │ │ inlinestaticconstexpr │ │ │ │ │ │ │ │ │
│ │ │

Return the default combined face orientation flag (i.e., the default set of orientations, defined by orientation, rotate, and flip for a face in 3d).

│ │ │ -
Deprecated
Use numbers::default_geometric_orientation instead.
│ │ │ +
Deprecated
Use numbers::default_geometric_orientation instead.
│ │ │ │ │ │

Definition at line 2147 of file reference_cell.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ reversed_combined_line_orientation()

│ │ │ @@ -1078,15 +1078,15 @@ │ │ │ │ │ │ │ │ │ inlinestaticconstexpr │ │ │ │ │ │ │ │ │
│ │ │

Return the reversed (non-default orientation) line orientation flag. As lines only have two possible orientations, this function and ReferenceCell::default_combined_face_orientation() encode all of its possible orientation states.

│ │ │ -
Deprecated
Use numbers::reverse_line_orientation instead.
│ │ │ +
Deprecated
Use numbers::reverse_line_orientation instead.
│ │ │ │ │ │

Definition at line 2155 of file reference_cell.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ child_cell_on_face() [1/2]

│ │ │ @@ -1111,15 +1111,15 @@ │ │ │ │ │ │ │ │ │ inline │ │ │ │ │ │ │ │ │
│ │ │

Return which child cells are adjacent to a certain face of the parent cell.

│ │ │ -
Deprecated
Use the version of this function which takes the orientation as the third parameter instead.
│ │ │ +
Deprecated
Use the version of this function which takes the orientation as the third parameter instead.
│ │ │ │ │ │

Definition at line 2165 of file reference_cell.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ child_cell_on_face() [2/2]

│ │ │ @@ -1484,15 +1484,15 @@ │ │ │ │ │ │ │ │ │ inline │ │ │ │ │ │ │ │ │
│ │ │

Return whether the line with index line is oriented in standard direction within a cell, given the face_orientation of the face within the current cell, and line_orientation for the line within that face.

│ │ │ -
Deprecated
Use face_to_cell_line_orientation() instead.
│ │ │ +
Deprecated
Use face_to_cell_line_orientation() instead.
│ │ │ │ │ │

Definition at line 3419 of file reference_cell.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ face_to_cell_line_orientation()

│ │ │ @@ -1766,15 +1766,15 @@ │ │ │ │ │ │ │ │ │
│ │ │

Return \(i\)-th unit tangent vector to a face of the reference cell. The vectors are arranged in such an order that the cross product between the two vectors returns the face normal vector.

│ │ │
Precondition
\(i\) must be between zero and dim-1.
│ │ │
│ │ │ The template argument dim must equal the dimension of the space in which the reference cell you are querying lives (i.e., it must equal the result of get_dimension()).
│ │ │ -
Deprecated
Use face_tangent_vector() instead.
│ │ │ +
Deprecated
Use face_tangent_vector() instead.
│ │ │ │ │ │

Definition at line 3251 of file reference_cell.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ face_normal_vector()

│ │ │ @@ -1829,15 +1829,15 @@ │ │ │ │ │ │ inline │ │ │ │ │ │ │ │ │
│ │ │

Return the unit normal vector of a face of the reference cell.

│ │ │
Precondition
The template argument dim must equal the dimension of the space in which the reference cell you are querying lives (i.e., it must equal the result of get_dimension()).
│ │ │ -
Deprecated
Use face_normal_vector() instead.
│ │ │ +
Deprecated
Use face_normal_vector() instead.
│ │ │ │ │ │

Definition at line 3356 of file reference_cell.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ n_face_orientations()

│ │ │ @@ -1893,15 +1893,15 @@ │ │ │ │ │ │ inline │ │ │ │ │ │ │ │ │
│ │ │

Determine the orientation of the current entity described by its vertices vertices_1 relative to an entity described by vertices_0. The two arrays given as arguments can be arrays of global vertex indices or local vertex indices, arrays of vertex locations, or arrays of any other objects identifying the vertices and the order in which they are encountered in a cell.

│ │ │

The size of the arrays, i.e., the template argument N, must be equal to or larger than the number of vertices of the current entity. If it is larger, only those elements of the input and output arrays are read from or written to that correspond to valid vertex indices.

│ │ │ -
Deprecated
Use get_combined_orientation() instead.
│ │ │ +
Deprecated
Use get_combined_orientation() instead.
│ │ │ │ │ │

Definition at line 3577 of file reference_cell.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ get_combined_orientation()

│ │ │ @@ -1958,15 +1958,15 @@ │ │ │ │ │ │ inline │ │ │ │ │ │ │ │ │
│ │ │

Inverse function of compute_orientation(): Given a set of vertex-associated objects (such as vertex indices, locations, etc.) and a desired orientation permutation, return the permuted vertex information.

│ │ │

The size of the input and output arrays, i.e., the template argument N, must be equal to or larger than the number of vertices of the current entity. If it is larger, only those elements of the input and output arrays are read from or written to that correspond to valid vertex indices.

│ │ │ -
Deprecated
Use permute_by_combined_orientation() instead.
│ │ │ +
Deprecated
Use permute_by_combined_orientation() instead.
│ │ │ │ │ │

Definition at line 3653 of file reference_cell.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ permute_by_combined_orientation()

│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classSUNDIALS_1_1KINSOL.html │ │ │ @@ -499,16 +499,16 @@ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │
std::function<VectorType &()> SUNDIALS::KINSOL< VectorType >::get_solution_scaling
│ │ │
│ │ │

A function object that users may supply and that is intended to return a vector whose components are the weights used by KINSOL to compute the vector norm of the solution. The implementation of this function is optional, and it is used only if implemented.

│ │ │ -

The intent for this scaling factor is for problems in which the different components of a solution have vastly different numerical magnitudes – typically because they have different physical units and represent different things. For example, if one were to solve a nonlinear Stokes problem, the solution vector has components that correspond to velocities and other components that correspond to pressures. These have different physical units and depending on which units one chooses, they may have roughly comparable numerical sizes or maybe they don't. To give just one example, in simulations of flow in the Earth's interior, one has velocities on the order of maybe ten centimeters per year, and pressures up to around 100 GPa. If one expresses this in SI units, this corresponds to velocities of around \(0.000,000,003=3 \times 10^{-9}\) m/s, and pressures around \(10^9 \text{kg}/\text{m}/\text{s}^2\), i.e., vastly different. In such cases, computing the \(l_2\) norm of a solution-type vector (e.g., the difference between the previous and the current solution) makes no sense because the norm will either be dominated by the velocity components or the pressure components. The scaling vector this function returns is intended to provide each component of the solution with a scaling factor that is generally chosen as the inverse of a "typical velocity" or "typical pressure" so that upon multiplication of a vector component by the corresponding scaling vector component, one obtains a number that is of order of magnitude of one (i.e., a reasonably small multiple of one times the typical velocity/pressure). The KINSOL manual states this as follows: "The user should supply values \_form#2720, │ │ │ -which are diagonal elements of the scaling matrix such that \_form#2755 has │ │ │ +

The intent for this scaling factor is for problems in which the different components of a solution have vastly different numerical magnitudes – typically because they have different physical units and represent different things. For example, if one were to solve a nonlinear Stokes problem, the solution vector has components that correspond to velocities and other components that correspond to pressures. These have different physical units and depending on which units one chooses, they may have roughly comparable numerical sizes or maybe they don't. To give just one example, in simulations of flow in the Earth's interior, one has velocities on the order of maybe ten centimeters per year, and pressures up to around 100 GPa. If one expresses this in SI units, this corresponds to velocities of around \(0.000,000,003=3 \times 10^{-9}\) m/s, and pressures around \(10^9 \text{kg}/\text{m}/\text{s}^2\), i.e., vastly different. In such cases, computing the \(l_2\) norm of a solution-type vector (e.g., the difference between the previous and the current solution) makes no sense because the norm will either be dominated by the velocity components or the pressure components. The scaling vector this function returns is intended to provide each component of the solution with a scaling factor that is generally chosen as the inverse of a "typical velocity" or "typical pressure" so that upon multiplication of a vector component by the corresponding scaling vector component, one obtains a number that is of order of magnitude of one (i.e., a reasonably small multiple of one times the typical velocity/pressure). The KINSOL manual states this as follows: "The user should supply values \_form#2733, │ │ │ +which are diagonal elements of the scaling matrix such that \_form#2749 has │ │ │ all components roughly the same magnitude when \_form#321 is close to a │ │ │ solution".

│ │ │

If no function is provided to a KINSOL object, then this is interpreted as implicitly saying that all of these scaling factors should be considered as one.

│ │ │
Note
This variable represents a user provided callback. See there for a description of how to deal with errors and other requirements and conventions. In particular, KINSOL can deal with "recoverable" errors in some circumstances, so callbacks can throw exceptions of type RecoverableUserCallbackError.
│ │ │ │ │ │

Definition at line 649 of file kinsol.h.

│ │ │ ├── html2text {} │ │ │ │ @@ -339,16 +339,16 @@ │ │ │ │ the pressure components. The scaling vector this function returns is intended │ │ │ │ to provide each component of the solution with a scaling factor that is │ │ │ │ generally chosen as the inverse of a "typical velocity" or "typical pressure" │ │ │ │ so that upon multiplication of a vector component by the corresponding scaling │ │ │ │ vector component, one obtains a number that is of order of magnitude of one │ │ │ │ (i.e., a reasonably small multiple of one times the typical velocity/pressure). │ │ │ │ The _K_I_N_S_O_L manual states this as follows: "The user should supply values │ │ │ │ -\_form#2720, which are diagonal elements of the scaling matrix such that │ │ │ │ -\_form#2755 has all components roughly the same magnitude when \_form#321 is │ │ │ │ +\_form#2733, which are diagonal elements of the scaling matrix such that │ │ │ │ +\_form#2749 has all components roughly the same magnitude when \_form#321 is │ │ │ │ close to a solution". │ │ │ │ If no function is provided to a _K_I_N_S_O_L object, then this is interpreted as │ │ │ │ implicitly saying that all of these scaling factors should be considered as │ │ │ │ one. │ │ │ │ Note │ │ │ │ This variable represents a _u_s_e_r_ _p_r_o_v_i_d_e_d_ _c_a_l_l_b_a_c_k. See there for a │ │ │ │ description of how to deal with errors and other requirements and │ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classSphericalManifold.html │ │ │ @@ -1528,15 +1528,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │
const Point<spacedim> SphericalManifold< dim, spacedim >::center
│ │ │
│ │ │

The center of the spherical coordinate system.

│ │ │ -
Deprecated
Use get_center() instead.
│ │ │ +
Deprecated
Use get_center() instead.
│ │ │ │ │ │

Definition at line 359 of file manifold_lib.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ p_center

│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classTriangulation.html │ │ │ @@ -942,15 +942,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │
using Triangulation< dim, spacedim >::CellStatus = ::CellStatus
│ │ │
│ │ │

The elements of this enum are used to inform functions how a specific cell is going to change. This is used in the course of transferring data from one mesh to a refined or coarsened version of the mesh, for example. Note that this may me different than the refine_flag() and coarsen_flag() set on a cell, for example in parallel calculations, because of refinement constraints that an individual machine does not see.

│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2242 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ raw_cell_iterator

│ │ │ @@ -1446,15 +1446,15 @@ │ │ │ ( │ │ │ ) │ │ │ const │ │ │ │ │ │ │ │ │
│ │ │

Return the MPI communicator used by this triangulation. In the case of a serial Triangulation object, MPI_COMM_SELF is returned.

│ │ │ -
Deprecated
Use get_mpi_communicator() instead.
│ │ │ +
Deprecated
Use get_mpi_communicator() instead.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ global_active_cell_index_partitioner()

│ │ │ │ │ │
│ │ │ @@ -6444,15 +6444,15 @@ │ │ │ staticconstexpr │ │ │ │ │ │ │ │ │
│ │ │ Initial value:
=
│ │ │
::CellStatus::cell_will_persist
│ │ │
CellStatus::cell_will_persist
@ cell_will_persist
Definition cell_status.h:36
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2248 of file tria.h.

│ │ │ │ │ │ │ │ │ │ │ │ │ │ │

◆ CELL_REFINE

│ │ │ @@ -6474,15 +6474,15 @@ │ │ │ staticconstexpr │ │ │ │ │ │ │ │ │
│ │ │ Initial value:
=
│ │ │
::CellStatus::cell_will_be_refined
│ │ │
CellStatus::cell_will_be_refined
@ cell_will_be_refined
Definition cell_status.h:40
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2255 of file tria.h.

│ │ │ │ │ │ │ │ │ │ │ │ │ │ │

◆ CELL_COARSEN

│ │ │ @@ -6504,15 +6504,15 @@ │ │ │ staticconstexpr │ │ │ │ │ │ │ │ │
│ │ │ Initial value:
=
│ │ │
::CellStatus::children_will_be_coarsened
│ │ │
CellStatus::children_will_be_coarsened
@ children_will_be_coarsened
Definition cell_status.h:44
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2262 of file tria.h.

│ │ │ │ │ │ │ │ │ │ │ │ │ │ │

◆ CELL_INVALID

│ │ │ @@ -6534,15 +6534,15 @@ │ │ │ staticconstexpr │ │ │ │ │ │ │ │ │
│ │ │ Initial value:
=
│ │ │
::CellStatus::cell_invalid
│ │ │
CellStatus::cell_invalid
@ cell_invalid
Definition cell_status.h:48
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2269 of file tria.h.

│ │ │ │ │ │ │ │ │ │ │ │ │ │ │

◆ signals

│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classUtilities_1_1MPI_1_1ConsensusAlgorithms_1_1Process.html │ │ │ @@ -128,15 +128,15 @@ │ │ │ │ │ │ │ │ │ │ │ │
RequestTypeThe type of the elements of the vector to sent.
AnswerTypeThe type of the elements of the vector to received.
│ │ │
│ │ │ │ │ │
Note
Since the payloads of the messages are optional, users have to deal with buffers themselves. The ConsensusAlgorithm classes (1) deliver only references to empty vectors (of size 0) the data to be sent can be inserted to or read from, and (2) communicate these vectors blindly.
│ │ │ -
Deprecated
Instead of deriving a class from this base class and providing a corresponding object to one of the run() functions, use the free functions in this namespace that take function objects as arguments.
│ │ │ +
Deprecated
Instead of deriving a class from this base class and providing a corresponding object to one of the run() functions, use the free functions in this namespace that take function objects as arguments.
│ │ │ │ │ │

Definition at line 164 of file mpi_consensus_algorithms.h.

│ │ │ │ │ │ │ │ │ │ │ │ │ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classUtilities_1_1MPI_1_1RemotePointEvaluation.html │ │ │ @@ -262,15 +262,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │

│ │ │ Public Member Functions

virtual ~Process ()=default
virtual std::vector< unsigned int > compute_targets ()=0
toleranceTolerance in terms of unit cell coordinates for determining all cells around a point passed to the class during reinit(). Depending on the problem, it might be necessary to adjust the tolerance in order to be able to identify a cell. Floating point arithmetic implies that a point will, in general, not lie exactly on a vertex, edge, or face.
enforce_unique_mappingEnforce unique mapping, i.e., (one-to-one) relation of points and cells.
rtree_levelRTree level to be used during the construction of the bounding boxes.
marked_verticesFunction that marks relevant vertices to make search of active cells around point more efficient.
│ │ │ │ │ │ │ │ │ -
Deprecated
│ │ │ +
Deprecated
│ │ │ │ │ │

Definition at line 61 of file mpi_remote_point_evaluation.cc.

│ │ │ │ │ │ │ │ │ │ │ │ │ │ │

◆ ~RemotePointEvaluation()

│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classinternal_1_1TriangulationImplementation_1_1Triangulation.html │ │ │ @@ -959,15 +959,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │
using Triangulation< dim, spacedim >::CellStatus = ::CellStatus
│ │ │
│ │ │

The elements of this enum are used to inform functions how a specific cell is going to change. This is used in the course of transferring data from one mesh to a refined or coarsened version of the mesh, for example. Note that this may me different than the refine_flag() and coarsen_flag() set on a cell, for example in parallel calculations, because of refinement constraints that an individual machine does not see.

│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2242 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ raw_cell_iterator

│ │ │ @@ -1463,15 +1463,15 @@ │ │ │ ( │ │ │ ) │ │ │ const │ │ │ │ │ │ │ │ │
│ │ │

Return the MPI communicator used by this triangulation. In the case of a serial Triangulation object, MPI_COMM_SELF is returned.

│ │ │ -
Deprecated
Use get_mpi_communicator() instead.
│ │ │ +
Deprecated
Use get_mpi_communicator() instead.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ global_active_cell_index_partitioner()

│ │ │ │ │ │
│ │ │ @@ -6463,15 +6463,15 @@ │ │ │ staticconstexpr │ │ │ │ │ │ │ │ │
│ │ │ Initial value:
=
│ │ │
::CellStatus::cell_will_persist
│ │ │
CellStatus::cell_will_persist
@ cell_will_persist
Definition cell_status.h:36
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2248 of file tria.h.

│ │ │ │ │ │ │ │ │ │ │ │ │ │ │

◆ CELL_REFINE

│ │ │ @@ -6493,15 +6493,15 @@ │ │ │ staticconstexpr │ │ │ │ │ │ │ │ │
│ │ │ Initial value:
=
│ │ │
::CellStatus::cell_will_be_refined
│ │ │
CellStatus::cell_will_be_refined
@ cell_will_be_refined
Definition cell_status.h:40
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2255 of file tria.h.

│ │ │ │ │ │ │ │ │ │ │ │ │ │ │

◆ CELL_COARSEN

│ │ │ @@ -6523,15 +6523,15 @@ │ │ │ staticconstexpr │ │ │ │ │ │ │ │ │
│ │ │ Initial value:
=
│ │ │
::CellStatus::children_will_be_coarsened
│ │ │
CellStatus::children_will_be_coarsened
@ children_will_be_coarsened
Definition cell_status.h:44
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2262 of file tria.h.

│ │ │ │ │ │ │ │ │ │ │ │ │ │ │

◆ CELL_INVALID

│ │ │ @@ -6553,15 +6553,15 @@ │ │ │ staticconstexpr │ │ │ │ │ │ │ │ │
│ │ │ Initial value:
=
│ │ │
::CellStatus::cell_invalid
│ │ │
CellStatus::cell_invalid
@ cell_invalid
Definition cell_status.h:48
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2269 of file tria.h.

│ │ │ │ │ │ │ │ │ │ │ │ │ │ │

◆ signals

│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classparallel_1_1DistributedTriangulationBase.html │ │ │ @@ -1123,15 +1123,15 @@ │ │ │ │ │ │ │ │ │ inherited │ │ │ │ │ │ │ │ │
│ │ │

The elements of this enum are used to inform functions how a specific cell is going to change. This is used in the course of transferring data from one mesh to a refined or coarsened version of the mesh, for example. Note that this may me different than the refine_flag() and coarsen_flag() set on a cell, for example in parallel calculations, because of refinement constraints that an individual machine does not see.

│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2242 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ raw_cell_iterator

│ │ │ @@ -2079,15 +2079,15 @@ │ │ │ │ │ │ │ │ │ inherited │ │ │ │ │ │ │ │ │
│ │ │

Return the MPI communicator used by this triangulation. In the case of a serial Triangulation object, MPI_COMM_SELF is returned.

│ │ │ -
Deprecated
Use get_mpi_communicator() instead.
│ │ │ +
Deprecated
Use get_mpi_communicator() instead.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ get_communicator() [2/2]

│ │ │ │ │ │
│ │ │ @@ -2106,15 +2106,15 @@ │ │ │ │ │ │ │ │ │ inherited │ │ │ │ │ │ │ │ │
│ │ │

Return the MPI communicator used by this triangulation. In the case of a serial Triangulation object, MPI_COMM_SELF is returned.

│ │ │ -
Deprecated
Use get_mpi_communicator() instead.
│ │ │ +
Deprecated
Use get_mpi_communicator() instead.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ set_mesh_smoothing() [1/2]

│ │ │ │ │ │
│ │ │ @@ -13618,15 +13618,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2248 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_PERSIST [2/2]

│ │ │ @@ -13643,15 +13643,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2248 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_REFINE [1/2]

│ │ │ @@ -13668,15 +13668,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2255 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_REFINE [2/2]

│ │ │ @@ -13693,15 +13693,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2255 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_COARSEN [1/2]

│ │ │ @@ -13718,15 +13718,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2262 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_COARSEN [2/2]

│ │ │ @@ -13743,15 +13743,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2262 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_INVALID [1/2]

│ │ │ @@ -13768,15 +13768,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2269 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_INVALID [2/2]

│ │ │ @@ -13793,15 +13793,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2269 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ signals [1/2]

│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classparallel_1_1TriangulationBase.html │ │ │ @@ -972,15 +972,15 @@ │ │ │ │ │ │ │ │ │ inherited │ │ │ │ │ │ │ │ │
│ │ │

The elements of this enum are used to inform functions how a specific cell is going to change. This is used in the course of transferring data from one mesh to a refined or coarsened version of the mesh, for example. Note that this may me different than the refine_flag() and coarsen_flag() set on a cell, for example in parallel calculations, because of refinement constraints that an individual machine does not see.

│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2242 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ raw_cell_iterator

│ │ │ @@ -4104,15 +4104,15 @@ │ │ │ │ │ │ │ │ │ inherited │ │ │ │ │ │ │ │ │
│ │ │

Return the MPI communicator used by this triangulation. In the case of a serial Triangulation object, MPI_COMM_SELF is returned.

│ │ │ -
Deprecated
Use get_mpi_communicator() instead.
│ │ │ +
Deprecated
Use get_mpi_communicator() instead.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ set_mesh_smoothing()

│ │ │ │ │ │
│ │ │ @@ -9325,15 +9325,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2248 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_REFINE

│ │ │ @@ -9350,15 +9350,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2255 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_COARSEN

│ │ │ @@ -9375,15 +9375,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2262 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_INVALID

│ │ │ @@ -9400,15 +9400,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2269 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ signals

│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classparallel_1_1distributed_1_1Triangulation.html │ │ │ @@ -1147,15 +1147,15 @@ │ │ │ │ │ │ │ │ │ inherited │ │ │ │ │ │ │ │ │
│ │ │

The elements of this enum are used to inform functions how a specific cell is going to change. This is used in the course of transferring data from one mesh to a refined or coarsened version of the mesh, for example. Note that this may me different than the refine_flag() and coarsen_flag() set on a cell, for example in parallel calculations, because of refinement constraints that an individual machine does not see.

│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2242 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ raw_cell_iterator

│ │ │ @@ -3065,15 +3065,15 @@ │ │ │ │ │ │ │ │ │ inherited │ │ │ │ │ │ │ │ │
│ │ │

Return the MPI communicator used by this triangulation. In the case of a serial Triangulation object, MPI_COMM_SELF is returned.

│ │ │ -
Deprecated
Use get_mpi_communicator() instead.
│ │ │ +
Deprecated
Use get_mpi_communicator() instead.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ get_communicator() [2/2]

│ │ │ │ │ │
│ │ │ @@ -3092,15 +3092,15 @@ │ │ │ │ │ │ │ │ │ inherited │ │ │ │ │ │ │ │ │
│ │ │

Return the MPI communicator used by this triangulation. In the case of a serial Triangulation object, MPI_COMM_SELF is returned.

│ │ │ -
Deprecated
Use get_mpi_communicator() instead.
│ │ │ +
Deprecated
Use get_mpi_communicator() instead.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ set_mesh_smoothing() [1/2]

│ │ │ │ │ │
│ │ │ @@ -14039,15 +14039,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2248 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_PERSIST [2/2]

│ │ │ @@ -14064,15 +14064,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2248 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_REFINE [1/2]

│ │ │ @@ -14089,15 +14089,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2255 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_REFINE [2/2]

│ │ │ @@ -14114,15 +14114,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2255 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_COARSEN [1/2]

│ │ │ @@ -14139,15 +14139,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2262 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_COARSEN [2/2]

│ │ │ @@ -14164,15 +14164,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2262 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_INVALID [1/2]

│ │ │ @@ -14189,15 +14189,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2269 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_INVALID [2/2]

│ │ │ @@ -14214,15 +14214,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2269 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ signals [1/2]

│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classparallel_1_1distributed_1_1Triangulation_3_011_00_01spacedim_01_4.html │ │ │ @@ -1028,15 +1028,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │
using Triangulation< dim, spacedim >::CellStatus
│ │ │
│ │ │

The elements of this enum are used to inform functions how a specific cell is going to change. This is used in the course of transferring data from one mesh to a refined or coarsened version of the mesh, for example. Note that this may me different than the refine_flag() and coarsen_flag() set on a cell, for example in parallel calculations, because of refinement constraints that an individual machine does not see.

│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2242 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ raw_cell_iterator

│ │ │ @@ -2728,15 +2728,15 @@ │ │ │ ( │ │ │ ) │ │ │ const │ │ │ │ │ │ │ │ │
│ │ │

Return the MPI communicator used by this triangulation. In the case of a serial Triangulation object, MPI_COMM_SELF is returned.

│ │ │ -
Deprecated
Use get_mpi_communicator() instead.
│ │ │ +
Deprecated
Use get_mpi_communicator() instead.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ get_communicator() [2/2]

│ │ │ │ │ │
│ │ │ @@ -2747,15 +2747,15 @@ │ │ │ ( │ │ │ ) │ │ │ const │ │ │ │ │ │ │ │ │
│ │ │

Return the MPI communicator used by this triangulation. In the case of a serial Triangulation object, MPI_COMM_SELF is returned.

│ │ │ -
Deprecated
Use get_mpi_communicator() instead.
│ │ │ +
Deprecated
Use get_mpi_communicator() instead.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ set_mesh_smoothing() [1/2]

│ │ │ │ │ │
│ │ │ @@ -11326,15 +11326,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexpr │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2248 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_PERSIST [2/2]

│ │ │ @@ -11351,15 +11351,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexpr │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2248 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_REFINE [1/2]

│ │ │ @@ -11376,15 +11376,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexpr │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2255 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_REFINE [2/2]

│ │ │ @@ -11401,15 +11401,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexpr │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2255 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_COARSEN [1/2]

│ │ │ @@ -11426,15 +11426,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexpr │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2262 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_COARSEN [2/2]

│ │ │ @@ -11451,15 +11451,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexpr │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2262 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_INVALID [1/2]

│ │ │ @@ -11476,15 +11476,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexpr │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2269 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_INVALID [2/2]

│ │ │ @@ -11501,15 +11501,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexpr │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2269 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ signals [1/2]

│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classparallel_1_1fullydistributed_1_1Triangulation.html │ │ │ @@ -1105,15 +1105,15 @@ │ │ │ │ │ │ │ │ │ inherited │ │ │ │ │ │ │ │ │
│ │ │

The elements of this enum are used to inform functions how a specific cell is going to change. This is used in the course of transferring data from one mesh to a refined or coarsened version of the mesh, for example. Note that this may me different than the refine_flag() and coarsen_flag() set on a cell, for example in parallel calculations, because of refinement constraints that an individual machine does not see.

│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2242 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ raw_cell_iterator

│ │ │ @@ -2497,15 +2497,15 @@ │ │ │ │ │ │ │ │ │ inherited │ │ │ │ │ │ │ │ │
│ │ │

Return the MPI communicator used by this triangulation. In the case of a serial Triangulation object, MPI_COMM_SELF is returned.

│ │ │ -
Deprecated
Use get_mpi_communicator() instead.
│ │ │ +
Deprecated
Use get_mpi_communicator() instead.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ get_communicator() [2/2]

│ │ │ │ │ │
│ │ │ @@ -2524,15 +2524,15 @@ │ │ │ │ │ │ │ │ │ inherited │ │ │ │ │ │ │ │ │
│ │ │

Return the MPI communicator used by this triangulation. In the case of a serial Triangulation object, MPI_COMM_SELF is returned.

│ │ │ -
Deprecated
Use get_mpi_communicator() instead.
│ │ │ +
Deprecated
Use get_mpi_communicator() instead.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ set_mesh_smoothing() [1/2]

│ │ │ │ │ │
│ │ │ @@ -13488,15 +13488,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2248 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_PERSIST [2/2]

│ │ │ @@ -13513,15 +13513,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2248 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_REFINE [1/2]

│ │ │ @@ -13538,15 +13538,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2255 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_REFINE [2/2]

│ │ │ @@ -13563,15 +13563,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2255 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_COARSEN [1/2]

│ │ │ @@ -13588,15 +13588,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2262 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_COARSEN [2/2]

│ │ │ @@ -13613,15 +13613,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2262 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_INVALID [1/2]

│ │ │ @@ -13638,15 +13638,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2269 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_INVALID [2/2]

│ │ │ @@ -13663,15 +13663,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2269 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ signals [1/2]

│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classparallel_1_1shared_1_1Triangulation.html │ │ │ @@ -1108,15 +1108,15 @@ │ │ │ │ │ │ │ │ │ inherited │ │ │ │ │ │ │ │ │
│ │ │

The elements of this enum are used to inform functions how a specific cell is going to change. This is used in the course of transferring data from one mesh to a refined or coarsened version of the mesh, for example. Note that this may me different than the refine_flag() and coarsen_flag() set on a cell, for example in parallel calculations, because of refinement constraints that an individual machine does not see.

│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2242 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ raw_cell_iterator

│ │ │ @@ -2409,15 +2409,15 @@ │ │ │ │ │ │ │ │ │ inherited │ │ │ │ │ │ │ │ │
│ │ │

Return the MPI communicator used by this triangulation. In the case of a serial Triangulation object, MPI_COMM_SELF is returned.

│ │ │ -
Deprecated
Use get_mpi_communicator() instead.
│ │ │ +
Deprecated
Use get_mpi_communicator() instead.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ get_communicator() [2/2]

│ │ │ │ │ │
│ │ │ @@ -2436,15 +2436,15 @@ │ │ │ │ │ │ │ │ │ inherited │ │ │ │ │ │ │ │ │
│ │ │

Return the MPI communicator used by this triangulation. In the case of a serial Triangulation object, MPI_COMM_SELF is returned.

│ │ │ -
Deprecated
Use get_mpi_communicator() instead.
│ │ │ +
Deprecated
Use get_mpi_communicator() instead.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ set_mesh_smoothing() [1/2]

│ │ │ │ │ │
│ │ │ @@ -13721,15 +13721,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2248 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_PERSIST [2/2]

│ │ │ @@ -13746,15 +13746,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2248 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_REFINE [1/2]

│ │ │ @@ -13771,15 +13771,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2255 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_REFINE [2/2]

│ │ │ @@ -13796,15 +13796,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2255 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_COARSEN [1/2]

│ │ │ @@ -13821,15 +13821,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2262 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_COARSEN [2/2]

│ │ │ @@ -13846,15 +13846,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2262 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_INVALID [1/2]

│ │ │ @@ -13871,15 +13871,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2269 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ CELL_INVALID [2/2]

│ │ │ @@ -13896,15 +13896,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ staticconstexprinherited │ │ │ │ │ │ │ │ │
│ │ │ -
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
Deprecated
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ │ │ │

Definition at line 2269 of file tria.h.

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ signals [1/2]

│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/deprecated.html │ │ │ @@ -113,99 +113,99 @@ │ │ │ │ │ │
│ │ │
Deprecated List
│ │ │
│ │ │
│ │ │
│ │ │
Member AffineConstraints< number >::add_selected_constraints (const AffineConstraints &constraints_in, const IndexSet &filter)
│ │ │ -
This function is a combination of the get_view() function and merge() in that it selects a subset of constraints from another constraints object that is then merged into the current one. But the current function does not deal well with index sets. Furthermore, it simply discards parts of constraints that constrain one degree of freedom against ones that are not selected in the filter – something that should probably be considered a bug. Use get_view() and merge() instead.
│ │ │ +
This function is a combination of the get_view() function and merge() in that it selects a subset of constraints from another constraints object that is then merged into the current one. But the current function does not deal well with index sets. Furthermore, it simply discards parts of constraints that constrain one degree of freedom against ones that are not selected in the filter – something that should probably be considered a bug. Use get_view() and merge() instead.
│ │ │
Member AffineConstraints< number >::AffineConstraints (const IndexSet &locally_stored_constraints)
│ │ │ -
This constructor is equivalent to calling the following one with both of its arguments equal to the index set provided here. This is not wrong, but inefficient. Use the following constructor instead.
│ │ │ +
This constructor is equivalent to calling the following one with both of its arguments equal to the index set provided here. This is not wrong, but inefficient. Use the following constructor instead.
│ │ │
Member AffineConstraints< number >::reinit (const IndexSet &locally_stored_constraints)
│ │ │ -
Use the reinit() function with two index set arguments instead.
│ │ │ +
Use the reinit() function with two index set arguments instead.
│ │ │
Member CELL_COARSEN
│ │ │ -
Use CellStatus::cell_will_be_coarsened instead
│ │ │ +
Use CellStatus::cell_will_be_coarsened instead
│ │ │
Member CELL_INVALID
│ │ │ -
Use CellStatus::cell_invalid instead
│ │ │ +
Use CellStatus::cell_invalid instead
│ │ │
Member CELL_PERSIST
│ │ │ -
Use CellStatus::cell_will_persist instead
│ │ │ +
Use CellStatus::cell_will_persist instead
│ │ │
Member CELL_REFINE
│ │ │ -
Use CellStatus::cell_will_be_refined instead
│ │ │ +
Use CellStatus::cell_will_be_refined instead
│ │ │
Member DataOutBase::default_suffix (const OutputFormat output_format)
│ │ │ -
Using Tecplot binary output is deprecated.
│ │ │ +
Using Tecplot binary output is deprecated.
│ │ │
Member DoFTools::extract_constant_modes (const DoFHandler< dim, spacedim > &dof_handler, const ComponentMask &component_mask, std::vector< std::vector< bool > > &constant_modes)
│ │ │ -
│ │ │ +
│ │ │
Member DoFTools::extract_level_constant_modes (const unsigned int level, const DoFHandler< dim, spacedim > &dof_handler, const ComponentMask &component_mask, std::vector< std::vector< bool > > &constant_modes)
│ │ │ -
│ │ │ +
│ │ │
Member DoFTools::extract_locally_active_dofs (const DoFHandler< dim, spacedim > &dof_handler, IndexSet &dof_set)
│ │ │ -
Use the previous function instead.
│ │ │ +
Use the previous function instead.
│ │ │
Member DoFTools::extract_locally_active_level_dofs (const DoFHandler< dim, spacedim > &dof_handler, IndexSet &dof_set, const unsigned int level)
│ │ │ -
Use the previous function instead.
│ │ │ +
Use the previous function instead.
│ │ │
Member DoFTools::extract_locally_relevant_dofs (const DoFHandler< dim, spacedim > &dof_handler, IndexSet &dof_set)
│ │ │ -
Use the previous function instead.
│ │ │ +
Use the previous function instead.
│ │ │
Member DoFTools::extract_locally_relevant_level_dofs (const DoFHandler< dim, spacedim > &dof_handler, const unsigned int level, IndexSet &dof_set)
│ │ │ -
Use the previous function instead.
│ │ │ +
Use the previous function instead.
│ │ │
Member DoFTools::get_active_fe_indices (const DoFHandler< dim, spacedim > &dof_handler, std::vector< unsigned int > &active_fe_indices)
│ │ │ -
Use DoFHandler::get_active_fe_indices() that returns the result vector.
│ │ │ +
Use DoFHandler::get_active_fe_indices() that returns the result vector.
│ │ │
Member DoFTools::map_dofs_to_support_points (const Mapping< dim, spacedim > &mapping, const DoFHandler< dim, spacedim > &dof_handler, std::map< types::global_dof_index, Point< spacedim > > &support_points, const ComponentMask &mask={})
│ │ │ -
Use the function that returns the std::map instead.
│ │ │ +
Use the function that returns the std::map instead.
│ │ │
Member DoFTools::map_dofs_to_support_points (const hp::MappingCollection< dim, spacedim > &mapping, const DoFHandler< dim, spacedim > &dof_handler, std::map< types::global_dof_index, Point< spacedim > > &support_points, const ComponentMask &mask={})
│ │ │ -
Use the function that returns the std::map instead.
│ │ │ +
Use the function that returns the std::map instead.
│ │ │
Member FEEvaluationData< dim, Number, is_face >::get_normal_vector (const unsigned int q_point) const
│ │ │
Use normal_vector() instead.
│ │ │
Member FEFaceEvaluation< dim, fe_degree, n_q_points_1d, n_components_, Number, VectorizedArrayType >::integrate_scatter (const bool integrate_values, const bool integrate_gradients, VectorType &output_vector)
│ │ │ -
Please use the integrate_scatter() function with the EvaluationFlags argument.
│ │ │ +
Please use the integrate_scatter() function with the EvaluationFlags argument.
│ │ │
Member FEInterfaceValues< dim, spacedim >::normal (const unsigned int q_point_index) const
│ │ │ -
Use the function normal_vector().
│ │ │ +
Use the function normal_vector().
│ │ │
Member FEInterfaceViews::Vector< dim, spacedim >::average_hessian (const unsigned int interface_dof_index, const unsigned int q_point) const
│ │ │ -
Use the average_of_hessians() function instead.
│ │ │ +
Use the average_of_hessians() function instead.
│ │ │
Member FEInterfaceViews::Vector< dim, spacedim >::jump_gradient (const unsigned int interface_dof_index, const unsigned int q_point) const
│ │ │ -
Use the average_of_gradients() function instead.
│ │ │ +
Use the average_of_gradients() function instead.
│ │ │
Member FEInterfaceViews::Vector< dim, spacedim >::jump_hessian (const unsigned int interface_dof_index, const unsigned int q_point) const
│ │ │ -
Use the average_of_hessians() function instead.
│ │ │ +
Use the average_of_hessians() function instead.
│ │ │
Member FEPointEvaluationBase< n_components_, dim, spacedim, Number >::real_point (const unsigned int point_index) const
│ │ │ -
Use the function quadrature_point() instead.
│ │ │ +
Use the function quadrature_point() instead.
│ │ │
Member FETools::Compositing::compute_nonzero_components (const FiniteElement< dim, spacedim > *fe1, const unsigned int N1, const FiniteElement< dim, spacedim > *fe2=nullptr, const unsigned int N2=0, const FiniteElement< dim, spacedim > *fe3=nullptr, const unsigned int N3=0, const FiniteElement< dim, spacedim > *fe4=nullptr, const unsigned int N4=0, const FiniteElement< dim, spacedim > *fe5=nullptr, const unsigned int N5=0, const bool do_tensor_product=true)
│ │ │
Use the versions of this function that take a vector of elements or an initializer list as arguments.
│ │ │
Member FETools::Compositing::compute_restriction_is_additive_flags (const FiniteElement< dim, spacedim > *fe1, const unsigned int N1, const FiniteElement< dim, spacedim > *fe2=nullptr, const unsigned int N2=0, const FiniteElement< dim, spacedim > *fe3=nullptr, const unsigned int N3=0, const FiniteElement< dim, spacedim > *fe4=nullptr, const unsigned int N4=0, const FiniteElement< dim, spacedim > *fe5=nullptr, const unsigned int N5=0)
│ │ │
Use the versions of this function that take a vector of elements or an initializer list as arguments.
│ │ │
Member FETools::Compositing::multiply_dof_numbers (const FiniteElement< dim, spacedim > *fe1, const unsigned int N1, const FiniteElement< dim, spacedim > *fe2=nullptr, const unsigned int N2=0, const FiniteElement< dim, spacedim > *fe3=nullptr, const unsigned int N3=0, const FiniteElement< dim, spacedim > *fe4=nullptr, const unsigned int N4=0, const FiniteElement< dim, spacedim > *fe5=nullptr, const unsigned int N5=0)
│ │ │
Use the versions of this function that take a vector of elements or an initializer list as arguments.
│ │ │
Member FiniteElement< dim, spacedim >::fill_fe_face_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const Quadrature< dim - 1 > &quadrature, const Mapping< dim, spacedim > &mapping, const typename Mapping< dim, spacedim >::InternalDataBase &mapping_internal, const internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &mapping_data, const InternalDataBase &fe_internal, internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const
│ │ │ -
Use the version taking a hp::QCollection argument.
│ │ │ +
Use the version taking a hp::QCollection argument.
│ │ │
Member FiniteElement< dim, spacedim >::get_face_data (const UpdateFlags update_flags, const Mapping< dim, spacedim > &mapping, const Quadrature< dim - 1 > &quadrature, internal::FEValuesImplementation::FiniteElementRelatedData< dim, spacedim > &output_data) const
│ │ │ -
Use the version taking a hp::QCollection argument.
│ │ │ +
Use the version taking a hp::QCollection argument.
│ │ │
Member get_active_fe_indices (std::vector< unsigned int > &active_fe_indices) const
│ │ │ -
Use get_active_fe_indices() that returns the result vector.
│ │ │ +
Use get_active_fe_indices() that returns the result vector.
│ │ │
Member get_communicator () const
│ │ │ -
Use get_mpi_communicator() instead.
│ │ │ +
Use get_mpi_communicator() instead.
│ │ │
Member GridTools::fix_up_distorted_child_cells (const typename Triangulation< dim, spacedim >::DistortedCellList &distorted_cells, Triangulation< dim, spacedim > &triangulation)
│ │ │ -
This function predates deal.II's use of manifolds and use of cell-local transfinite interpolation to place new points and is no longer necessary. See Manifolds::get_default_points_and_weights() for more information.
│ │ │ +
This function predates deal.II's use of manifolds and use of cell-local transfinite interpolation to place new points and is no longer necessary. See Manifolds::get_default_points_and_weights() for more information.
│ │ │
Member identity
│ │ │
Use std_cxx20::type_identity instead.
│ │ │
Member IndexSet::pop_back ()
│ │ │ -
This function is deprecated. Conceptually, an index set is a set; it should not be seen as a sorted container in which it is clear what element is stored "last".
│ │ │ +
This function is deprecated. Conceptually, an index set is a set; it should not be seen as a sorted container in which it is clear what element is stored "last".
│ │ │
Member IndexSet::pop_front ()
│ │ │ -
This function is deprecated. Conceptually, an index set is a set; it should not be seen as a sorted container in which it is clear what element is stored "first".
│ │ │ +
This function is deprecated. Conceptually, an index set is a set; it should not be seen as a sorted container in which it is clear what element is stored "first".
│ │ │
Member KellyErrorEstimator< 1, spacedim >::estimate (const Mapping< 1, spacedim > &mapping, const DoFHandler< 1, spacedim > &dof, const hp::QCollection< 0 > &quadrature, const std::map< types::boundary_id, const Function< spacedim, Number > * > &neumann_bc, const ReadVector< Number > &solution, Vector< float > &error, const ComponentMask &component_mask={}, const Function< spacedim > *coefficients=nullptr, const unsigned int n_threads=numbers::invalid_unsigned_int, const types::subdomain_id subdomain_id=numbers::invalid_subdomain_id, const types::material_id material_id=numbers::invalid_material_id, const Strategy strategy=cell_diameter_over_24)
│ │ │
Use the version of this function which takes a hp::MappingCollection instead.
│ │ │
Member KellyErrorEstimator< 1, spacedim >::estimate (const Mapping< 1, spacedim > &mapping, const DoFHandler< 1, spacedim > &dof, const hp::QCollection< 0 > &quadrature, const std::map< types::boundary_id, const Function< spacedim, Number > * > &neumann_bc, const ArrayView< const ReadVector< Number > * > &solutions, ArrayView< Vector< float > * > &errors, const ComponentMask &component_mask={}, const Function< spacedim > *coefficients=nullptr, const unsigned int n_threads=numbers::invalid_unsigned_int, const types::subdomain_id subdomain_id=numbers::invalid_subdomain_id, const types::material_id material_id=numbers::invalid_material_id, const Strategy strategy=cell_diameter_over_24)
│ │ │
Use the version of this function which takes a hp::MappingCollection instead.
│ │ │
Member KellyErrorEstimator< dim, spacedim >::estimate (const Mapping< dim, spacedim > &mapping, const DoFHandler< dim, spacedim > &dof, const hp::QCollection< dim - 1 > &quadrature, const std::map< types::boundary_id, const Function< spacedim, Number > * > &neumann_bc, const ReadVector< Number > &solution, Vector< float > &error, const ComponentMask &component_mask={}, const Function< spacedim > *coefficients=nullptr, const unsigned int n_threads=numbers::invalid_unsigned_int, const types::subdomain_id subdomain_id=numbers::invalid_subdomain_id, const types::material_id material_id=numbers::invalid_material_id, const Strategy strategy=cell_diameter_over_24)
│ │ │
Use the version of this function which takes a hp::MappingCollection instead.
│ │ │
Member KellyErrorEstimator< dim, spacedim >::estimate (const Mapping< dim, spacedim > &mapping, const DoFHandler< dim, spacedim > &dof, const hp::QCollection< dim - 1 > &quadrature, const std::map< types::boundary_id, const Function< spacedim, Number > * > &neumann_bc, const ArrayView< const ReadVector< Number > * > &solutions, ArrayView< Vector< float > * > &errors, const ComponentMask &component_mask={}, const Function< spacedim > *coefficients=nullptr, const unsigned int n_threads=numbers::invalid_unsigned_int, const types::subdomain_id subdomain_id=numbers::invalid_subdomain_id, const types::material_id material_id=numbers::invalid_material_id, const Strategy strategy=cell_diameter_over_24)
│ │ │
Use the version of this function which takes a hp::MappingCollection instead.
│ │ │
Class Legacy::SolutionTransfer< dim, VectorType, spacedim >
│ │ │
Use SolutionTransfer instead.
│ │ │
Member LinearAlgebra::distributed::BlockVector< Number, MemorySpace >::import (const LinearAlgebra::ReadWriteVector< Number > &V, VectorOperation::values operation, std::shared_ptr< const Utilities::MPI::CommunicationPatternBase > communication_pattern={})
│ │ │ -
Use import_elements() instead.
│ │ │ +
Use import_elements() instead.
│ │ │
Member LinearAlgebra::distributed::Vector< Number, MemorySpace >::import (const Vector< Number, MemorySpace2 > &src, VectorOperation::values operation)
│ │ │ -
Use import_elements() instead.
│ │ │ -
Member LinearAlgebra::distributed::Vector< Number, MemorySpace >::import (const LinearAlgebra::ReadWriteVector< Number > &V, VectorOperation::values operation, std::shared_ptr< const Utilities::MPI::CommunicationPatternBase > communication_pattern={})
│ │ │
Use import_elements() instead.
│ │ │ +
Member LinearAlgebra::distributed::Vector< Number, MemorySpace >::import (const LinearAlgebra::ReadWriteVector< Number > &V, VectorOperation::values operation, std::shared_ptr< const Utilities::MPI::CommunicationPatternBase > communication_pattern={})
│ │ │ +
Use import_elements() instead.
│ │ │
Member LinearAlgebra::EpetraWrappers::Vector::import (const ReadWriteVector< double > &V, const VectorOperation::values operation, const std::shared_ptr< const Utilities::MPI::CommunicationPatternBase > &communication_pattern={})
│ │ │
Use import_elements() instead.
│ │ │
Member LinearAlgebra::ReadWriteVector< Number >::import (const Vector< Number > &V, VectorOperation::values operation, const std::shared_ptr< const Utilities::MPI::CommunicationPatternBase > &communication_pattern={})
│ │ │
Use import_elements() instead.
│ │ │
Member LinearAlgebra::ReadWriteVector< Number >::import (const distributed::Vector< Number, MemorySpace > &V, VectorOperation::values operation, const std::shared_ptr< const Utilities::MPI::CommunicationPatternBase > &communication_pattern={})
│ │ │
Use import_elements() instead.
│ │ │
Member LinearAlgebra::ReadWriteVector< Number >::import (const PETScWrappers::MPI::Vector &V, VectorOperation::values operation, const std::shared_ptr< const Utilities::MPI::CommunicationPatternBase > &communication_pattern={})
│ │ │ @@ -217,33 +217,33 @@ │ │ │
Member LinearAlgebra::ReadWriteVector< Number >::import (const EpetraWrappers::Vector &V, VectorOperation::values operation, const std::shared_ptr< const Utilities::MPI::CommunicationPatternBase > &communication_pattern={})
│ │ │
Use import_elements() instead.
│ │ │
Member LinearAlgebra::TpetraWrappers::Vector< Number, MemorySpace >::import (const ReadWriteVector< Number > &V, VectorOperation::values operation, std::shared_ptr< const Utilities::MPI::CommunicationPatternBase > communication_pattern={})
│ │ │
Use import_elements() instead.
│ │ │
Member LinearAlgebra::TpetraWrappers::Vector< Number, MemorySpace >::import_elements (const ReadWriteVector< Number > &V, VectorOperation::values operation, const std::shared_ptr< const Utilities::MPI::CommunicationPatternBase > &communication_pattern)
│ │ │
Use Teuchos::RCP<> instead of std::shared_ptr<>.
│ │ │
Member Mapping< dim, spacedim >::fill_fe_face_values (const typename Triangulation< dim, spacedim >::cell_iterator &cell, const unsigned int face_no, const Quadrature< dim - 1 > &quadrature, const typename Mapping< dim, spacedim >::InternalDataBase &internal_data, internal::FEValuesImplementation::MappingRelatedData< dim, spacedim > &output_data) const
│ │ │ -
Use the version taking a hp::QCollection argument.
│ │ │ +
Use the version taking a hp::QCollection argument.
│ │ │
Member Mapping< dim, spacedim >::get_face_data (const UpdateFlags update_flags, const Quadrature< dim - 1 > &quadrature) const
│ │ │ -
Use the version taking a hp::QCollection argument.
│ │ │ +
Use the version taking a hp::QCollection argument.
│ │ │
Member MeshWorker::integration_loop (IteratorType begin, std_cxx20::type_identity_t< IteratorType > end, DoFInfo< dim, spacedim > &dof_info, IntegrationInfoBox< dim, spacedim > &box, const LocalIntegrator< dim, spacedim > &integrator, AssemblerType &assembler, const LoopControl &lctrl=LoopControl())
│ │ │
This function is deprecated, along with the LocalIntegrator class. Use the MeshWorker::loop() function directly, with three function objects that perform the cell, boundary, and interior face integration.
│ │ │
Class MeshWorker::LocalIntegrator< dim, spacedim, number >
│ │ │ -
This class is deprecated. It used to be the basis for integration via the MeshWorker::integration_loop() function, but the same functionality is available via MeshWorker::loop().
│ │ │ +
This class is deprecated. It used to be the basis for integration via the MeshWorker::integration_loop() function, but the same functionality is available via MeshWorker::loop().
│ │ │
Member MeshWorker::LocalIntegrator< dim, spacedim, number >::input_vector_names
│ │ │ -
Because the library itself does not use this field, it is better placed in derived classes.
│ │ │ +
Because the library itself does not use this field, it is better placed in derived classes.
│ │ │
Member MeshWorker::LocalIntegrator< dim, spacedim, number >::output_names
│ │ │ -
Because the library itself does not use this field, it is better placed in derived classes.
│ │ │ +
Because the library itself does not use this field, it is better placed in derived classes.
│ │ │
Member NonlinearSolverSelector< VectorType >::NonlinearSolverSelector (const AdditionalData &additional_data)
│ │ │
Use the other constructor with MPI_Comm instead.
│ │ │
Member ObserverPointer< T, P >::clear ()
│ │ │ -
This function is deprecated. It does not use the semantics we usually use for this class, and its use is surely going to be confusing.
│ │ │ +
This function is deprecated. It does not use the semantics we usually use for this class, and its use is surely going to be confusing.
│ │ │
Member parallel::distributed::SolutionTransfer
│ │ │ -
Use SolutionTransfer instead.
│ │ │ +
Use SolutionTransfer instead.
│ │ │
Class PathSearch
│ │ │ -
Use the std::filesystem facilities instead.
│ │ │ +
Use the std::filesystem facilities instead.
│ │ │
Member PETScWrappers::SolverBiCG::SolverBiCG (SolverControl &cn, const MPI_Comm mpi_communicator, const AdditionalData &data=AdditionalData())
│ │ │
│ │ │
Member PETScWrappers::SolverBicgstab::SolverBicgstab (SolverControl &cn, const MPI_Comm mpi_communicator, const AdditionalData &data=AdditionalData())
│ │ │
│ │ │
Member PETScWrappers::SolverCG::SolverCG (SolverControl &cn, const MPI_Comm mpi_communicator, const AdditionalData &data=AdditionalData())
│ │ │
│ │ │
Member PETScWrappers::SolverCGS::SolverCGS (SolverControl &cn, const MPI_Comm mpi_communicator, const AdditionalData &data=AdditionalData())
│ │ │ @@ -269,15 +269,15 @@ │ │ │
Member PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::decide_for_coarsening_and_refinement
│ │ │
This callback is equivalent to decide_and_prepare_for_remeshing except that it returns the decision whether or not to stop operations via the last reference argument of the function object instead of a plain return value. This callback is deprecated. Use decide_and_prepare_for_remeshing instead.
│ │ │
Member PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::distribute
│ │ │
This callback is equivalent to update_constrained_components, but is deprecated. Use update_constrained_components instead.
│ │ │
Member PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::interpolate
│ │ │
This callback is equivalent to transfer_solution_vectors_to_new_mesh, but is deprecated. Use transfer_solution_vectors_to_new_mesh instead.
│ │ │
Member PolarManifold< dim, spacedim >::center
│ │ │ -
Use get_center() instead.
│ │ │ +
Use get_center() instead.
│ │ │
Member QProjector< dim >::DataSetDescriptor::face (const ReferenceCell &reference_cell, const unsigned int face_no, const bool face_orientation, const bool face_flip, const bool face_rotation, const unsigned int n_quadrature_points)
│ │ │
Use the version of this function which takes a combined_orientation argument instead.
│ │ │
Member QProjector< dim >::DataSetDescriptor::face (const ReferenceCell &reference_cell, const unsigned int face_no, const bool face_orientation, const bool face_flip, const bool face_rotation, const hp::QCollection< dim - 1 > &quadrature)
│ │ │
Use the version of this function which takes a combined_orientation argument instead.
│ │ │
Member QProjector< dim >::DataSetDescriptor::subface (const ReferenceCell &reference_cell, const unsigned int face_no, const unsigned int subface_no, const bool face_orientation, const bool face_flip, const bool face_rotation, const unsigned int n_quadrature_points, const internal::SubfaceCase< dim > ref_case=internal::SubfaceCase< dim >::case_isotropic)
│ │ │
Use the version of this function which takes a combined_orientation argument instead.
│ │ │
Member QProjector< dim >::project_to_face (const ReferenceCell &reference_cell, const SubQuadrature &quadrature, const unsigned int face_no, std::vector< Point< dim > > &q_points)
│ │ │ @@ -289,63 +289,63 @@ │ │ │
Member QProjector< dim >::project_to_oriented_subface (const ReferenceCell &reference_cell, const SubQuadrature &quadrature, const unsigned int face_no, const unsigned int subface_no, const bool face_orientation, const bool face_flip, const bool face_rotation, const internal::SubfaceCase< dim > ref_case)
│ │ │
Use the version of project_to_subface() which takes a combined_orientation argument instead.
│ │ │
Member QProjector< dim >::project_to_subface (const ReferenceCell &reference_cell, const SubQuadrature &quadrature, const unsigned int face_no, const unsigned int subface_no, std::vector< Point< dim > > &q_points, const RefinementCase< dim - 1 > &ref_case=RefinementCase< dim - 1 >::isotropic_refinement)
│ │ │
Use the version of project_to_subface() which takes a combined_orientation argument instead.
│ │ │
Member QProjector< dim >::project_to_subface (const ReferenceCell &reference_cell, const SubQuadrature &quadrature, const unsigned int face_no, const unsigned int subface_no, const RefinementCase< dim - 1 > &ref_case=RefinementCase< dim - 1 >::isotropic_refinement)
│ │ │
Use the version of project_to_subface() which takes a combined_orientation argument instead.
│ │ │
Member ReferenceCell::child_cell_on_face (const unsigned int face, const unsigned int subface) const
│ │ │ -
Use the version of this function which takes the orientation as the third parameter instead.
│ │ │ +
Use the version of this function which takes the orientation as the third parameter instead.
│ │ │
Member ReferenceCell::compute_orientation (const std::array< T, N > &vertices_0, const std::array< T, N > &vertices_1) const
│ │ │ -
Use get_combined_orientation() instead.
│ │ │ +
Use get_combined_orientation() instead.
│ │ │
Member ReferenceCell::default_combined_face_orientation ()
│ │ │ -
Use numbers::default_geometric_orientation instead.
│ │ │ +
Use numbers::default_geometric_orientation instead.
│ │ │
Member ReferenceCell::permute_according_orientation (const std::array< T, N > &vertices, const unsigned int orientation) const
│ │ │ -
Use permute_by_combined_orientation() instead.
│ │ │ +
Use permute_by_combined_orientation() instead.
│ │ │
Member ReferenceCell::reversed_combined_line_orientation ()
│ │ │ -
Use numbers::reverse_line_orientation instead.
│ │ │ +
Use numbers::reverse_line_orientation instead.
│ │ │
Member ReferenceCell::standard_vs_true_line_orientation (const unsigned int line, const unsigned int face, const types::geometric_orientation face_orientation, const types::geometric_orientation line_orientation) const
│ │ │ -
Use face_to_cell_line_orientation() instead.
│ │ │ +
Use face_to_cell_line_orientation() instead.
│ │ │
Member ReferenceCell::unit_normal_vectors (const unsigned int face_no) const
│ │ │ -
Use face_normal_vector() instead.
│ │ │ +
Use face_normal_vector() instead.
│ │ │
Member ReferenceCell::unit_tangential_vectors (const unsigned int face_no, const unsigned int i) const
│ │ │ -
Use face_tangent_vector() instead.
│ │ │ +
Use face_tangent_vector() instead.
│ │ │
Member set_active_fe_indices (const std::vector< unsigned int > &active_fe_indices)
│ │ │ -
Use set_active_fe_indices() with the types::fe_index datatype.
│ │ │ +
Use set_active_fe_indices() with the types::fe_index datatype.
│ │ │
Member SmartPointer
│ │ │ -
Use the new name of the class, ObserverPointer, instead.
│ │ │ +
Use the new name of the class, ObserverPointer, instead.
│ │ │
Member SolverGMRES< VectorType >::AdditionalData::max_n_tmp_vectors
│ │ │
Use max_basis_size instead.
│ │ │
Member SparsityTools::distribute_sparsity_pattern (BlockDynamicSparsityPattern &dsp, const std::vector< IndexSet > &owned_set_per_cpu, const MPI_Comm mpi_comm, const IndexSet &myrange)
│ │ │
Use the distribute_sparsity_pattern() with a single index set for the present MPI process only.
│ │ │
Member SphericalManifold< dim, spacedim >::center
│ │ │ -
Use get_center() instead.
│ │ │ +
Use get_center() instead.
│ │ │
Member Subscriptor
│ │ │
Use the new name of the class, ObserverPointer, instead.
│ │ │
Member Triangulation< dim, spacedim >::CELL_COARSEN
│ │ │ -
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │
Member Triangulation< dim, spacedim >::CELL_INVALID
│ │ │ -
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │
Member Triangulation< dim, spacedim >::CELL_PERSIST
│ │ │ -
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │
Member Triangulation< dim, spacedim >::CELL_REFINE
│ │ │ -
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │
Member Triangulation< dim, spacedim >::CellStatus
│ │ │ -
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │ +
This is an alias for backward compatibility. Use CellStatus directly.
│ │ │
Member Triangulation< dim, spacedim >::get_communicator () const
│ │ │ -
Use get_mpi_communicator() instead.
│ │ │ +
Use get_mpi_communicator() instead.
│ │ │
Member TrilinosWrappers::MPI::Vector::import (const LinearAlgebra::ReadWriteVector< double > &rwv, const VectorOperation::values operation)
│ │ │
Use import_elements() instead.
│ │ │
Member types::geometric_entity_type
│ │ │ -
This type was previously only used in library internals and is deprecated without replacement.
│ │ │ +
This type was previously only used in library internals and is deprecated without replacement.
│ │ │
Member Utilities::MPI::ConsensusAlgorithms::Interface< RequestType, AnswerType >::run (Process< RequestType, AnswerType > &process, const MPI_Comm comm)
│ │ │
Instead of deriving a class from the Process base class and providing a corresponding object to this function, use the other run() function in this class that takes function objects as arguments.
│ │ │
Class Utilities::MPI::ConsensusAlgorithms::Process< RequestType, AnswerType >
│ │ │ -
Instead of deriving a class from this base class and providing a corresponding object to one of the run() functions, use the free functions in this namespace that take function objects as arguments.
│ │ │ +
Instead of deriving a class from this base class and providing a corresponding object to one of the run() functions, use the free functions in this namespace that take function objects as arguments.
│ │ │
Member Utilities::MPI::RemotePointEvaluation< dim, spacedim >::RemotePointEvaluation (const double tolerance, const bool enforce_unique_mapping=false, const unsigned int rtree_level=0, const std::function< std::vector< bool >()> &marked_vertices={})
│ │ │ -
│ │ │ +
│ │ │
│ │ │
│ │ │
│ │ │ │ │ │ │ │ │ │ │ │ │ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/dof__handler_8h.html │ │ │ @@ -523,15 +523,15 @@ │ │ │ │ │ │
│ │ │ │ │ │

│ │ │

For each locally owned cell, set the active finite element index to the corresponding value given in active_fe_indices.

│ │ │

The vector active_fe_indices needs to have as many entries as there are active cells. The FE indices must be in the order in which we iterate over active cells. Vector entries corresponding to active cells that are not locally owned are ignored.

│ │ │

Active FE indices will only be set for locally owned cells. Ghost and artificial cells will be ignored; no active FE index will be assigned to them. To exchange active FE indices on ghost cells, call distribute_dofs() afterwards.

│ │ │ -
Deprecated
Use set_active_fe_indices() with the types::fe_index datatype.
│ │ │ +
Deprecated
Use set_active_fe_indices() with the types::fe_index datatype.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ get_active_fe_indices() [1/2]

│ │ │ │ │ │
│ │ │ @@ -566,15 +566,15 @@ │ │ │ │ │ │ │ │ │
│ │ │

For each locally relevant cell, extract the active finite element index and fill the vector active_fe_indices in the order in which we iterate over active cells. This vector is resized, if necessary.

│ │ │

As we do not know the active FE index on artificial cells, they are set to the invalid value numbers::invalid_fe_index.

│ │ │

For DoFHandler objects without hp-capabilities, the vector will consist of zeros, indicating that all cells use the same finite element. In hp-mode, the values may be different, though.

│ │ │

The returned vector has as many entries as there are active cells.

│ │ │ -
Deprecated
Use get_active_fe_indices() that returns the result vector.
│ │ │ +
Deprecated
Use get_active_fe_indices() that returns the result vector.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ set_future_fe_indices()

│ │ │ │ │ │
│ │ │ @@ -1272,15 +1272,15 @@ │ │ │ ( │ │ │ ) │ │ │ const │ │ │ │ │ │ │ │ │
│ │ │

Return MPI communicator used by the underlying triangulation.

│ │ │ -
Deprecated
Use get_mpi_communicator() instead.
│ │ │ +
Deprecated
Use get_mpi_communicator() instead.
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ prepare_for_serialization_of_active_fe_indices()

│ │ │ │ │ │
│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/group__Exceptions.html │ │ │ @@ -5447,15 +5447,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ static │ │ │ │ │ │ │ │ │
│ │ │ -
Todo
Write description
│ │ │ +
Todo
Write description
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ ExcGridNotCoarser()

│ │ │ │ │ │
│ │ │ @@ -5473,15 +5473,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ static │ │ │ │ │ │ │ │ │
│ │ │ -
Todo
Write description
│ │ │ +
Todo
Write description
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ ExcGridsDontMatch()

│ │ │ │ │ │
│ │ │ @@ -5499,15 +5499,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ static │ │ │ │ │ │ │ │ │
│ │ │ -
Todo
Write description
│ │ │ +
Todo
Write description
│ │ │

Exception

│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ ExcNoFESelected() [2/2]

│ │ │ │ │ │ @@ -5552,15 +5552,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ static │ │ │ │ │ │ │ │ │
│ │ │ -
Todo
Write description
│ │ │ +
Todo
Write description
│ │ │ │ │ │
│ │ │ │ │ │ │ │ │

◆ ExcNoComponentSelected()

│ │ │ │ │ │
│ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/namespaceDataOutBase.html │ │ │ @@ -1450,15 +1450,15 @@ │ │ │
  • │ │ │ vtu: .vtu
    • │ │ │
  • │ │ │ svg: .svg
    • │ │ │
  • │ │ │ deal_II_intermediate: .d2.
    • │ │ │ │ │ │ -
    Deprecated
    Using Tecplot binary output is deprecated.
    │ │ │ +
    Deprecated
    Using Tecplot binary output is deprecated.
    │ │ │ │ │ │

    Definition at line 2504 of file data_out_base.cc.

    │ │ │ │ │ │
    │ │ │ │ │ │ │ │ │

    ◆ operator<<()

    │ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/namespaceDoFTools.html │ │ │ @@ -980,15 +980,15 @@ │ │ │ │ │ │ │ │ │ std::vector< std::vector< bool > > & constant_modes ) │ │ │ │ │ │ │ │ │
    │ │ │

    Same as above.

    │ │ │ -
    Deprecated
    │ │ │ +
    Deprecated
    │ │ │ │ │ │

    Definition at line 1556 of file dof_tools.cc.

    │ │ │ │ │ │
    │ │ │ │ │ │ │ │ │

    ◆ extract_level_constant_modes() [1/2]

    │ │ │ @@ -1048,15 +1048,15 @@ │ │ │ │ │ │ │ │ │ std::vector< std::vector< bool > > & constant_modes ) │ │ │ │ │ │ │ │ │
    │ │ │

    Same as above.

    │ │ │ -
    Deprecated
    │ │ │ +
    Deprecated
    │ │ │ │ │ │

    Definition at line 1582 of file dof_tools.cc.

    │ │ │ │ │ │
    │ │ │ │ │ │ │ │ │

    ◆ extract_rigid_body_modes()

    │ │ │ @@ -1293,15 +1293,15 @@ │ │ │ │ │ │ IndexSet & dof_set ) │ │ │ │ │ │ │ │ │
    │ │ │

    Extract the set of global DoF indices that are active on the current DoFHandler. For regular DoFHandlers, these are all DoF indices, but for DoFHandler objects built on parallel::distributed::Triangulation this set is a superset of DoFHandler::locally_owned_dofs() and contains all DoF indices that live on all locally owned cells (including on the interface to ghost cells). However, it does not contain the DoF indices that are exclusively defined on ghost or artificial cells (see the glossary).

    │ │ │

    The degrees of freedom identified by this function equal those obtained from the dof_indices_with_subdomain_association() function when called with the locally owned subdomain id.

    │ │ │ -
    Deprecated
    Use the previous function instead.
    │ │ │ +
    Deprecated
    Use the previous function instead.
    │ │ │ │ │ │

    Definition at line 1107 of file dof_tools.cc.

    │ │ │ │ │ │
    │ │ │ │ │ │ │ │ │

    ◆ extract_locally_active_level_dofs() [1/2]

    │ │ │ @@ -1351,15 +1351,15 @@ │ │ │ │ │ │ │ │ │ const unsigned int level ) │ │ │ │ │ │ │ │ │
    │ │ │

    Same function as above but for a certain (multigrid-)level. This function returns all DoF indices that live on all locally owned cells (including on the interface to ghost cells) on the given level.

    │ │ │ -
    Deprecated
    Use the previous function instead.
    │ │ │ +
    Deprecated
    Use the previous function instead.
    │ │ │ │ │ │

    Definition at line 1154 of file dof_tools.cc.

    │ │ │ │ │ │
    │ │ │ │ │ │ │ │ │

    ◆ extract_locally_relevant_dofs() [1/2]

    │ │ │ @@ -1400,15 +1400,15 @@ │ │ │ │ │ │ │ │ │ IndexSet & dof_set ) │ │ │ │ │ │ │ │ │
    │ │ │

    Extract the set of global DoF indices that are active on the current DoFHandler. For regular DoFHandlers, these are all DoF indices, but for DoFHandler objects built on parallel::distributed::Triangulation this set is the union of DoFHandler::locally_owned_dofs() and the DoF indices on all ghost cells. In essence, it is the DoF indices on all cells that are not artificial (see the glossary).

    │ │ │ -
    Deprecated
    Use the previous function instead.
    │ │ │ +
    Deprecated
    Use the previous function instead.
    │ │ │ │ │ │

    Definition at line 1204 of file dof_tools.cc.

    │ │ │ │ │ │
    │ │ │ │ │ │ │ │ │

    ◆ locally_owned_dofs_per_component()

    │ │ │ @@ -1530,15 +1530,15 @@ │ │ │ │ │ │ │ │ │ IndexSet & dof_set ) │ │ │ │ │ │ │ │ │
    │ │ │

    Same as extract_locally_relevant_dofs() but for multigrid DoFs for the given level.

    │ │ │ -
    Deprecated
    Use the previous function instead.
    │ │ │ +
    Deprecated
    Use the previous function instead.
    │ │ │ │ │ │

    Definition at line 1260 of file dof_tools.cc.

    │ │ │ │ │ │
    │ │ │ │ │ │ │ │ │

    ◆ get_subdomain_association()

    │ │ │ @@ -2060,15 +2060,15 @@ │ │ │ std::vector< unsigned int > & active_fe_indices ) │ │ │ │ │ │ │ │ │
    │ │ │

    For each active cell of a DoFHandler, extract the active finite element index and fill the vector given as second argument. This vector is assumed to have as many entries as there are active cells.

    │ │ │

    For DoFHandler objects without hp-capabilities given as first argument, the returned vector will consist of only zeros, indicating that all cells use the same finite element. In hp-mode, the values may be different, though.

    │ │ │

    As we do not know the active FE index on artificial cells, we set them to the invalid value numbers::invalid_fe_index.

    │ │ │ -
    Deprecated
    Use DoFHandler::get_active_fe_indices() that returns the result vector.
    │ │ │ +
    Deprecated
    Use DoFHandler::get_active_fe_indices() that returns the result vector.
    │ │ │ │ │ │

    Definition at line 1679 of file dof_tools.cc.

    │ │ │ │ │ │
    │ │ │ │ │ │ │ │ │

    ◆ count_dofs_on_patch()

    │ │ │ @@ -2342,15 +2342,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ const ComponentMask & mask = {} ) │ │ │ │ │ │ │ │ │
    │ │ │ -

    A version of the function of same name that returns the map via its third argument. This function is deprecated.

    Deprecated
    Use the function that returns the std::map instead.
    │ │ │ +

    A version of the function of same name that returns the map via its third argument. This function is deprecated.

    Deprecated
    Use the function that returns the std::map instead.
    │ │ │ │ │ │

    Definition at line 2617 of file dof_tools.cc.

    │ │ │ │ │ │
    │ │ │ │ │ │ │ │ │

    ◆ map_dofs_to_support_points() [6/6]

    │ │ │ @@ -2378,15 +2378,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ const ComponentMask & mask = {} ) │ │ │ │ │ │ │ │ │
    │ │ │ -

    A version of the function of same name that returns the map via its third argument. This function is deprecated.

    Deprecated
    Use the function that returns the std::map instead.
    │ │ │ +

    A version of the function of same name that returns the map via its third argument. This function is deprecated.

    Deprecated
    Use the function that returns the std::map instead.
    │ │ │ │ │ │

    Definition at line 2638 of file dof_tools.cc.

    │ │ │ │ │ │
    │ │ │ │ │ │ │ │ │

    ◆ map_support_points_to_dofs()

    │ │ │ @@ -2412,15 +2412,15 @@ │ │ │ std::map< Point< spacedim >, types::global_dof_index, Comp > & point_to_index_map ) │ │ │ │ │ │ │ │ │
    │ │ │

    This is the opposite function to the one above. It generates a map where the keys are the support points of the degrees of freedom, while the values are the DoF indices. For a definition of support points, see this glossary entry.

    │ │ │

    Since there is no natural order in the space of points (except for the 1d case), you have to provide a map with an explicitly specified comparator object. This function is therefore templatized on the comparator object. Previous content of the map object is deleted in this function.

    │ │ │

    Just as with the function above, it is assumed that the finite element in use here actually supports the notion of support points of all its components.

    │ │ │ -
    Todo
    This function should generate a multimap, rather than just a map, since several dofs may be located at the same support point. Currently, only the last value in the map returned by map_dofs_to_support_points() for each point will be returned.
    │ │ │ +
    Todo
    This function should generate a multimap, rather than just a map, since several dofs may be located at the same support point. Currently, only the last value in the map returned by map_dofs_to_support_points() for each point will be returned.
    │ │ │ │ │ │
    │ │ │ │ │ │ │ │ │

    ◆ distribute_cell_to_dof_vector()

    │ │ │ │ │ │
    │ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/namespaceGridTools.html │ │ │ @@ -2382,15 +2382,15 @@ │ │ │ Triangulation< dim, spacedim > & triangulation ) │ │ │ │ │ │ │ │ │
    │ │ │

    Given a triangulation and a list of cells whose children have become distorted as a result of mesh refinement, try to fix these cells up by moving the center node around.

    │ │ │

    The function returns a list of cells with distorted children that couldn't be fixed up for whatever reason. The returned list is therefore a subset of the input argument.

    │ │ │

    For a definition of the concept of distorted cells, see the glossary entry. The first argument passed to the current function is typically the exception thrown by the Triangulation::execute_coarsening_and_refinement function.

    │ │ │ -
    Deprecated
    This function predates deal.II's use of manifolds and use of cell-local transfinite interpolation to place new points and is no longer necessary. See Manifolds::get_default_points_and_weights() for more information.
    │ │ │ +
    Deprecated
    This function predates deal.II's use of manifolds and use of cell-local transfinite interpolation to place new points and is no longer necessary. See Manifolds::get_default_points_and_weights() for more information.
    │ │ │ │ │ │

    Definition at line 2754 of file grid_tools.cc.

    │ │ │ │ │ │
    │ │ │ │ │ │ │ │ │

    ◆ get_patch_around_cell()

    │ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/namespaceLocalIntegrators_1_1Divergence.html │ │ │ @@ -260,15 +260,15 @@ │ │ │ │ │ │
    │ │ │

    The residual of the divergence operator in weak form.

    │ │ │ \[ - \int_Z │ │ │ \nabla v \cdot \mathbf u \,dx \] │ │ │

    │ │ │

    This is the weak divergence operator and the test space should be at least H1. The trial functions may be discontinuous.

    │ │ │ -
    Todo
    Verify: The function cell_matrix() is the Frechet derivative of this function with respect to the test functions.
    │ │ │ +
    Todo
    Verify: The function cell_matrix() is the Frechet derivative of this function with respect to the test functions.
    │ │ │ │ │ │

    Definition at line 125 of file divergence.h.

    │ │ │ │ │ │
    │ │ │ │ │ │ │ │ │

    ◆ gradient_matrix()

    │ │ │ @@ -381,15 +381,15 @@ │ │ │ │ │ │
    │ │ │

    The residual of the gradient operator in weak form.

    │ │ │ \[ -\int_Z │ │ │ \nabla\cdot \mathbf v u \,dx \] │ │ │

    │ │ │

    This is the weak gradient operator and the test space should be at least Hdiv. The trial functions may be discontinuous.

    │ │ │ -
    Todo
    Verify: The function gradient_matrix() is the Frechet derivative of this function with respect to the test functions.
    │ │ │ +
    Todo
    Verify: The function gradient_matrix() is the Frechet derivative of this function with respect to the test functions.
    │ │ │ │ │ │

    Definition at line 229 of file divergence.h.

    │ │ │ │ │ │
    │ │ │ │ │ │ │ │ │

    ◆ u_dot_n_matrix() [1/2]

    │ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/namespaceparallel_1_1distributed.html │ │ │ @@ -149,15 +149,15 @@ │ │ │ using parallel::distributed::SolutionTransfer │ │ │ │ │ │ │ │ │
    │ │ │ Initial value:
    │ │ │
    ::SolutionTransfer<dim, VectorType, spacedim>
    │ │ │
    parallel::distributed::SolutionTransfer
    ::SolutionTransfer< dim, VectorType, spacedim > SolutionTransfer
    Definition solution_transfer.h:33
    │ │ │ -
    Deprecated
    Use SolutionTransfer instead.
    │ │ │ +
    Deprecated
    Use SolutionTransfer instead.
    │ │ │ │ │ │

    Definition at line 33 of file solution_transfer.h.

    │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/namespacetypes.html │ │ │ @@ -348,15 +348,15 @@ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │
    using types::geometric_entity_type = std::uint8_t
    │ │ │
    │ │ │

    The type used to denote geometric entity types.

    │ │ │ -
    Deprecated
    This type was previously only used in library internals and is deprecated without replacement.
    │ │ │ +
    Deprecated
    This type was previously only used in library internals and is deprecated without replacement.
    │ │ │ │ │ │

    Definition at line 192 of file types.h.

    │ │ │ │ │ │
    │ │ │ │ │ │ │ │ │

    ◆ blas_int

    │ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/navtreeindex1.js │ │ │ ├── js-beautify {} │ │ │ │ @@ -139,26 +139,26 @@ │ │ │ │ "chunk__sparse__matrix_8h.html": [142, 0, 2, 0, 13, 11], │ │ │ │ "chunk__sparse__matrix_8h_source.html": [142, 0, 2, 0, 13, 11], │ │ │ │ "chunk__sparsity__pattern_8cc.html": [142, 0, 4, 11, 6], │ │ │ │ "chunk__sparsity__pattern_8cc_source.html": [142, 0, 4, 11, 6], │ │ │ │ "chunk__sparsity__pattern_8h.html": [142, 0, 2, 0, 13, 12], │ │ │ │ "chunk__sparsity__pattern_8h_source.html": [142, 0, 2, 0, 13, 12], │ │ │ │ "citelist.html": [141], │ │ │ │ - "classAdditionalData.html": [2, 11, 3, 21], │ │ │ │ "classAdditionalData.html": [2, 11, 1, 2, 21], │ │ │ │ - "classAdditionalData.html#a48b81b5ec1c358ecc9e0fb684c3221ce": [2, 11, 3, 21, 2], │ │ │ │ + "classAdditionalData.html": [2, 11, 3, 21], │ │ │ │ "classAdditionalData.html#a48b81b5ec1c358ecc9e0fb684c3221ce": [2, 11, 1, 2, 21, 2], │ │ │ │ - "classAdditionalData.html#a4c797fd8cd256f3433eef8233fe977a4": [2, 11, 3, 21, 3], │ │ │ │ + "classAdditionalData.html#a48b81b5ec1c358ecc9e0fb684c3221ce": [2, 11, 3, 21, 2], │ │ │ │ "classAdditionalData.html#a4c797fd8cd256f3433eef8233fe977a4": [2, 11, 1, 2, 21, 3], │ │ │ │ - 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"classLinearAlgebra_1_1TpetraWrappers_1_1SparseMatrixIterators_1_1AccessorBase.html#a90bf16d7cd11ea57c71adfddf71bef99": [3, 0, 53, 2, 0, 3, 13], │ │ │ │ "classLinearAlgebra_1_1TpetraWrappers_1_1SparseMatrixIterators_1_1AccessorBase.html#a90bf16d7cd11ea57c71adfddf71bef99": [3, 0, 53, 2, 0, 2, 12], │ │ │ │ + "classLinearAlgebra_1_1TpetraWrappers_1_1SparseMatrixIterators_1_1AccessorBase.html#a90bf16d7cd11ea57c71adfddf71bef99": [3, 0, 53, 2, 0, 3, 13], │ │ │ │ "classLinearAlgebra_1_1TpetraWrappers_1_1SparseMatrixIterators_1_1AccessorBase.html#a90bf16d7cd11ea57c71adfddf71bef99": [4, 0, 34, 2, 0, 0, 10], │ │ │ │ - "classLinearAlgebra_1_1TpetraWrappers_1_1SparseMatrixIterators_1_1AccessorBase.html#a90bf16d7cd11ea57c71adfddf71bef99": [4, 0, 34, 2, 0, 2, 12], │ │ │ │ - "classLinearAlgebra_1_1TpetraWrappers_1_1SparseMatrixIterators_1_1AccessorBase.html#a90bf16d7cd11ea57c71adfddf71bef99": [4, 0, 34, 2, 0, 3, 13] │ │ │ │ + "classLinearAlgebra_1_1TpetraWrappers_1_1SparseMatrixIterators_1_1AccessorBase.html#a90bf16d7cd11ea57c71adfddf71bef99": [4, 0, 34, 2, 0, 3, 13], │ │ │ │ + "classLinearAlgebra_1_1TpetraWrappers_1_1SparseMatrixIterators_1_1AccessorBase.html#a90bf16d7cd11ea57c71adfddf71bef99": [4, 0, 34, 2, 0, 2, 12] │ │ │ │ }; │ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/navtreeindex127.js │ │ │ ├── js-beautify {} │ │ │ │ @@ -1,38 +1,38 @@ │ │ │ │ var NAVTREEINDEX127 = { │ │ │ │ "classLinearAlgebra_1_1TpetraWrappers_1_1SparseMatrixIterators_1_1AccessorBase.html#a9b7dce661fba9d1bfebe003f46d114f6": [3, 0, 53, 2, 0, 0, 3], │ │ │ │ - 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    using SmartPointer = ObserverPointer<T, P>
    │ │ │
    │ │ │

    A type alias for the ObserverPointer class that makes sure the previous name of the class, SmartPointer, continues to be available.

    │ │ │ -
    Deprecated
    Use the new name of the class, ObserverPointer, instead.
    │ │ │ +
    Deprecated
    Use the new name of the class, ObserverPointer, instead.
    │ │ │ │ │ │

    Definition at line 285 of file observer_pointer.h.

    │ │ │ │ │ │
    │ │ │ │ │ │

    Function Documentation

    │ │ │ │ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/step_47.html │ │ │ @@ -242,15 +242,15 @@ │ │ │ &&\forall \mathbf x \in \partial\Omega. │ │ │ \end{align*} │ │ │

    │ │ │

    The same trick with the mixed system does not work here, because we would end up with both Dirichlet and Neumann boundary conditions for \(u\), but none for \(v\).

    │ │ │

    The solution to this conundrum arrived with the Discontinuous Galerkin method wave in the 1990s and early 2000s: In much the same way as one can use discontinuous shape functions for the Laplace equation by penalizing the size of the discontinuity to obtain a scheme for an equation that has one derivative on each shape function, we can use a scheme that uses continuous (but not \(C^1\) continuous) shape functions and penalize the jump in the derivative to obtain a scheme for an equation that has two derivatives on each shape function. In analogy to the Interior Penalty (IP) method for the Laplace equation, this scheme for the biharmonic equation is typically called the \(C^0\) IP (or C0IP) method, since it uses \(C^0\) (continuous but not continuously differentiable) shape functions with an interior penalty formulation.

    │ │ │

    It is worth noting that the C0IP method is not the only one that has been developed for the biharmonic equation. step-82 shows an alternative method.

    │ │ │

    Derivation of the C0IP method

    │ │ │ -

    We base this program on the \(C^0\) IP method presented by Susanne Brenner and Li-Yeng Sung in the paper " \_form#1256 Interior Penalty Method │ │ │ +

    We base this program on the \(C^0\) IP method presented by Susanne Brenner and Li-Yeng Sung in the paper " \_form#1248 Interior Penalty Method │ │ │ for Linear Fourth Order Boundary Value Problems on polygonal │ │ │ domains" [Brenner2005] where the method is derived for the biharmonic equation with "clamped" boundary conditions.

    │ │ │

    As mentioned, this method relies on the use of \(C^0\) Lagrange finite elements where the \(C^1\) continuity requirement is relaxed and has been replaced with interior penalty techniques. To derive this method, we consider a \(C^0\) shape function \(v_h\) which vanishes on \(\partial\Omega\). We introduce notation \( \mathbb{F} \) as the set of all faces of \(\mathbb{T}\), \( \mathbb{F}^b \) as the set of boundary faces, and \( \mathbb{F}^i \) as the set of interior faces for use further down below. Since the higher order derivatives of \(v_h\) have two values on each interface \(e\in \mathbb{F}\) (shared by the two cells \(K_{+},K_{-} \in \mathbb{T}\)), we cope with this discontinuity by defining the following single-valued functions on \(e\):

    │ │ │ \begin{align*} \jump{\frac{\partial^k v_h}{\partial \mathbf n^k}} │ │ │ &= │ │ │ \frac{\partial^k v_h|_{K_+}}{\partial \mathbf n^k} \bigg |_e │ │ │ - \frac{\partial^k v_h|_{K_-}}{\partial \mathbf n^k} \bigg |_e, │ │ │ ├── html2text {} │ │ │ │ @@ -174,15 +174,15 @@ │ │ │ │ (C^0\) IP (or C0IP) method, since it uses \(C^0\) (continuous but not │ │ │ │ continuously differentiable) shape functions with an interior penalty │ │ │ │ formulation. │ │ │ │ It is worth noting that the C0IP method is not the only one that has been │ │ │ │ developed for the biharmonic equation. _s_t_e_p_-_8_2 shows an alternative method. │ │ │ │ ******** DDeerriivvaattiioonn ooff tthhee CC00IIPP mmeetthhoodd ******** │ │ │ │ We base this program on the \(C^0\) IP method presented by Susanne Brenner and │ │ │ │ -Li-Yeng Sung in the paper " \_form#1256 Interior Penalty Method for Linear │ │ │ │ +Li-Yeng Sung in the paper " \_form#1248 Interior Penalty Method for Linear │ │ │ │ Fourth Order Boundary Value Problems on polygonal domains" [[BBrreennnneerr22000055]] where │ │ │ │ the method is derived for the biharmonic equation with "clamped" boundary │ │ │ │ conditions. │ │ │ │ As mentioned, this method relies on the use of \(C^0\) Lagrange finite elements │ │ │ │ where the \(C^1\) continuity requirement is relaxed and has been replaced with │ │ │ │ interior penalty techniques. To derive this method, we consider a \(C^0\) shape │ │ │ │ function \(v_h\) which vanishes on \(\partial\Omega\). We introduce notation \ │ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/step_58.html │ │ │ @@ -565,16 +565,16 @@ │ │ │ \left(\psi^{(n,2)}+\psi^{(n,1)}\right)\right] │ │ │ + │ │ │ V \left[\frac 12 \left(\psi^{(n,2)}+\psi^{(n,1)}\right)\right] = 0. │ │ │ \end{align*} │ │ │

    │ │ │

    Here, the "previous" solution \(\psi^{(n,1)}\) (or the "initial │ │ │ condition" for this part of the time step) is the output of the first phase rotation half-step; the output of the current step will be denoted by \(\psi^{(n,2)}\). \(k_{n+1}=t_{n+1}-t_n\) is the length of the time step. (One could argue whether \(\psi^{(n,1)}\) and \(\psi^{(n,1)}\) live at time step \(n\) or \(n+1\) and what their upper indices should be. This is a philosophical discussion without practical impact, and one might think of \(\psi^{(n,1)}\) as something like \(\psi^{(n+\tfrac 13)}\), and \(\psi^{(n,2)}\) as \(\psi^{(n+\tfrac 23)}\) if that helps clarify things – though, again \(n+\frac 13\) is not to be understood as "one third time step after │ │ │ - \_form#444" but more like "we've already done one third of the work necessary │ │ │ -for time step \_form#3339".)

    │ │ │ + \_form#398" but more like "we've already done one third of the work necessary │ │ │ +for time step \_form#3291".)

    │ │ │

    If we multiply the whole equation with \(k_{n+1}\) and sort terms with the unknown \(\psi^{(n+1,2)}\) to the left and those with the known \(\psi^{(n,2)}\) to the right, then we obtain the following (spatial) partial differential equation that needs to be solved in each time step:

    │ │ │ \begin{align*} -i\psi^{(n,2)} │ │ │ - │ │ │ \frac 14 k_{n+1} \Delta \psi^{(n,2)} │ │ │ + │ │ │ \frac 12 k_{n+1} V \psi^{(n,2)} │ │ │ = │ │ │ ├── html2text {} │ │ │ │ @@ -378,16 +378,16 @@ │ │ │ │ step; the output of the current step will be denoted by \(\psi^{(n,2)}\). \(k_ │ │ │ │ {n+1}=t_{n+1}-t_n\) is the length of the time step. (One could argue whether \ │ │ │ │ (\psi^{(n,1)}\) and \(\psi^{(n,1)}\) live at time step \(n\) or \(n+1\) and │ │ │ │ what their upper indices should be. This is a philosophical discussion without │ │ │ │ practical impact, and one might think of \(\psi^{(n,1)}\) as something like \ │ │ │ │ (\psi^{(n+\tfrac 13)}\), and \(\psi^{(n,2)}\) as \(\psi^{(n+\tfrac 23)}\) if │ │ │ │ that helps clarify things – though, again \(n+\frac 13\) is not to be │ │ │ │ -understood as "one third time step after \_form#444" but more like "we've │ │ │ │ -already done one third of the work necessary for time step \_form#3339".) │ │ │ │ +understood as "one third time step after \_form#398" but more like "we've │ │ │ │ +already done one third of the work necessary for time step \_form#3291".) │ │ │ │ If we multiply the whole equation with \(k_{n+1}\) and sort terms with the │ │ │ │ unknown \(\psi^{(n+1,2)}\) to the left and those with the known \(\psi^{ │ │ │ │ (n,2)}\) to the right, then we obtain the following (spatial) partial │ │ │ │ differential equation that needs to be solved in each time step: │ │ │ │ \begin{align*} -i\psi^{(n,2)} - \frac 14 k_{n+1} \Delta \psi^{(n,2)} + \frac 12 │ │ │ │ k_{n+1} V \psi^{(n,2)} = -i\psi^{(n,1)} + \frac 14 k_{n+1} \Delta \psi^{(n,1)} │ │ │ │ - \frac 12 k_{n+1} V \psi^{(n,1)}. \end{align*} │ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/structTensorAccessors_1_1ReturnType.html │ │ │ @@ -149,18 +149,18 @@ │ │ │ │ │ │ using TensorAccessors::ReturnType< deref_steps, T >::value_type │ │ │ │ │ │ │ │ │

    │ │ │ Initial value:
    │ │ │
    typename ReturnType<deref_steps - 1,
    │ │ │ -
    typename ValueType<T>::value_type>::value_type
    │ │ │ +
    typename ValueType<T>::value_type>::value_type
    │ │ │ │ │ │
    TensorAccessors::ValueType::value_type
    typename T::value_type value_type
    Definition tensor_accessors.h:106
    │ │ │ -
    std::iterator_traits< ::SparseMatrixIterators::Iterator< number, Constness > >::value_type
    typename ::SparseMatrixIterators::Iterator< number, Constness >::value_type value_type
    Definition sparse_matrix.h:475
    │ │ │ +
    std::iterator_traits< ::TrilinosWrappers::SparseMatrixIterators::Iterator< Constness > >::value_type
    typename ::TrilinosWrappers::SparseMatrixIterators::Iterator< Constness >::value_type value_type
    Definition trilinos_sparse_matrix.h:477
    │ │ │
    │ │ │

    Definition at line 138 of file tensor_accessors.h.

    │ │ │ │ │ │
    │ │ │ │ │ │
    The documentation for this struct was generated from the following file:
      │ │ │
    • include/deal.II/base/tensor_accessors.h
      • │ │ │ ├── html2text {} │ │ │ │ @@ -29,19 +29,19 @@ │ │ │ │ typename _R_e_t_u_r_n_T_y_p_e_:_:_v_a_l_u_e___t_y_p_e>_:_:_v_a_l_u_e___t_y_p_e │ │ │ │ _T_e_n_s_o_r_A_c_c_e_s_s_o_r_s_:_:_R_e_t_u_r_n_T_y_p_e │ │ │ │ DDeeffiinniittiioonn _t_e_n_s_o_r___a_c_c_e_s_s_o_r_s_._h_:_1_3_7 │ │ │ │ _T_e_n_s_o_r_A_c_c_e_s_s_o_r_s_:_:_V_a_l_u_e_T_y_p_e_:_:_v_a_l_u_e___t_y_p_e │ │ │ │ typename T::value_type value_type │ │ │ │ DDeeffiinniittiioonn _t_e_n_s_o_r___a_c_c_e_s_s_o_r_s_._h_:_1_0_6 │ │ │ │ -_s_t_d_:_:_i_t_e_r_a_t_o_r___t_r_a_i_t_s_<_ _:_:_S_p_a_r_s_e_M_a_t_r_i_x_I_t_e_r_a_t_o_r_s_:_:_I_t_e_r_a_t_o_r_<_ _n_u_m_b_e_r_,_ _C_o_n_s_t_n_e_s_s_ _> │ │ │ │ -_>_:_:_v_a_l_u_e___t_y_p_e │ │ │ │ -typename ::SparseMatrixIterators::Iterator< number, Constness >::value_type │ │ │ │ -value_type │ │ │ │ -DDeeffiinniittiioonn _s_p_a_r_s_e___m_a_t_r_i_x_._h_:_4_7_5 │ │ │ │ +_s_t_d_:_:_i_t_e_r_a_t_o_r___t_r_a_i_t_s_<_ _:_:_T_r_i_l_i_n_o_s_W_r_a_p_p_e_r_s_:_:_S_p_a_r_s_e_M_a_t_r_i_x_I_t_e_r_a_t_o_r_s_:_:_I_t_e_r_a_t_o_r_< │ │ │ │ +_C_o_n_s_t_n_e_s_s_ _>_ _>_:_:_v_a_l_u_e___t_y_p_e │ │ │ │ +typename ::TrilinosWrappers::SparseMatrixIterators::Iterator< Constness >:: │ │ │ │ +value_type value_type │ │ │ │ +DDeeffiinniittiioonn _t_r_i_l_i_n_o_s___s_p_a_r_s_e___m_a_t_r_i_x_._h_:_4_7_7 │ │ │ │ Definition at line _1_3_8 of file _t_e_n_s_o_r___a_c_c_e_s_s_o_r_s_._h. │ │ │ │ =============================================================================== │ │ │ │ The documentation for this struct was generated from the following file: │ │ │ │ * include/deal.II/base/_t_e_n_s_o_r___a_c_c_e_s_s_o_r_s_._h │ │ │ │ * _T_e_n_s_o_r_A_c_c_e_s_s_o_r_s │ │ │ │ * _R_e_t_u_r_n_T_y_p_e │ │ │ │ * Generated by _[_d_o_x_y_g_e_n_]1.15.0 │ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/structinternal_1_1FEEvaluationImpl.html │ │ │ @@ -188,18 +188,18 @@ │ │ │ │ │ │
      │ │ │ Initial value:
      EvaluatorTensorProduct<variant,
      │ │ │
      dim,
      │ │ │
      fe_degree + 1,
      │ │ │
      n_q_points_1d,
      │ │ │
      Number,
      │ │ │ -
      Number2>
      │ │ │ +
      Number2>
      │ │ │ │ │ │ +
      internal::FEEvaluationImplCollocation::Number2
      typename FEEvaluationData< dim, Number, false >::shape_info_number_type Number2
      Definition evaluation_kernels.h:1758
      │ │ │
      internal::FEEvaluationImpl::variant
      static const EvaluatorVariant variant
      Definition evaluation_kernels.h:115
      │ │ │ -
      internal::FEEvaluationImpl::Number2
      typename FEEvaluationData< dim, Number, false >::shape_info_number_type Number2
      Definition evaluation_kernels.h:117
      │ │ │
      │ │ │

      Definition at line 120 of file evaluation_kernels.h.

      │ │ │ │ │ │
      │ │ │ │ │ │

      Member Function Documentation

      │ │ │ │ │ │ ├── html2text {} │ │ │ │ @@ -74,20 +74,20 @@ │ │ │ │ dim, │ │ │ │ fe_degree + 1, │ │ │ │ n_q_points_1d, │ │ │ │ Number, │ │ │ │ _N_u_m_b_e_r_2> │ │ │ │ _i_n_t_e_r_n_a_l_:_:_E_v_a_l_u_a_t_o_r_T_e_n_s_o_r_P_r_o_d_u_c_t │ │ │ │ DDeeffiinniittiioonn _t_e_n_s_o_r___p_r_o_d_u_c_t___k_e_r_n_e_l_s_._h_:_1_5_7_3 │ │ │ │ +_i_n_t_e_r_n_a_l_:_:_F_E_E_v_a_l_u_a_t_i_o_n_I_m_p_l_C_o_l_l_o_c_a_t_i_o_n_:_:_N_u_m_b_e_r_2 │ │ │ │ +typename FEEvaluationData< dim, Number, false >::shape_info_number_type Number2 │ │ │ │ +DDeeffiinniittiioonn _e_v_a_l_u_a_t_i_o_n___k_e_r_n_e_l_s_._h_:_1_7_5_8 │ │ │ │ _i_n_t_e_r_n_a_l_:_:_F_E_E_v_a_l_u_a_t_i_o_n_I_m_p_l_:_:_v_a_r_i_a_n_t │ │ │ │ static const EvaluatorVariant variant │ │ │ │ DDeeffiinniittiioonn _e_v_a_l_u_a_t_i_o_n___k_e_r_n_e_l_s_._h_:_1_1_5 │ │ │ │ -_i_n_t_e_r_n_a_l_:_:_F_E_E_v_a_l_u_a_t_i_o_n_I_m_p_l_:_:_N_u_m_b_e_r_2 │ │ │ │ -typename FEEvaluationData< dim, Number, false >::shape_info_number_type Number2 │ │ │ │ -DDeeffiinniittiioonn _e_v_a_l_u_a_t_i_o_n___k_e_r_n_e_l_s_._h_:_1_1_7 │ │ │ │ Definition at line _1_2_0 of file _e_v_a_l_u_a_t_i_o_n___k_e_r_n_e_l_s_._h. │ │ │ │ ********** MMeemmbbeerr FFuunnccttiioonn DDooccuummeennttaattiioonn ********** │ │ │ │ ********** _?◆_? eevvaalluuaattee(()) ********** │ │ │ │ template<_M_a_t_r_i_x_F_r_e_e_F_u_n_c_t_i_o_n_s_:_:_E_l_e_m_e_n_t_T_y_p_e type, _i_n_t dim, _i_n_t fe_degree, _i_n_t │ │ │ │ n_q_points_1d, typename Number> │ │ │ │ void _i_n_t_e_r_n_a_l_:_: │ │ │ │ _F_E_E_v_a_l_u_a_t_i_o_n_I_m_p_l< │ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/structinternal_1_1FEEvaluationImplCollocation.html │ │ │ @@ -170,18 +170,18 @@ │ │ │ │ │ │
      │ │ │ Initial value:
      EvaluatorTensorProduct<evaluate_evenodd,
      │ │ │
      dim,
      │ │ │
      fe_degree + 1,
      │ │ │
      fe_degree + 1,
      │ │ │
      Number,
      │ │ │ -
      Number2>
      │ │ │ +
      Number2>
      │ │ │ │ │ │ │ │ │ -
      internal::FEEvaluationImpl::Number2
      typename FEEvaluationData< dim, Number, false >::shape_info_number_type Number2
      Definition evaluation_kernels.h:117
      │ │ │ +
      internal::FEEvaluationImplCollocation::Number2
      typename FEEvaluationData< dim, Number, false >::shape_info_number_type Number2
      Definition evaluation_kernels.h:1758
      │ │ │
      │ │ │

      Definition at line 1760 of file evaluation_kernels.h.

      │ │ │ │ │ │
      │ │ │ │ │ │

      Member Function Documentation

      │ │ │ │ │ │ ├── html2text {} │ │ │ │ @@ -54,17 +54,17 @@ │ │ │ │ Number, │ │ │ │ _N_u_m_b_e_r_2> │ │ │ │ _i_n_t_e_r_n_a_l_:_:_e_v_a_l_u_a_t_e___e_v_e_n_o_d_d │ │ │ │ @ evaluate_evenodd │ │ │ │ DDeeffiinniittiioonn _t_e_n_s_o_r___p_r_o_d_u_c_t___k_e_r_n_e_l_s_._h_:_5_5 │ │ │ │ _i_n_t_e_r_n_a_l_:_:_E_v_a_l_u_a_t_o_r_T_e_n_s_o_r_P_r_o_d_u_c_t │ │ │ │ DDeeffiinniittiioonn _t_e_n_s_o_r___p_r_o_d_u_c_t___k_e_r_n_e_l_s_._h_:_1_5_7_3 │ │ │ │ -_i_n_t_e_r_n_a_l_:_:_F_E_E_v_a_l_u_a_t_i_o_n_I_m_p_l_:_:_N_u_m_b_e_r_2 │ │ │ │ +_i_n_t_e_r_n_a_l_:_:_F_E_E_v_a_l_u_a_t_i_o_n_I_m_p_l_C_o_l_l_o_c_a_t_i_o_n_:_:_N_u_m_b_e_r_2 │ │ │ │ typename FEEvaluationData< dim, Number, false >::shape_info_number_type Number2 │ │ │ │ -DDeeffiinniittiioonn _e_v_a_l_u_a_t_i_o_n___k_e_r_n_e_l_s_._h_:_1_1_7 │ │ │ │ +DDeeffiinniittiioonn _e_v_a_l_u_a_t_i_o_n___k_e_r_n_e_l_s_._h_:_1_7_5_8 │ │ │ │ Definition at line _1_7_6_0 of file _e_v_a_l_u_a_t_i_o_n___k_e_r_n_e_l_s_._h. │ │ │ │ ********** MMeemmbbeerr FFuunnccttiioonn DDooccuummeennttaattiioonn ********** │ │ │ │ ********** _?◆_? eevvaalluuaattee(()) ********** │ │ │ │ template<_i_n_t dim, _i_n_t fe_degree, typename Number> │ │ │ │ void _i_n_t_e_r_n_a_l_:_: │ │ │ │ _F_E_E_v_a_l_u_a_t_i_o_n_I_m_p_l_C_o_l_l_o_c_a_t_i_o_n< ( const unsigned _i_n_t nn__ccoommppoonneennttss, │ │ │ │ dim, fe_degree, Number >:: │ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/structinternal_1_1FEFaceEvaluationImpl.html │ │ │ @@ -170,19 +170,19 @@ │ │ │
      │ │ │ Initial value:
      EvaluatorTensorProduct<symmetric_evaluate ? evaluate_evenodd :
      │ │ │
      evaluate_general,
      │ │ │
      dim - 1,
      │ │ │
      fe_degree + 1,
      │ │ │
      n_q_points_1d,
      │ │ │
      Number,
      │ │ │ -
      Number2>
      │ │ │ +
      Number2>
      │ │ │ │ │ │ │ │ │ │ │ │ -
      internal::FEEvaluationImpl::Number2
      typename FEEvaluationData< dim, Number, false >::shape_info_number_type Number2
      Definition evaluation_kernels.h:117
      │ │ │ +
      internal::FEEvaluationImplCollocation::Number2
      typename FEEvaluationData< dim, Number, false >::shape_info_number_type Number2
      Definition evaluation_kernels.h:1758
      │ │ │
      │ │ │

      Definition at line 54 of file evaluation_kernels_face.h.

      │ │ │ │ │ │
      │ │ │ │ │ │

      Member Function Documentation

      │ │ │ │ │ │ ├── html2text {} │ │ │ │ @@ -63,17 +63,17 @@ │ │ │ │ @ evaluate_general │ │ │ │ DDeeffiinniittiioonn _t_e_n_s_o_r___p_r_o_d_u_c_t___k_e_r_n_e_l_s_._h_:_4_3 │ │ │ │ _i_n_t_e_r_n_a_l_:_:_e_v_a_l_u_a_t_e___e_v_e_n_o_d_d │ │ │ │ @ evaluate_evenodd │ │ │ │ DDeeffiinniittiioonn _t_e_n_s_o_r___p_r_o_d_u_c_t___k_e_r_n_e_l_s_._h_:_5_5 │ │ │ │ _i_n_t_e_r_n_a_l_:_:_E_v_a_l_u_a_t_o_r_T_e_n_s_o_r_P_r_o_d_u_c_t │ │ │ │ DDeeffiinniittiioonn _t_e_n_s_o_r___p_r_o_d_u_c_t___k_e_r_n_e_l_s_._h_:_1_5_7_3 │ │ │ │ -_i_n_t_e_r_n_a_l_:_:_F_E_E_v_a_l_u_a_t_i_o_n_I_m_p_l_:_:_N_u_m_b_e_r_2 │ │ │ │ +_i_n_t_e_r_n_a_l_:_:_F_E_E_v_a_l_u_a_t_i_o_n_I_m_p_l_C_o_l_l_o_c_a_t_i_o_n_:_:_N_u_m_b_e_r_2 │ │ │ │ typename FEEvaluationData< dim, Number, false >::shape_info_number_type Number2 │ │ │ │ -DDeeffiinniittiioonn _e_v_a_l_u_a_t_i_o_n___k_e_r_n_e_l_s_._h_:_1_1_7 │ │ │ │ +DDeeffiinniittiioonn _e_v_a_l_u_a_t_i_o_n___k_e_r_n_e_l_s_._h_:_1_7_5_8 │ │ │ │ Definition at line _5_4 of file _e_v_a_l_u_a_t_i_o_n___k_e_r_n_e_l_s___f_a_c_e_._h. │ │ │ │ ********** MMeemmbbeerr FFuunnccttiioonn DDooccuummeennttaattiioonn ********** │ │ │ │ ********** _?◆_? ccrreeaattee__eevvaalluuaattoorr__tteennssoorr__pprroodduucctt(()) ********** │ │ │ │ template<_b_o_o_l symmetric_evaluate, _i_n_t dim, _i_n_t fe_degree, _i_n_t n_q_points_1d, │ │ │ │ typename Number> │ │ │ │ _E_v_a_l _i_n_t_e_r_n_a_l_:_: │ │ │ │ _F_E_F_a_c_e_E_v_a_l_u_a_t_i_o_n_I_m_p_l< const │ │ ├── ./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/todo.html │ │ │ @@ -119,59 +119,59 @@ │ │ │
      Class Algorithms::OperatorBase
      │ │ │
      Update this documentation and the one of Operator
      │ │ │
      Class AnyData
      │ │ │
      GK: Deprecate access to AnyData by index and change to a map.
      │ │ │
      Class BlockInfo
      │ │ │
      Extend the functions local() and renumber() to allow for hp-capablilites.
      │ │ │
      Class BlockSparsityPatternBase< SparsityPatternType >
      │ │ │ -
      Handle optimization of diagonal elements of the underlying SparsityPattern correctly.
      │ │ │ +
      Handle optimization of diagonal elements of the underlying SparsityPattern correctly.
      │ │ │
      Member create_boundary_mass_matrix (const Mapping< dim, spacedim > &mapping, const DoFHandler< dim, spacedim > &dof, const Quadrature< dim - 1 > &q, SparseMatrix< number > &matrix, const std::map< types::boundary_id, const Function< spacedim, number > * > &boundary_functions, Vector< number > &rhs_vector, std::vector< types::global_dof_index > &dof_to_boundary_mapping, const Function< spacedim, number > *const weight=0, std::vector< unsigned int > component_mapping={})
      │ │ │
      This function does not work for finite elements with cell-dependent shape functions.
      │ │ │
      Class DataOutFaces< dim, spacedim >
      │ │ │
      Reimplement this whole class using actual FEFaceValues and MeshWorker.
      │ │ │
      Member DataOutFaces< dim, spacedim >::build_patches (const Mapping< dim, spacedim > &mapping, const unsigned int n_subdivisions=0)
      │ │ │
      The mapping argument should be replaced by a hp::MappingCollection in case of a DoFHandler with hp-capabilities.
      │ │ │
      Class Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >
      │ │ │
      Make this class thread safe for Sacado number and ADOL-C tapeless numbers (if supported).
      │ │ │
      Member DoFTools::ExcFiniteElementsDontMatch ()
      │ │ │ -
      Write description
      │ │ │ +
      Write description
      │ │ │
      Member DoFTools::ExcGridNotCoarser ()
      │ │ │ -
      Write description
      │ │ │ +
      Write description
      │ │ │
      Member DoFTools::ExcGridsDontMatch ()
      │ │ │ -
      Write description
      │ │ │ +
      Write description
      │ │ │
      Member DoFTools::ExcInvalidBoundaryIndicator ()
      │ │ │ -
      Write description
      │ │ │ +
      Write description
      │ │ │
      Member DoFTools::map_support_points_to_dofs (const Mapping< dim, spacedim > &mapping, const DoFHandler< dim, spacedim > &dof_handler, std::map< Point< spacedim >, types::global_dof_index, Comp > &point_to_index_map)
      │ │ │ -
      This function should generate a multimap, rather than just a map, since several dofs may be located at the same support point. Currently, only the last value in the map returned by map_dofs_to_support_points() for each point will be returned.
      │ │ │ +
      This function should generate a multimap, rather than just a map, since several dofs may be located at the same support point. Currently, only the last value in the map returned by map_dofs_to_support_points() for each point will be returned.
      │ │ │
      Class FE_ABF< dim >
      │ │ │ -
      Even if this element is implemented for two and three space dimensions, the definition of the node values relies on consistently oriented faces in 3d. Therefore, care should be taken on complicated meshes.
      │ │ │ +
      Even if this element is implemented for two and three space dimensions, the definition of the node values relies on consistently oriented faces in 3d. Therefore, care should be taken on complicated meshes.
      │ │ │
      Class FE_BDM< dim >
      │ │ │ -

      The 3d version exhibits some numerical instabilities, in particular for higher order

      │ │ │ -

      Restriction matrices are missing.

      │ │ │ +

      The 3d version exhibits some numerical instabilities, in particular for higher order

      │ │ │ +

      Restriction matrices are missing.

      │ │ │
      │ │ │
      Class FE_Nedelec< dim >
      │ │ │ -
      Even if this element is implemented for two and three space dimensions, the definition of the node values relies on consistently oriented faces in 3d. Therefore, care should be taken on complicated meshes.
      │ │ │ +
      Even if this element is implemented for two and three space dimensions, the definition of the node values relies on consistently oriented faces in 3d. Therefore, care should be taken on complicated meshes.
      │ │ │
      Class FE_Poly< dim, spacedim >
      │ │ │ -
      Since nearly all functions for spacedim != dim are specialized, this class needs cleaning up.
      │ │ │ +
      Since nearly all functions for spacedim != dim are specialized, this class needs cleaning up.
      │ │ │
      Class FE_RT_Bubbles< dim >
      │ │ │
      Implement restriction matrices
      │ │ │
      Member FESubfaceValues< dim, spacedim >::ExcFaceHasNoSubfaces ()
      │ │ │
      Document this
      │ │ │
      Member FESubfaceValues< dim, spacedim >::ExcReinitCalledWithBoundaryFace ()
      │ │ │
      Document this
      │ │ │
      Member GinkgoWrappers::SolverBase< ValueType, IndexType >::system_matrix
      │ │ │
      Templatize based on Matrix type.
      │ │ │
      Member internal::TriangulationImplementation::TriaObjects::next_free_pair_object (const Triangulation< dim, spacedim > &tria)
      │ │ │
      This function is not instantiated for the codim-one case
      │ │ │
      Member internal::TriangulationImplementation::TriaObjects::next_free_single_object (const Triangulation< dim, spacedim > &tria)
      │ │ │
      This function is not instantiated for the codim-one case
      │ │ │
      Member LocalIntegrators::Divergence::cell_residual (Vector< number > &result, const FEValuesBase< dim > &fetest, const ArrayView< const std::vector< double > > &input, const double factor=1.)
      │ │ │ -
      Verify: The function cell_matrix() is the Frechet derivative of this function with respect to the test functions.
      │ │ │ +
      Verify: The function cell_matrix() is the Frechet derivative of this function with respect to the test functions.
      │ │ │
      Member LocalIntegrators::Divergence::gradient_residual (Vector< number > &result, const FEValuesBase< dim > &fetest, const std::vector< double > &input, const double factor=1.)
      │ │ │ -
      Verify: The function gradient_matrix() is the Frechet derivative of this function with respect to the test functions.
      │ │ │ +
      Verify: The function gradient_matrix() is the Frechet derivative of this function with respect to the test functions.
      │ │ │
      Class Mapping< dim, spacedim >
      │ │ │
      Document what happens in the codimension-1 case.
      │ │ │
      Member Mapping< dim, spacedim >::transform (const ArrayView< const Tensor< 2, dim > > &input, const MappingKind kind, const typename Mapping< dim, spacedim >::InternalDataBase &internal, const ArrayView< Tensor< 2, spacedim > > &output) const =0
      │ │ │
      The formulas for mapping_covariant_gradient, mapping_contravariant_gradient and mapping_piola_gradient are only true as stated for linear mappings. If, for example, the mapping is bilinear (or has a higher order polynomial degree) then there is a missing term associated with the derivative of \(J\).
      │ │ │
      Class MatrixBlock< MatrixType >
      │ │ │
      Example for the product preconditioner of the pressure Schur complement.
      │ │ │
      Member MatrixBlock< MatrixType >::add (const std::vector< size_type > &indices, const FullMatrix< number > &full_matrix, const bool elide_zero_values=true)
      │ │ │ @@ -179,19 +179,19 @@ │ │ │
      Member MatrixBlock< MatrixType >::add (const std::vector< size_type > &row_indices, const std::vector< size_type > &col_indices, const FullMatrix< number > &full_matrix, const bool elide_zero_values=true)
      │ │ │
      elide_zero_values is currently ignored.
      │ │ │
      Member MatrixBlock< MatrixType >::add (const size_type row_index, const std::vector< size_type > &col_indices, const std::vector< number > &values, const bool elide_zero_values=true)
      │ │ │
      elide_zero_values is currently ignored.
      │ │ │
      Class MeshWorker::Assembler::MGMatrixSimple< MatrixType >
      │ │ │
      The matrix structures needed for assembling level matrices with local refinement and continuous elements are missing.
      │ │ │
      Class MeshWorker::Assembler::ResidualLocalBlocksToGlobalBlocks< VectorType >
      │ │ │ -
      Comprehensive model currently not implemented.
      │ │ │ +
      Comprehensive model currently not implemented.
      │ │ │
      Class MeshWorker::DoFInfoBox< dim, DOFINFO >
      │ │ │
      Currently, we are storing an object for the cells and two for each face. We could gather all face data pertaining to the cell itself in one object, saving a bit of memory and a few operations, but sacrificing some cleanliness.
      │ │ │
      Class MGTransferBase< VectorType >
      │ │ │ -
      update the following documentation, since it does not reflect the latest changes in structure.
      │ │ │ +
      update the following documentation, since it does not reflect the latest changes in structure.
      │ │ │
      Class PolynomialsAdini< dim >
      │ │ │
      This polynomial space is implemented in 2d only and does not compute derivatives of order 3 or higher.
      │ │ │ │ │ │ │ │ │ │ │ │ │ │ │