/usr/include/deal.II/dofs/dof_tools.h is in libdeal.ii-dev 8.4.2-2+b1.
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//
// Copyright (C) 1999 - 2016 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef dealii__dof_tools_h
#define dealii__dof_tools_h
#include <deal.II/base/config.h>
#include <deal.II/base/exceptions.h>
#include <deal.II/base/table.h>
#include <deal.II/base/index_set.h>
#include <deal.II/base/point.h>
#include <deal.II/lac/constraint_matrix.h>
#include <deal.II/lac/sparsity_pattern.h>
#include <deal.II/dofs/function_map.h>
#include <deal.II/dofs/dof_handler.h>
#include <deal.II/fe/fe.h>
#include <deal.II/fe/component_mask.h>
#include <deal.II/hp/mapping_collection.h>
#include <vector>
#include <set>
#include <map>
DEAL_II_NAMESPACE_OPEN
template<int dim, class T> class Table;
class SparsityPattern;
template <typename number> class Vector;
template <int dim, typename Number> class Function;
template <int dim, int spacedim> class FiniteElement;
template <int dim, int spacedim> class DoFHandler;
namespace hp
{
template <int dim, int spacedim> class DoFHandler;
template <int dim, int spacedim> class MappingCollection;
}
class ConstraintMatrix;
template <class MeshType> class InterGridMap;
template <int dim, int spacedim> class Mapping;
namespace GridTools
{
template <typename CellIterator> struct PeriodicFacePair;
}
//TODO: map_support_points_to_dofs should generate a multimap, rather than just a map, since several dofs may be located at the same support point
/**
* This is a collection of functions operating on, and manipulating the
* numbers of degrees of freedom. The documentation of the member functions
* will provide more information, but for functions that exist in multiple
* versions, there are sections in this global documentation stating some
* commonalities.
*
* <h3>Setting up sparsity patterns</h3>
*
* When assembling system matrices, the entries are usually of the form
* $a_{ij} = a(\phi_i, \phi_j)$, where $a$ is a bilinear functional, often an
* integral. When using sparse matrices, we therefore only need to reserve
* space for those $a_{ij}$ only, which are nonzero, which is the same as to
* say that the basis functions $\phi_i$ and $\phi_j$ have a nonempty
* intersection of their support. Since the support of basis functions is
* bound only on cells on which they are located or to which they are
* adjacent, to determine the sparsity pattern it is sufficient to loop over
* all cells and connect all basis functions on each cell with all other basis
* functions on that cell. There may be finite elements for which not all
* basis functions on a cell connect with each other, but no use of this case
* is made since no examples where this occurs are known to the author.
*
*
* <h3>DoF numberings on boundaries</h3>
*
* When projecting the traces of functions to the boundary or parts thereof,
* one needs to build matrices and vectors that act only on those degrees of
* freedom that are located on the boundary, rather than on all degrees of
* freedom. One could do that by simply building matrices in which the entries
* for all interior DoFs are zero, but such matrices are always very rank
* deficient and not very practical to work with.
*
* What is needed instead in this case is a numbering of the boundary degrees
* of freedom, i.e. we should enumerate all the degrees of freedom that are
* sitting on the boundary, and exclude all other (interior) degrees of
* freedom. The map_dof_to_boundary_indices() function does exactly this: it
* provides a vector with as many entries as there are degrees of freedom on
* the whole domain, with each entry being the number in the numbering of the
* boundary or DoFHandler::invalid_dof_index if the dof is not on the
* boundary.
*
* With this vector, one can get, for any given degree of freedom, a unique
* number among those DoFs that sit on the boundary; or, if your DoF was
* interior to the domain, the result would be DoFHandler::invalid_dof_index.
* We need this mapping, for example, to build the mass matrix on the boundary
* (for this, see make_boundary_sparsity_pattern() function, the corresponding
* section below, as well as the MatrixCreator namespace documentation).
*
* Actually, there are two map_dof_to_boundary_indices() functions, one
* producing a numbering for all boundary degrees of freedom and one producing
* a numbering for only parts of the boundary, namely those parts for which
* the boundary indicator is listed in a set of indicators given to the
* function. The latter case is needed if, for example, we would only want to
* project the boundary values for the Dirichlet part of the boundary. You
* then give the function a list of boundary indicators referring to Dirichlet
* parts on which the projection is to be performed. The parts of the boundary
* on which you want to project need not be contiguous; however, it is not
* guaranteed that the indices of each of the boundary parts are continuous,
* i.e. the indices of degrees of freedom on different parts may be
* intermixed.
*
* Degrees of freedom on the boundary but not on one of the specified boundary
* parts are given the index DoFHandler::invalid_dof_index, as if they were in
* the interior. If no boundary indicator was given or if no face of a cell
* has a boundary indicator contained in the given list, the vector of new
* indices consists solely of DoFHandler::invalid_dof_index.
*
* (As a side note, for corner cases: The question what a degree of freedom on
* the boundary is, is not so easy. It should really be a degree of freedom
* of which the respective basis function has nonzero values on the boundary.
* At least for Lagrange elements this definition is equal to the statement
* that the off-point, or what deal.II calls support_point, of the shape
* function, i.e. the point where the function assumes its nominal value (for
* Lagrange elements this is the point where it has the function value 1), is
* located on the boundary. We do not check this directly, the criterion is
* rather defined through the information the finite element class gives: the
* FiniteElement class defines the numbers of basis functions per vertex, per
* line, and so on and the basis functions are numbered after this
* information; a basis function is to be considered to be on the face of a
* cell (and thus on the boundary if the cell is at the boundary) according to
* it belonging to a vertex, line, etc but not to the interior of the cell.
* The finite element uses the same cell-wise numbering so that we can say
* that if a degree of freedom was numbered as one of the dofs on lines, we
* assume that it is located on the line. Where the off-point actually is, is
* a secret of the finite element (well, you can ask it, but we don't do it
* here) and not relevant in this context.)
*
*
* <h3>Setting up sparsity patterns for boundary matrices</h3>
*
* In some cases, one wants to only work with DoFs that sit on the boundary.
* One application is, for example, if rather than interpolating non-
* homogenous boundary values, one would like to project them. For this, we
* need two things: a way to identify nodes that are located on (parts of) the
* boundary, and a way to build matrices out of only degrees of freedom that
* are on the boundary (i.e. much smaller matrices, in which we do not even
* build the large zero block that stems from the fact that most degrees of
* freedom have no support on the boundary of the domain). The first of these
* tasks is done by the map_dof_to_boundary_indices() function (described
* above).
*
* The second part requires us first to build a sparsity pattern for the
* couplings between boundary nodes, and then to actually build the components
* of this matrix. While actually computing the entries of these small
* boundary matrices is discussed in the MatrixCreator namespace, the creation
* of the sparsity pattern is done by the create_boundary_sparsity_pattern()
* function. For its work, it needs to have a numbering of all those degrees
* of freedom that are on those parts of the boundary that we are interested
* in. You can get this from the map_dof_to_boundary_indices() function. It
* then builds the sparsity pattern corresponding to integrals like
* $\int_\Gamma \varphi_{b2d(i)} \varphi_{b2d(j)} dx$, where $i$ and $j$ are
* indices into the matrix, and $b2d(i)$ is the global DoF number of a degree
* of freedom sitting on a boundary (i.e., $b2d$ is the inverse of the mapping
* returned by map_dof_to_boundary_indices() function).
*
*
* @ingroup dofs
* @author Wolfgang Bangerth, Guido Kanschat and others
*/
namespace DoFTools
{
/**
* The flags used in tables by certain <tt>make_*_pattern</tt> functions to
* describe whether two components of the solution couple in the bilinear
* forms corresponding to cell or face terms. An example of using these
* flags is shown in the introduction of step-46.
*
* In the descriptions of the individual elements below, remember that these
* flags are used as elements of tables of size FiniteElement::n_components
* times FiniteElement::n_components where each element indicates whether
* two components do or do not couple.
*/
enum Coupling
{
/**
* Two components do not couple.
*/
none,
/**
* Two components do couple.
*/
always,
/**
* Two components couple only if their shape functions are both nonzero on
* a given face. This flag is only used when computing integrals over
* faces of cells, e.g., in DoFTools::make_flux_sparsity_pattern().
*/
nonzero
};
/**
* @name Functions to support code that generically uses both DoFHandler and
* hp::DoFHandler
* @{
*/
/**
* Maximal number of degrees of freedom on a cell.
*
* @relates DoFHandler
*/
template <int dim, int spacedim>
unsigned int
max_dofs_per_cell (const DoFHandler<dim,spacedim> &dh);
/**
* Maximal number of degrees of freedom on a cell.
*
* @relates hp::DoFHandler
*/
template <int dim, int spacedim>
unsigned int
max_dofs_per_cell (const hp::DoFHandler<dim,spacedim> &dh);
/**
* Maximal number of degrees of freedom on a face.
*
* This function exists for both non-hp and hp DoFHandlers, to allow for a
* uniform interface to query this property.
*
* @relates DoFHandler
*/
template <int dim, int spacedim>
unsigned int
max_dofs_per_face (const DoFHandler<dim,spacedim> &dh);
/**
* Maximal number of degrees of freedom on a face.
*
* This function exists for both non-hp and hp DoFHandlers, to allow for a
* uniform interface to query this property.
*
* @relates hp::DoFHandler
*/
template <int dim, int spacedim>
unsigned int
max_dofs_per_face (const hp::DoFHandler<dim,spacedim> &dh);
/**
* Maximal number of degrees of freedom on a vertex.
*
* This function exists for both non-hp and hp DoFHandlers, to allow for a
* uniform interface to query this property.
*
* @relates DoFHandler
*/
template <int dim, int spacedim>
unsigned int
max_dofs_per_vertex (const DoFHandler<dim,spacedim> &dh);
/**
* Maximal number of degrees of freedom on a vertex.
*
* This function exists for both non-hp and hp DoFHandlers, to allow for a
* uniform interface to query this property.
*
* @relates hp::DoFHandler
*/
template <int dim, int spacedim>
unsigned int
max_dofs_per_vertex (const hp::DoFHandler<dim,spacedim> &dh);
/**
* Number of vector components in the finite element object used by this
* DoFHandler.
*
* This function exists for both non-hp and hp DoFHandlers, to allow for a
* uniform interface to query this property.
*
* @relates DoFHandler
*/
template <int dim, int spacedim>
unsigned int
n_components (const DoFHandler<dim,spacedim> &dh);
/**
* Number of vector components in the finite element object used by this
* DoFHandler.
*
* This function exists for both non-hp and hp DoFHandlers, to allow for a
* uniform interface to query this property.
*
* @relates hp::DoFHandler
*/
template <int dim, int spacedim>
unsigned int
n_components (const hp::DoFHandler<dim,spacedim> &dh);
/**
* Find out whether the FiniteElement used by this DoFHandler is primitive
* or not.
*
* This function exists for both non-hp and hp DoFHandlers, to allow for a
* uniform interface to query this property.
*
* @relates DoFHandler
*/
template <int dim, int spacedim>
bool
fe_is_primitive (const DoFHandler<dim,spacedim> &dh);
/**
* Find out whether the FiniteElement used by this DoFHandler is primitive
* or not.
*
* This function exists for both non-hp and hp DoFHandlers, to allow for a
* uniform interface to query this property.
*
* @relates hp::DoFHandler
*/
template <int dim, int spacedim>
bool
fe_is_primitive (const hp::DoFHandler<dim,spacedim> &dh);
/**
* @}
*/
/**
* @name Sparsity pattern generation
* @{
*/
/**
* Compute which entries of a matrix built on the given @p dof_handler may
* possibly be nonzero, and create a sparsity pattern object that represents
* these nonzero locations.
*
* This function computes the possible positions of non-zero entries in the
* global system matrix by <i>simulating</i> which entries one would write
* to during the actual assembly of a matrix. For this, the function assumes
* that each finite element basis function is non-zero on a cell only if its
* degree of freedom is associated with the interior, a face, an edge or a
* vertex of this cell. As a result, a matrix entry $A_{ij}$ that is
* computed from two basis functions $\varphi_i$ and $\varphi_j$ with
* (global) indices $i$ and $j$ (for example, using a bilinear form
* $A_{ij}=a(\varphi_i,\varphi_j)$) can be non-zero only if these shape
* functions correspond to degrees of freedom that are defined on at least
* one common cell. Therefore, this function just loops over all cells,
* figures out the global indices of all degrees of freedom, and presumes
* that all matrix entries that couple any of these indices will result in a
* nonzero matrix entry. These will then be added to the sparsity pattern.
* As this process of generating the sparsity pattern does not take into
* account the equation to be solved later on, the resulting sparsity
* pattern is symmetric.
*
* This algorithm makes no distinction between shape functions on each cell,
* i.e., it simply couples all degrees of freedom on a cell with all other
* degrees of freedom on a cell. This is often the case, and always a safe
* assumption. However, if you know something about the structure of your
* operator and that it does not couple certain shape functions with certain
* test functions, then you can get a sparser sparsity pattern by calling a
* variant of the current function described below that allows to specify
* which vector components couple with which other vector components.
*
* The method described above lives on the assumption that coupling between
* degrees of freedom only happens if shape functions overlap on at least
* one cell. This is the case with most usual finite element formulations
* involving conforming elements. However, for formulations such as the
* Discontinuous Galerkin finite element method, the bilinear form contains
* terms on interfaces between cells that couple shape functions that live
* on one cell with shape functions that live on a neighboring cell. The
* current function would not see these couplings, and would consequently
* not allocate entries in the sparsity pattern. You would then get into
* trouble during matrix assembly because you try to write into matrix
* entries for which no space has been allocated in the sparsity pattern.
* This can be avoided by calling the DoFTools::make_flux_sparsity_pattern()
* function instead, which takes into account coupling between degrees of
* freedom on neighboring cells.
*
* There are other situations where bilinear forms contain non-local terms,
* for example in treating integral equations. These require different
* methods for building the sparsity patterns that depend on the exact
* formulation of the problem. You will have to do this yourself then.
*
* @param[in] dof_handler The DoFHandler or hp::DoFHandler object that
* describes which degrees of freedom live on which cells.
*
* @param[out] sparsity_pattern The sparsity pattern to be filled with
* entries.
*
* @param[in] constraints The process for generating entries described above
* is purely local to each cell. Consequently, the sparsity pattern does not
* provide for matrix entries that will only be written into during the
* elimination of hanging nodes or other constraints. They have to be taken
* care of by a subsequent call to ConstraintMatrix::condense().
* Alternatively, the constraints on degrees of freedom can already be taken
* into account at the time of creating the sparsity pattern. For this, pass
* the ConstraintMatrix object as the third argument to the current
* function. No call to ConstraintMatrix::condense() is then necessary. This
* process is explained in step-6, step-27, and other tutorial programs.
*
* @param[in] keep_constrained_dofs In case the constraints are already
* taken care of in this function by passing in a ConstraintMatrix object,
* it is possible to abandon some off-diagonal entries in the sparsity
* pattern if these entries will also not be written into during the actual
* assembly of the matrix this sparsity pattern later serves. Specifically,
* when using an assembly method that uses
* ConstraintMatrix::distribute_local_to_global(), no entries will ever be
* written into those matrix rows or columns that correspond to constrained
* degrees of freedom. In such cases, you can set the argument @p
* keep_constrained_dofs to @p false to avoid allocating these entries in
* the sparsity pattern.
*
* @param[in] subdomain_id If specified, the sparsity pattern is built only
* on cells that have a subdomain_id equal to the given argument. This is
* useful in parallel contexts where the matrix and sparsity pattern (for
* example a TrilinosWrappers::SparsityPattern) may be distributed and not
* every MPI process needs to build the entire sparsity pattern; in that
* case, it is sufficient if every process only builds that part of the
* sparsity pattern that corresponds to the subdomain_id for which it is
* responsible. This feature is used in step-32. (This argument is not
* usually needed for objects of type parallel::distributed::Triangulation
* because the current function only loops over locally owned cells anyway;
* thus, this argument typically only makes sense if you want to use the
* subdomain_id for anything other than indicating which processor owns a
* cell, for example which geometric component of the domain a cell belongs
* to.)
*
* @note The actual type of the sparsity pattern may be SparsityPattern,
* DynamicSparsityPattern, BlockSparsityPattern,
* BlockDynamicSparsityPattern, or any other class that satisfies similar
* requirements. It is assumed that the size of the sparsity pattern matches
* the number of degrees of freedom and that enough unused nonzero entries
* are left to fill the sparsity pattern if the sparsity pattern is of
* "static" kind (see
* @ref Sparsity
* for more information on what this means). The nonzero entries generated
* by this function are added to possible previous content of the object,
* i.e., previously added entries are not removed.
*
* @note If the sparsity pattern is represented by an object of type
* SparsityPattern (as opposed to, for example, DynamicSparsityPattern), you
* need to remember using SparsityPattern::compress() after generating the
* pattern.
*
* @ingroup constraints
*/
template <typename DoFHandlerType, typename SparsityPatternType>
void
make_sparsity_pattern (const DoFHandlerType &dof_handler,
SparsityPatternType &sparsity_pattern,
const ConstraintMatrix &constraints = ConstraintMatrix(),
const bool keep_constrained_dofs = true,
const types::subdomain_id subdomain_id = numbers::invalid_subdomain_id);
/**
* Compute which entries of a matrix built on the given @p dof_handler may
* possibly be nonzero, and create a sparsity pattern object that represents
* these nonzero locations.
*
* This function is a simple variation on the previous
* make_sparsity_pattern() function (see there for a description of all of
* the common arguments), but it provides functionality for vector finite
* elements that allows to be more specific about which variables couple in
* which equation.
*
* For example, if you wanted to solve the Stokes equations,
*
* @f{align*}{
* -\Delta \mathbf u + \nabla p &= 0,\\ \text{div}\ u &= 0
* @f}
*
* in two space dimensions, using stable Q2/Q1 mixed elements (using the
* FESystem class), then you don't want all degrees of freedom to couple in
* each equation. More specifically, in the first equation, only $u_x$ and
* $p$ appear; in the second equation, only $u_y$ and $p$ appear; and in the
* third equation, only $u_x$ and $u_y$ appear. (Note that this discussion
* only talks about vector components of the solution variable and the
* different equation, and has nothing to do with degrees of freedom, or in
* fact with any kind of discretization.) We can describe this by the
* following pattern of "couplings":
*
* @f[
* \left[
* \begin{array}{ccc}
* 1 & 0 & 1 \\
* 0 & 1 & 1 \\
* 1 & 1 & 0
* \end{array}
* \right]
* @f]
*
* where "1" indicates that two variables (i.e., vector components of the
* FESystem) couple in the respective equation, and a "0" means no coupling.
* These zeros imply that upon discretization via a standard finite element
* formulation, we will not write entries into the matrix that, for example,
* couple pressure test functions with pressure shape functions (and similar
* for the other zeros above). It is then a waste to allocate memory for
* these entries in the matrix and the sparsity pattern, and you can avoid
* this by creating a mask such as the one above that describes this to the
* (current) function that computes the sparsity pattern. As stated above,
* the mask shown above refers to components of the composed FESystem,
* rather than to degrees of freedom or shape functions.
*
* This function is designed to accept a coupling pattern, like the one
* shown above, through the @p couplings parameter, which contains values of
* type #Coupling. It builds the matrix structure just like the previous
* function, but does not create matrix elements if not specified by the
* coupling pattern. If the couplings are symmetric, then so will be the
* resulting sparsity pattern.
*
* There is a complication if some or all of the shape functions of the
* finite element in use are non-zero in more than one component (in deal.II
* speak: they are
* @ref GlossPrimitive "non-primitive finite elements").
* In this case, the coupling element corresponding to the first non-zero
* component is taken and additional ones for this component are ignored.
*
* @ingroup constraints
*/
template <typename DoFHandlerType, typename SparsityPatternType>
void
make_sparsity_pattern (const DoFHandlerType &dof_handler,
const Table<2, Coupling> &coupling,
SparsityPatternType &sparsity_pattern,
const ConstraintMatrix &constraints = ConstraintMatrix(),
const bool keep_constrained_dofs = true,
const types::subdomain_id subdomain_id = numbers::invalid_subdomain_id);
/**
* Construct a sparsity pattern that allows coupling degrees of freedom on
* two different but related meshes.
*
* The idea is that if the two given DoFHandler objects correspond to two
* different meshes (and potentially to different finite elements used on
* these cells), but that if the two triangulations they are based on are
* derived from the same coarse mesh through hierarchical refinement, then
* one may set up a problem where one would like to test shape functions
* from one mesh against the shape functions from another mesh. In
* particular, this means that shape functions from a cell on the first mesh
* are tested against those on the second cell that are located on the
* corresponding cell; this correspondence is something that the
* IntergridMap class can determine.
*
* This function then constructs a sparsity pattern for which the degrees of
* freedom that represent the rows come from the first given DoFHandler,
* whereas the ones that correspond to columns come from the second
* DoFHandler.
*/
template <typename DoFHandlerType, typename SparsityPatternType>
void
make_sparsity_pattern (const DoFHandlerType &dof_row,
const DoFHandlerType &dof_col,
SparsityPatternType &sparsity);
/**
* Compute which entries of a matrix built on the given @p dof_handler may
* possibly be nonzero, and create a sparsity pattern object that represents
* these nonzero locations. This function is a variation of the
* make_sparsity_pattern() functions above in that it assumes that the
* bilinear form you want to use to generate the matrix also contains terms
* that integrate over the <i>faces</i> between cells (i.e., it contains
* "fluxes" between cells, explaining the name of the function).
*
* This function is useful for Discontinuous Galerkin methods where the
* standard make_sparsity_pattern() function would only create nonzero
* entries for all degrees of freedom on one cell coupling to all other
* degrees of freedom on the same cell; however, in DG methods, all or some
* degrees of freedom on each cell also couple to the degrees of freedom on
* other cells connected to the current one by a common face. The current
* function also creates the nonzero entries in the matrix resulting from
* these additional couplings. In other words, this function computes a
* strict super-set of nonzero entries compared to the work done by
* make_sparsity_pattern().
*
* @param[in] dof_handler The DoFHandler or hp::DoFHandler object that
* describes which degrees of freedom live on which cells.
*
* @param[out] sparsity_pattern The sparsity pattern to be filled with
* entries.
*
* @note The actual type of the sparsity pattern may be SparsityPattern,
* DynamicSparsityPattern, BlockSparsityPattern,
* BlockDynamicSparsityPattern, or any other class that satisfies similar
* requirements. It is assumed that the size of the sparsity pattern matches
* the number of degrees of freedom and that enough unused nonzero entries
* are left to fill the sparsity pattern if the sparsity pattern is of
* "static" kind (see
* @ref Sparsity
* for more information on what this means). The nonzero entries generated
* by this function are added to possible previous content of the object,
* i.e., previously added entries are not removed.
*
* @note If the sparsity pattern is represented by an object of type
* SparsityPattern (as opposed to, for example, DynamicSparsityPattern), you
* need to remember using SparsityPattern::compress() after generating the
* pattern.
*
* @ingroup constraints
*/
template<typename DoFHandlerType, typename SparsityPatternType>
void
make_flux_sparsity_pattern (const DoFHandlerType &dof_handler,
SparsityPatternType &sparsity_pattern);
/**
* This function does essentially the same as the other
* make_flux_sparsity_pattern() function but allows the specification of a
* number of additional arguments. These carry the same meaning as discussed
* in the first make_sparsity_pattern() function above.
*
* @ingroup constraints
*/
template<typename DoFHandlerType, typename SparsityPatternType>
void
make_flux_sparsity_pattern (const DoFHandlerType &dof_handler,
SparsityPatternType &sparsity_pattern,
const ConstraintMatrix &constraints,
const bool keep_constrained_dofs = true,
const types::subdomain_id subdomain_id = numbers::invalid_unsigned_int);
/**
* This function does essentially the same as the other
* make_flux_sparsity_pattern() function but allows the specification of
* coupling matrices that state which components of the solution variable
* couple in each of the equations you are discretizing. This works in
* complete analogy as discussed in the second make_sparsity_pattern()
* function above.
*
* In fact, this function takes two such masks, one describing which
* variables couple with each other in the cell integrals that make up your
* bilinear form, and which variables coupld with each other in the face
* integrals. If you passed masks consisting of only 1s to both of these,
* then you would get the same sparsity pattern as if you had called the
* first of the make_sparsity_pattern() functions above. By setting some of
* the entries of these masks to zeros, you can get a sparser sparsity
* pattern.
*
* @ingroup constraints
*/
template <typename DoFHandlerType, typename SparsityPatternType>
void
make_flux_sparsity_pattern (const DoFHandlerType &dof,
SparsityPatternType &sparsity,
const Table<2,Coupling> &cell_integrals_mask,
const Table<2,Coupling> &face_integrals_mask);
/**
* Create the sparsity pattern for boundary matrices. See the general
* documentation of this class for more information.
*
* The function does essentially what the other make_sparsity_pattern()
* functions do, but assumes that the bilinear form that is used to build
* the matrix does not consist of domain integrals, but only of integrals
* over the boundary of the domain.
*/
template <typename DoFHandlerType, typename SparsityPatternType>
void
make_boundary_sparsity_pattern (const DoFHandlerType &dof,
const std::vector<types::global_dof_index> &dof_to_boundary_mapping,
SparsityPatternType &sparsity_pattern);
/**
* This function is a variation of the previous
* make_boundary_sparsity_pattern() function in which we assume that the
* boundary integrals that will give rise to the matrix extends only over
* those parts of the boundary whose boundary indicators are listed in the
* @p boundary_ids argument to this function.
*
* This function could have been written by passing a @p set of boundary_id
* numbers. However, most of the functions throughout deal.II dealing with
* boundary indicators take a mapping of boundary indicators and the
* corresponding boundary function, i.e., a FunctionMap argument.
* Correspondingly, this function does the same, though the actual boundary
* function is ignored here. (Consequently, if you don't have any such
* boundary functions, just create a map with the boundary indicators you
* want and set the function pointers to null pointers).
*/
template <typename DoFHandlerType, typename SparsityPatternType>
void
make_boundary_sparsity_pattern
(const DoFHandlerType &dof,
const typename FunctionMap<DoFHandlerType::space_dimension>::type &boundary_ids,
const std::vector<types::global_dof_index> &dof_to_boundary_mapping,
SparsityPatternType &sparsity);
/**
* @}
*/
/**
* @name Hanging nodes and other constraints
* @{
*/
/**
* Compute the constraints resulting from the presence of hanging nodes.
* Hanging nodes are best explained using a small picture:
*
* @image html hanging_nodes.png
*
* In order to make a finite element function globally continuous, we have
* to make sure that the dark red nodes have values that are compatible with
* the adjacent yellow nodes, so that the function has no jump when coming
* from the small cells to the large one at the top right. We therefore have
* to add conditions that constrain those "hanging nodes".
*
* The object into which these are inserted is later used to condense the
* global system matrix and right hand side, and to extend the solution
* vectors from the true degrees of freedom also to the constraint nodes.
* This function is explained in detail in the
* @ref step_6 "step-6"
* tutorial program and is used in almost all following programs as well.
*
* This function does not clear the constraint matrix object before use, in
* order to allow adding constraints from different sources to the same
* object. You therefore need to make sure it contains only constraints you
* still want; otherwise call the ConstraintMatrix::clear() function.
* Likewise, this function does not close the object since you may want to
* enter other constraints later on yourself.
*
* In the hp-case, i.e. when the argument is of type hp::DoFHandler, we
* consider constraints due to different finite elements used on two sides
* of a face between cells as hanging nodes as well. In other words, for hp
* finite elements, this function computes all constraints due to differing
* mesh sizes (h) or polynomial degrees (p) between adjacent cells.
*
* The template argument (and by consequence the type of the first argument
* to this function) can be either ::DoFHandler or hp::DoFHandler.
*
* @ingroup constraints
*/
template <typename DoFHandlerType>
void
make_hanging_node_constraints (const DoFHandlerType &dof_handler,
ConstraintMatrix &constraints);
/**
* This function is used when different variables in a problem are
* discretized on different grids, where one grid is strictly coarser than
* the other. An example are optimization problems where the control
* variable is often discretized on a coarser mesh than the state variable.
*
* The function's result can be stated as follows mathematically: Let ${\cal
* T}_0$ and ${\cal T}_1$ be two meshes where ${\cal T}_1$ results from
* ${\cal T}_0$ strictly by refining or leaving alone the cells of ${\cal
* T}_0$. Using the same finite element on both, there are function spaces
* ${\cal V}_0$ and ${\cal V}_1$ associated with these meshes. Then every
* function $v_0 \in {\cal V}_0$ can of course also be represented exactly
* in ${\cal V}_1$ since by construction ${\cal V}_0 \subset {\cal V}_1$.
* However, not every function in ${\cal V}_1$ can be expressed as a linear
* combination of the shape functions of ${\cal V}_0$. The functions that
* can be represented lie in a homogenous subspace of ${\cal V}_1$ (namely,
* ${\cal V}_0$, of course) and this subspace can be represented by a linear
* constraint of the form $CV=0$ where $V$ is the vector of nodal values of
* functions $v\in {\cal V}_1$. In other words, every function $v_h=\sum_j
* V_j \varphi_j^{(1)} \in {\cal V}_1$ that also satisfies $v_h\in {\cal
* V}_0$ automatically satisfies $CV=0$. This function computes the matrix
* $C$ in the form of a ConstraintMatrix object.
*
* The construction of these constraints is done as follows: for each of the
* degrees of freedom (i.e. shape functions) on the coarse grid, we compute
* its representation on the fine grid, i.e. how the linear combination of
* shape functions on the fine grid looks like that resembles the shape
* function on the coarse grid. From this information, we can then compute
* the constraints which have to hold if a solution of a linear equation on
* the fine grid shall be representable on the coarse grid. The exact
* algorithm how these constraints can be computed is rather complicated and
* is best understood by reading the source code, which contains many
* comments.
*
* The use of this function is as follows: it accepts as parameters two DoF
* Handlers, the first of which refers to the coarse grid and the second of
* which is the fine grid. On both, a finite element is represented by the
* DoF handler objects, which will usually have several vector components,
* which may belong to different base elements. The second and fourth
* parameter of this function therefore state which vector component on the
* coarse grid shall be used to restrict the stated component on the fine
* grid. The finite element used for the respective components on the two
* grids needs to be the same. An example may clarify this: consider an
* optimization problem with controls $q$ discretized on a coarse mesh and a
* state variable $u$ (and corresponding Lagrange multiplier $\lambda$)
* discretized on the fine mesh. These are discretized using piecewise
* constant discontinuous, continuous linear, and continuous linear
* elements, respectively. Only the parameter $q$ is represented on the
* coarse grid, thus the DoFHandler object on the coarse grid represents
* only one variable, discretized using piecewise constant discontinuous
* elements. Then, the parameter denoting the vector component on the coarse
* grid would be zero (the only possible choice, since the variable on the
* coarse grid is scalar). If the ordering of variables in the fine mesh
* FESystem is $u, q, \lambda$, then the fourth argument of the function
* corresponding to the vector component would be one (corresponding to the
* variable $q$; zero would be $u$, two would be $\lambda$).
*
* The function also requires an object of type IntergridMap representing
* how to get from the coarse mesh cells to the corresponding cells on the
* fine mesh. This could in principle be generated by the function itself
* from the two DoFHandler objects, but since it is probably available
* anyway in programs that use different meshes, the function simply takes
* it as an argument.
*
* The computed constraints are entered into a variable of type
* ConstraintMatrix; previous contents are not deleted.
*/
template <int dim, int spacedim>
void
compute_intergrid_constraints (const DoFHandler<dim,spacedim> &coarse_grid,
const unsigned int coarse_component,
const DoFHandler<dim,spacedim> &fine_grid,
const unsigned int fine_component,
const InterGridMap<DoFHandler<dim,spacedim> > &coarse_to_fine_grid_map,
ConstraintMatrix &constraints);
/**
* This function generates a matrix such that when a vector of data with as
* many elements as there are degrees of freedom of this component on the
* coarse grid is multiplied to this matrix, we obtain a vector with as many
* elements as there are global degrees of freedom on the fine grid. All the
* elements of the other vector components of the finite element fields on
* the fine grid are not touched.
*
* Triangulation of the fine grid can be distributed. When called in
* parallel, each process has to have a copy of the coarse grid. In this
* case, function returns transfer representation for a set of locally owned
* cells.
*
* The output of this function is a compressed format that can be used to
* construct corresponding sparse transfer matrix.
*/
template <int dim, int spacedim>
void
compute_intergrid_transfer_representation (const DoFHandler<dim,spacedim> &coarse_grid,
const unsigned int coarse_component,
const DoFHandler<dim,spacedim> &fine_grid,
const unsigned int fine_component,
const InterGridMap<DoFHandler<dim,spacedim> > &coarse_to_fine_grid_map,
std::vector<std::map<types::global_dof_index, float> > &transfer_representation);
/**
* @}
*/
/**
* @name Periodic boundary conditions
* @{
*/
/**
* Insert the (algebraic) constraints due to periodic boundary conditions
* into a ConstraintMatrix @p constraint_matrix.
*
* Given a pair of not necessarily active boundary faces @p face_1 and @p
* face_2, this functions constrains all DoFs associated with the boundary
* described by @p face_1 to the respective DoFs of the boundary described
* by @p face_2. More precisely:
*
* If @p face_1 and @p face_2 are both active faces it adds the DoFs of @p
* face_1 to the list of constrained DoFs in @p constraint_matrix and adds
* entries to constrain them to the corresponding values of the DoFs on @p
* face_2. This happens on a purely algebraic level, meaning, the global DoF
* with (local face) index <tt>i</tt> on @p face_1 gets constraint to the
* DoF with (local face) index <tt>i</tt> on @p face_2 (possibly corrected
* for orientation, see below).
*
* Otherwise, if @p face_1 and @p face_2 are not active faces, this function
* loops recursively over the children of @p face_1 and @p face_2. If only
* one of the two faces is active, then we recursively iterate over the
* children of the non-active ones and make sure that the solution function
* on the refined side equals that on the non-refined face in much the same
* way as we enforce hanging node constraints at places where differently
* refined cells come together. (However, unlike hanging nodes, we do not
* enforce the requirement that there be only a difference of one refinement
* level between the two sides of the domain you would like to be periodic).
*
* This routine only constrains DoFs that are not already constrained. If
* this routine encounters a DoF that already is constrained (for instance
* by Dirichlet boundary conditions), the old setting of the constraint
* (dofs the entry is constrained to, inhomogeneities) is kept and nothing
* happens.
*
* The flags in the @p component_mask (see
* @ref GlossComponentMask)
* denote which components of the finite element space shall be constrained
* with periodic boundary conditions. If it is left as specified by the
* default value all components are constrained. If it is different from the
* default value, it is assumed that the number of entries equals the number
* of components of the finite element. This can be used to enforce
* periodicity in only one variable in a system of equations.
*
* @p face_orientation, @p face_flip and @p face_rotation describe an
* orientation that should be applied to @p face_1 prior to matching and
* constraining DoFs. This has nothing to do with the actual orientation of
* the given faces in their respective cells (which for boundary faces is
* always the default) but instead how you want to see periodicity to be
* enforced. For example, by using these flags, you can enforce a condition
* of the kind $u(0,y)=u(1,1-y)$ (i.e., a Moebius band) or in 3d a twisted
* torus. More precisely, these flags match local face DoF indices in the
* following manner:
*
* In 2d: <tt>face_orientation</tt> must always be <tt>true</tt>,
* <tt>face_rotation</tt> is always <tt>false</tt>, and face_flip has the
* meaning of <tt>line_flip</tt>; this implies e.g. for <tt>Q1</tt>:
*
* @code
*
* face_orientation = true, face_flip = false, face_rotation = false:
*
* face1: face2:
*
* 1 1
* | <--> |
* 0 0
*
* Resulting constraints: 0 <-> 0, 1 <-> 1
*
* (Numbers denote local face DoF indices.)
*
*
* face_orientation = true, face_flip = true, face_rotation = false:
*
* face1: face2:
*
* 0 1
* | <--> |
* 1 0
*
* Resulting constraints: 1 <-> 0, 0 <-> 1
* @endcode
*
* And similarly for the case of Q1 in 3d:
*
* @code
*
* face_orientation = true, face_flip = false, face_rotation = false:
*
* face1: face2:
*
* 2 - 3 2 - 3
* | | <--> | |
* 0 - 1 0 - 1
*
* Resulting constraints: 0 <-> 0, 1 <-> 1, 2 <-> 2, 3 <-> 3
*
* (Numbers denote local face DoF indices.)
*
*
* face_orientation = false, face_flip = false, face_rotation = false:
*
* face1: face2:
*
* 1 - 3 2 - 3
* | | <--> | |
* 0 - 2 0 - 1
*
* Resulting constraints: 0 <-> 0, 2 <-> 1, 1 <-> 2, 3 <-> 3
*
*
* face_orientation = true, face_flip = true, face_rotation = false:
*
* face1: face2:
*
* 1 - 0 2 - 3
* | | <--> | |
* 3 - 2 0 - 1
*
* Resulting constraints: 3 <-> 0, 2 <-> 1, 1 <-> 2, 0 <-> 3
*
*
* face_orientation = true, face_flip = false, face_rotation = true
*
* face1: face2:
*
* 0 - 2 2 - 3
* | | <--> | |
* 1 - 3 0 - 1
*
* Resulting constraints: 1 <-> 0, 3 <-> 1, 0 <-> 2, 2 <-> 3
*
* and any combination of that...
* @endcode
*
* Optionally a matrix @p matrix along with an std::vector @p
* first_vector_components can be specified that describes how DoFs on @p
* face_1 should be modified prior to constraining to the DoFs of @p face_2.
* Here, two declarations are possible: If the std::vector @p
* first_vector_components is non empty the matrix is interpreted as a @p
* dim $\times$ @p dim rotation matrix that is applied to all vector valued
* blocks listed in @p first_vector_components of the FESystem. If @p
* first_vector_components is empty the matrix is interpreted as an
* interpolation matrix with size no_face_dofs $\times$ no_face_dofs.
*
* Detailed information can be found in the see
* @ref GlossPeriodicConstraints "Glossary entry on periodic boundary conditions".
*
* @author Matthias Maier, 2012 - 2015
*/
template<typename FaceIterator>
void
make_periodicity_constraints
(const FaceIterator &face_1,
const typename identity<FaceIterator>::type &face_2,
dealii::ConstraintMatrix &constraint_matrix,
const ComponentMask &component_mask = ComponentMask(),
const bool face_orientation = true,
const bool face_flip = false,
const bool face_rotation = false,
const FullMatrix<double> &matrix = FullMatrix<double>(),
const std::vector<unsigned int> &first_vector_components = std::vector<unsigned int>());
/**
* Insert the (algebraic) constraints due to periodic boundary conditions
* into a ConstraintMatrix @p constraint_matrix.
*
* This is the main high level interface for above low level variant of
* make_periodicity_constraints(). It takes a std::vector @p periodic_faces
* as argument and applies above make_periodicity_constraints() on each
* entry. @p periodic_faces can be created by
* GridTools::collect_periodic_faces.
*
* @note For DoFHandler objects that are built on a
* parallel::distributed::Triangulation object
* parallel::distributed::Triangulation::add_periodicity has to be called
* before calling this function..
*
* @see
* @ref GlossPeriodicConstraints "Glossary entry on periodic boundary conditions"
* and step-45 for further information.
*
* @author Daniel Arndt, Matthias Maier, 2013 - 2015
*/
template<typename DoFHandlerType>
void
make_periodicity_constraints
(const std::vector<GridTools::PeriodicFacePair<typename DoFHandlerType::cell_iterator> >
&periodic_faces,
dealii::ConstraintMatrix &constraint_matrix,
const ComponentMask &component_mask = ComponentMask(),
const std::vector<unsigned int> &first_vector_components = std::vector<unsigned int>());
/**
* Insert the (algebraic) constraints due to periodic boundary conditions
* into a ConstraintMatrix @p constraint_matrix.
*
* This function serves as a high level interface for the
* make_periodicity_constraints() function.
*
* Define a 'first' boundary as all boundary faces having boundary_id @p
* b_id1 and a 'second' boundary consisting of all faces belonging to @p
* b_id2.
*
* This function tries to match all faces belonging to the first boundary
* with faces belonging to the second boundary with the help of
* orthogonal_equality().
*
* If this matching is successful it constrains all DoFs associated with the
* 'first' boundary to the respective DoFs of the 'second' boundary
* respecting the relative orientation of the two faces.
*
* @note: This function is a convenience wrapper. It internally calls
* GridTools::collect_periodic_faces() with the supplied paramaters and
* feeds the output to above make_periodicity_constraints() variant. If you
* need more functionality use GridTools::collect_periodic_faces() directly.
*
* @see
* @ref GlossPeriodicConstraints "Glossary entry on periodic boundary conditions"
* for further information.
*
* @author Matthias Maier, 2012
*/
template<typename DoFHandlerType>
void
make_periodicity_constraints
(const DoFHandlerType &dof_handler,
const types::boundary_id b_id1,
const types::boundary_id b_id2,
const int direction,
dealii::ConstraintMatrix &constraint_matrix,
const ComponentMask &component_mask = ComponentMask());
/**
* This compatibility version of make_periodicity_constraints only works on
* grids with cells in
* @ref GlossFaceOrientation "standard orientation".
*
* Instead of defining a 'first' and 'second' boundary with the help of two
* boundary_ids this function defines a 'left' boundary as all faces with
* local face index <code>2*dimension</code> and boundary indicator @p b_id
* and, similarly, a 'right' boundary consisting of all face with local face
* index <code>2*dimension+1</code> and boundary indicator @p b_id.
*
* @note This version of make_periodicity_constraints will not work on
* meshes with cells not in
* @ref GlossFaceOrientation "standard orientation".
*
* @note: This function is a convenience wrapper. It internally calls
* GridTools::collect_periodic_faces() with the supplied paramaters and
* feeds the output to above make_periodicity_constraints() variant. If you
* need more functionality use GridTools::collect_periodic_faces() directly.
*
* @see
* @ref GlossPeriodicConstraints "Glossary entry on periodic boundary conditions"
* for further information.
*/
template<typename DoFHandlerType>
void
make_periodicity_constraints
(const DoFHandlerType &dof_handler,
const types::boundary_id b_id,
const int direction,
dealii::ConstraintMatrix &constraint_matrix,
const ComponentMask &component_mask = ComponentMask());
/**
* Take a vector of values which live on cells (e.g. an error per cell) and
* distribute it to the dofs in such a way that a finite element field
* results, which can then be further processed, e.g. for output. You should
* note that the resulting field will not be continuous at hanging nodes.
* This can, however, easily be arranged by calling the appropriate @p
* distribute function of a ConstraintMatrix object created for this
* DoFHandler object, after the vector has been fully assembled.
*
* It is assumed that the number of elements in @p cell_data equals the
* number of active cells and that the number of elements in @p dof_data
* equals <tt>dof_handler.n_dofs()</tt>.
*
* Note that the input vector may be a vector of any data type as long as it
* is convertible to @p double. The output vector, being a data vector on a
* DoF handler, always consists of elements of type @p double.
*
* In case the finite element used by this DoFHandler consists of more than
* one component, you need to specify which component in the output vector
* should be used to store the finite element field in; the default is zero
* (no other value is allowed if the finite element consists only of one
* component). All other components of the vector remain untouched, i.e.
* their contents are not changed.
*
* This function cannot be used if the finite element in use has shape
* functions that are non-zero in more than one vector component (in deal.II
* speak: they are non-primitive).
*/
template <typename DoFHandlerType, typename Number>
void
distribute_cell_to_dof_vector (const DoFHandlerType &dof_handler,
const Vector<Number> &cell_data,
Vector<double> &dof_data,
const unsigned int component = 0);
/**
* @}
*/
/**
* @name Identifying subsets of degrees of freedom with particular
* properties
* @{
*/
/**
* Extract the indices of the degrees of freedom belonging to certain vector
* components of a vector-valued finite element. The @p component_mask
* defines which components or blocks of an FESystem are to be extracted
* from the DoFHandler @p dof. The entries in the output array @p
* selected_dofs corresponding to degrees of freedom belonging to these
* components are then flagged @p true, while all others are set to @p
* false.
*
* The size of @p component_mask must be compatible with the number of
* components in the FiniteElement used by @p dof. The size of @p
* selected_dofs must equal DoFHandler::n_dofs(). Previous contents of this
* array are overwritten.
*
* If the finite element under consideration is not primitive, i.e., some or
* all of its shape functions are non-zero in more than one vector component
* (which holds, for example, for FE_Nedelec or FE_RaviartThomas elements),
* then shape functions cannot be associated with a single vector component.
* In this case, if <em>one</em> shape vector component of this element is
* flagged in @p component_mask (see
* @ref GlossComponentMask),
* then this is equivalent to selecting <em>all</em> vector components
* corresponding to this non-primitive base element.
*/
template <int dim, int spacedim>
void
extract_dofs (const DoFHandler<dim,spacedim> &dof_handler,
const ComponentMask &component_mask,
std::vector<bool> &selected_dofs);
/**
* The same function as above, but for a hp::DoFHandler.
*/
template <int dim, int spacedim>
void
extract_dofs (const hp::DoFHandler<dim,spacedim> &dof_handler,
const ComponentMask &component_mask,
std::vector<bool> &selected_dofs);
/**
* This function is the equivalent to the DoFTools::extract_dofs() functions
* above except that the selection of which degrees of freedom to extract is
* not done based on components (see
* @ref GlossComponent)
* but instead based on whether they are part of a particular block (see
* @ref GlossBlock).
* Consequently, the second argument is not a ComponentMask but a BlockMask
* object.
*
* @param dof_handler The DoFHandler object from which to extract degrees of
* freedom
* @param block_mask The block mask that describes which blocks to consider
* (see
* @ref GlossBlockMask)
* @param selected_dofs A vector of length DoFHandler::n_dofs() in which
* those entries are true that correspond to the selected blocks.
*/
template <int dim, int spacedim>
void
extract_dofs (const DoFHandler<dim,spacedim> &dof_handler,
const BlockMask &block_mask,
std::vector<bool> &selected_dofs);
/**
* The same function as above, but for a hp::DoFHandler.
*/
template <int dim, int spacedim>
void
extract_dofs (const hp::DoFHandler<dim,spacedim> &dof_handler,
const BlockMask &block_mask,
std::vector<bool> &selected_dofs);
/**
* Do the same thing as the corresponding extract_dofs() function for one
* level of a multi-grid DoF numbering.
*/
template <typename DoFHandlerType>
void
extract_level_dofs (const unsigned int level,
const DoFHandlerType &dof,
const ComponentMask &component_mask,
std::vector<bool> &selected_dofs);
/**
* Do the same thing as the corresponding extract_dofs() function for one
* level of a multi-grid DoF numbering.
*/
template <typename DoFHandlerType>
void
extract_level_dofs (const unsigned int level,
const DoFHandlerType &dof,
const BlockMask &component_mask,
std::vector<bool> &selected_dofs);
/**
* Extract all degrees of freedom which are at the boundary and belong to
* specified components of the solution. The function returns its results in
* the last non-default-valued parameter which contains @p true if a degree
* of freedom is at the boundary and belongs to one of the selected
* components, and @p false otherwise. The function is used in step-15.
*
* By specifying the @p boundary_id variable, you can select which boundary
* indicators the faces have to have on which the degrees of freedom are
* located that shall be extracted. If it is an empty list, then all
* boundary indicators are accepted.
*
* The size of @p component_mask (see
* @ref GlossComponentMask)
* shall equal the number of components in the finite element used by @p
* dof. The size of @p selected_dofs shall equal
* <tt>dof_handler.n_dofs()</tt>. Previous contents of this array or
* overwritten.
*
* Using the usual convention, if a shape function is non-zero in more than
* one component (i.e. it is non-primitive), then the element in the
* component mask is used that corresponds to the first non-zero components.
* Elements in the mask corresponding to later components are ignored.
*
* @note This function will not work for DoFHandler objects that are built
* on a parallel::distributed::Triangulation object. The reasons is that the
* output argument @p selected_dofs has to have a length equal to <i>all</i>
* global degrees of freedom. Consequently, this does not scale to very
* large problems. If you need the functionality of this function for
* parallel triangulations, then you need to use the other
* DoFTools::extract_boundary_dofs function.
*
* @param dof_handler The object that describes which degrees of freedom
* live on which cell
* @param component_mask A mask denoting the vector components of the finite
* element that should be considered (see also
* @ref GlossComponentMask).
* @param selected_dofs The IndexSet object that is returned and that will
* contain the indices of degrees of freedom that are located on the
* boundary (and correspond to the selected vector components and boundary
* indicators, depending on the values of the @p component_mask and @p
* boundary_ids arguments).
* @param boundary_ids If empty, this function extracts the indices of the
* degrees of freedom for all parts of the boundary. If it is a non- empty
* list, then the function only considers boundary faces with the boundary
* indicators listed in this argument.
*
* @see
* @ref GlossBoundaryIndicator "Glossary entry on boundary indicators"
*/
template <typename DoFHandlerType>
void
extract_boundary_dofs (const DoFHandlerType &dof_handler,
const ComponentMask &component_mask,
std::vector<bool> &selected_dofs,
const std::set<types::boundary_id> &boundary_ids = std::set<types::boundary_id>());
/**
* This function does the same as the previous one but it returns its result
* as an IndexSet rather than a std::vector@<bool@>. Thus, it can also be
* called for DoFHandler objects that are defined on
* parallel::distributed::Triangulation objects.
*
* @note If the DoFHandler object is indeed defined on a
* parallel::distributed::Triangulation, then the @p selected_dofs index set
* will contain only those degrees of freedom on the boundary that belong to
* the locally relevant set (see
* @ref GlossLocallyRelevantDof "locally relevant DoFs").
*
* @param dof_handler The object that describes which degrees of freedom
* live on which cell
* @param component_mask A mask denoting the vector components of the finite
* element that should be considered (see also
* @ref GlossComponentMask).
* @param selected_dofs The IndexSet object that is returned and that will
* contain the indices of degrees of freedom that are located on the
* boundary (and correspond to the selected vector components and boundary
* indicators, depending on the values of the @p component_mask and @p
* boundary_ids arguments).
* @param boundary_ids If empty, this function extracts the indices of the
* degrees of freedom for all parts of the boundary. If it is a non- empty
* list, then the function only considers boundary faces with the boundary
* indicators listed in this argument.
*
* @see
* @ref GlossBoundaryIndicator "Glossary entry on boundary indicators"
*/
template <typename DoFHandlerType>
void
extract_boundary_dofs (const DoFHandlerType &dof_handler,
const ComponentMask &component_mask,
IndexSet &selected_dofs,
const std::set<types::boundary_id> &boundary_ids = std::set<types::boundary_id>());
/**
* This function is similar to the extract_boundary_dofs() function but it
* extracts those degrees of freedom whose shape functions are nonzero on at
* least part of the selected boundary. For continuous elements, this is
* exactly the set of shape functions whose degrees of freedom are defined
* on boundary faces. On the other hand, if the finite element in used is a
* discontinuous element, all degrees of freedom are defined in the inside
* of cells and consequently none would be boundary degrees of freedom.
* Several of those would have shape functions that are nonzero on the
* boundary, however. This function therefore extracts all those for which
* the FiniteElement::has_support_on_face function says that it is nonzero
* on any face on one of the selected boundary parts.
*
* @see
* @ref GlossBoundaryIndicator "Glossary entry on boundary indicators"
*/
template <typename DoFHandlerType>
void
extract_dofs_with_support_on_boundary (const DoFHandlerType &dof_handler,
const ComponentMask &component_mask,
std::vector<bool> &selected_dofs,
const std::set<types::boundary_id> &boundary_ids = std::set<types::boundary_id>());
/**
* Extract a vector that represents the constant modes of the DoFHandler for
* the components chosen by <tt>component_mask</tt> (see
* @ref GlossComponentMask).
* The constant modes on a discretization are the null space of a Laplace
* operator on the selected components with Neumann boundary conditions
* applied. The null space is a necessary ingredient for obtaining a good
* AMG preconditioner when using the class
* TrilinosWrappers::PreconditionAMG. Since the ML AMG package only works
* on algebraic properties of the respective matrix, it has no chance to
* detect whether the matrix comes from a scalar or a vector valued problem.
* However, a near null space supplies exactly the needed information about
* the components placement of vector components within the matrix. The null
* space (or rather, the constant modes) is provided by the finite element
* underlying the given DoFHandler and for most elements, the null space
* will consist of as many vectors as there are true arguments in
* <tt>component_mask</tt> (see
* @ref GlossComponentMask),
* each of which will be one in one vector component and zero in all others.
* However, the representation of the constant function for e.g. FE_DGP is
* different (the first component on each element one, all other components
* zero), and some scalar elements may even have two constant modes
* (FE_Q_DG0). Therefore, we store this object in a vector of vectors, where
* the outer vector contains the collection of the actual constant modes on
* the DoFHandler. Each inner vector has as many components as there are
* (locally owned) degrees of freedom in the selected components. Note that
* any matrix associated with this null space must have been constructed
* using the same <tt>component_mask</tt> argument, since the numbering of
* DoFs is done relative to the selected dofs, not to all dofs.
*
* The main reason for this program is the use of the null space with the
* AMG preconditioner.
*/
template <typename DoFHandlerType>
void
extract_constant_modes (const DoFHandlerType &dof_handler,
const ComponentMask &component_mask,
std::vector<std::vector<bool> > &constant_modes);
/**
* @}
*/
/**
* @name Hanging nodes
* @{
*/
/**
* Select all dofs that will be constrained by interface constraints, i.e.
* all hanging nodes.
*
* The size of @p selected_dofs shall equal <tt>dof_handler.n_dofs()</tt>.
* Previous contents of this array or overwritten.
*/
template <int dim, int spacedim>
void
extract_hanging_node_dofs (const DoFHandler<dim,spacedim> &dof_handler,
std::vector<bool> &selected_dofs);
//@}
/**
* @name Parallelization and domain decomposition
* @{
*/
/**
* Flag all those degrees of freedom which are on cells with the given
* subdomain id. Note that DoFs on faces can belong to cells with differing
* subdomain ids, so the sets of flagged degrees of freedom are not mutually
* exclusive for different subdomain ids.
*
* If you want to get a unique association of degree of freedom with
* subdomains, use the @p get_subdomain_association function.
*/
template <typename DoFHandlerType>
void
extract_subdomain_dofs (const DoFHandlerType &dof_handler,
const types::subdomain_id subdomain_id,
std::vector<bool> &selected_dofs);
/**
* Extract the set of global DoF indices that are owned by the current
* processor. For regular DoFHandler objects, this set is the complete set
* with all DoF indices. In either case, it equals what
* DoFHandler::locally_owned_dofs() returns.
*/
template <typename DoFHandlerType>
void
extract_locally_owned_dofs (const DoFHandlerType &dof_handler,
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
* @ref GlossArtificialCell "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.
*/
template <typename DoFHandlerType>
void
extract_locally_active_dofs (const DoFHandlerType &dof_handler,
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
* @ref GlossArtificialCell "the glossary").
*/
template <typename DoFHandlerType>
void
extract_locally_relevant_dofs (const DoFHandlerType &dof_handler,
IndexSet &dof_set);
/**
*
* For each processor, determine the set of locally owned degrees of freedom
* as an IndexSet. This function then returns a vector of index sets, where
* the vector has size equal to the number of MPI processes that participate
* in the DoF handler object.
*
* The function can be used for objects of type dealii::Triangulation or
* parallel::shared::Triangulation. It will not work for objects of type
* parallel::distributed::Triangulation since for such triangulations we do
* not have information about all cells of the triangulation available
* locally, and consequently can not say anything definitive about the
* degrees of freedom active on other processors' locally owned cells.
*
* @author Denis Davydov, 2015
*/
template <typename DoFHandlerType>
std::vector<IndexSet>
locally_owned_dofs_per_subdomain (const DoFHandlerType &dof_handler);
/**
*
* For each processor, determine the set of locally relevant degrees of
* freedom as an IndexSet. This function then returns a vector of index
* sets, where the vector has size equal to the number of MPI processes that
* participate in the DoF handler object.
*
* The function can be used for objects of type dealii::Triangulation or
* parallel::shared::Triangulation. It will not work for objects of type
* parallel::distributed::Triangulation since for such triangulations we do
* not have information about all cells of the triangulation available
* locally, and consequently can not say anything definitive about the
* degrees of freedom active on other processors' locally owned cells.
*
* @author Jean-Paul Pelteret, 2015
*/
template <typename DoFHandlerType>
std::vector<IndexSet>
locally_relevant_dofs_per_subdomain (const DoFHandlerType &dof_handler);
/**
* Same as extract_locally_relevant_dofs() but for multigrid DoFs for the
* given @p level.
*/
template <typename DoFHandlerType>
void
extract_locally_relevant_level_dofs (const DoFHandlerType &dof_handler,
const unsigned int level,
IndexSet &dof_set);
/**
* For each degree of freedom, return in the output array to which subdomain
* (as given by the <tt>cell->subdomain_id()</tt> function) it belongs. The
* output array is supposed to have the right size already when calling this
* function.
*
* Note that degrees of freedom associated with faces, edges, and vertices
* may be associated with multiple subdomains if they are sitting on
* partition boundaries. In these cases, we put them into one of the
* associated partitions in an undefined way. This may sometimes lead to
* different numbers of degrees of freedom in partitions, even if the number
* of cells is perfectly equidistributed. While this is regrettable, it is
* not a problem in practice since the number of degrees of freedom on
* partition boundaries is asymptotically vanishing as we refine the mesh as
* long as the number of partitions is kept constant.
*
* This function returns the association of each DoF with one subdomain. If
* you are looking for the association of each @em cell with a subdomain,
* either query the <tt>cell->subdomain_id()</tt> function, or use the
* <tt>GridTools::get_subdomain_association</tt> function.
*
* Note that this function is of questionable use for DoFHandler objects
* built on parallel::distributed::Triangulation since in that case
* ownership of individual degrees of freedom by MPI processes is controlled
* by the DoF handler object, not based on some geometric algorithm in
* conjunction with subdomain id. In particular, the degrees of freedom
* identified by the functions in this namespace as associated with a
* subdomain are not the same the DoFHandler class identifies as those it
* owns.
*/
template <typename DoFHandlerType>
void
get_subdomain_association (const DoFHandlerType &dof_handler,
std::vector<types::subdomain_id> &subdomain);
/**
* Count how many degrees of freedom are uniquely associated with the given
* @p subdomain index.
*
* Note that there may be rare cases where cells with the given @p subdomain
* index exist, but none of its degrees of freedom are actually associated
* with it. In that case, the returned value will be zero.
*
* This function will generate an exception if there are no cells with the
* given @p subdomain index.
*
* This function returns the number of DoFs associated with one subdomain.
* If you are looking for the association of @em cells with this subdomain,
* use the <tt>GridTools::count_cells_with_subdomain_association</tt>
* function.
*
* Note that this function is of questionable use for DoFHandler objects
* built on parallel::distributed::Triangulation since in that case
* ownership of individual degrees of freedom by MPI processes is controlled
* by the DoF handler object, not based on some geometric algorithm in
* conjunction with subdomain id. In particular, the degrees of freedom
* identified by the functions in this namespace as associated with a
* subdomain are not the same the DoFHandler class identifies as those it
* owns.
*/
template <typename DoFHandlerType>
unsigned int
count_dofs_with_subdomain_association (const DoFHandlerType &dof_handler,
const types::subdomain_id subdomain);
/**
* Count how many degrees of freedom are uniquely associated with the given
* @p subdomain index.
*
* This function does what the previous one does except that it splits the
* result among the vector components of the finite element in use by the
* DoFHandler object. The last argument (which must have a length equal to
* the number of vector components) will therefore store how many degrees of
* freedom of each vector component are associated with the given subdomain.
*
* Note that this function is of questionable use for DoFHandler objects
* built on parallel::distributed::Triangulation since in that case
* ownership of individual degrees of freedom by MPI processes is controlled
* by the DoF handler object, not based on some geometric algorithm in
* conjunction with subdomain id. In particular, the degrees of freedom
* identified by the functions in this namespace as associated with a
* subdomain are not the same the DoFHandler class identifies as those it
* owns.
*/
template <typename DoFHandlerType>
void
count_dofs_with_subdomain_association (const DoFHandlerType &dof_handler,
const types::subdomain_id subdomain,
std::vector<unsigned int> &n_dofs_on_subdomain);
/**
* Return a set of indices that denotes the degrees of freedom that live on
* the given subdomain, i.e. that are on cells owned by the current
* processor. Note that this includes the ones that this subdomain "owns"
* (i.e. the ones for which get_subdomain_association() returns a value
* equal to the subdomain given here and that are selected by the
* extract_locally_owned_dofs() function) but also all of those that sit on
* the boundary between the given subdomain and other subdomain. In essence,
* degrees of freedom that sit on boundaries between subdomain will be in
* the index sets returned by this function for more than one subdomain.
*
* Note that this function is of questionable use for DoFHandler objects
* built on parallel::distributed::Triangulation since in that case
* ownership of individual degrees of freedom by MPI processes is controlled
* by the DoF handler object, not based on some geometric algorithm in
* conjunction with subdomain id. In particular, the degrees of freedom
* identified by the functions in this namespace as associated with a
* subdomain are not the same the DoFHandler class identifies as those it
* owns.
*/
template <typename DoFHandlerType>
IndexSet
dof_indices_with_subdomain_association (const DoFHandlerType &dof_handler,
const types::subdomain_id subdomain);
// @}
/**
* @name DoF indices on patches of cells
*
* Create structures containing a large set of degrees of freedom for small
* patches of cells. The resulting objects can be used in RelaxationBlockSOR
* and related classes to implement Schwarz preconditioners and smoothers,
* where the subdomains consist of small numbers of cells only.
*/
//@{
/**
* Create an incidence matrix that for every cell on a given level of a
* multilevel DoFHandler flags which degrees of freedom are associated with
* the corresponding cell. This data structure is a matrix with as many rows
* as there are cells on a given level, as many columns as there are degrees
* of freedom on this level, and entries that are either true or false. This
* data structure is conveniently represented by a SparsityPattern object.
*
* @note The ordering of rows (cells) follows the ordering of the standard
* cell iterators.
*/
template <typename DoFHandlerType, class Sparsity>
void make_cell_patches(Sparsity &block_list,
const DoFHandlerType &dof_handler,
const unsigned int level,
const std::vector<bool> &selected_dofs = std::vector<bool>(),
types::global_dof_index offset = 0);
/**
* Create an incidence matrix that for every vertex on a given level of a
* multilevel DoFHandler flags which degrees of freedom are associated with
* the adjacent cells. This data structure is a matrix with as many rows as
* there are vertices on a given level, as many columns as there are degrees
* of freedom on this level, and entries that are either true or false. This
* data structure is conveniently represented by a SparsityPattern object.
* The sparsity pattern may be empty when entering this function and will be
* reinitialized to the correct size.
*
* The function has some boolean arguments (listed below) controlling
* details of the generated patches. The default settings are those for
* Arnold-Falk-Winther type smoothers for divergence and curl conforming
* finite elements with essential boundary conditions. Other applications
* are possible, in particular changing <tt>boundary_patches</tt> for non-
* essential boundary conditions.
*
* @arg <tt>block_list</tt>: the SparsityPattern into which the patches will
* be stored.
*
* @arg <tt>dof_handler</tt>: The multilevel dof handler providing the
* topology operated on.
*
* @arg <tt>interior_dofs_only</tt>: for each patch of cells around a
* vertex, collect only the interior degrees of freedom of the patch and
* disregard those on the boundary of the patch. This is for instance the
* setting for smoothers of Arnold-Falk-Winther type.
*
* @arg <tt>boundary_patches</tt>: include patches around vertices at the
* boundary of the domain. If not, only patches around interior vertices
* will be generated.
*
* @arg <tt>level_boundary_patches</tt>: same for refinement edges towards
* coarser cells.
*
* @arg <tt>single_cell_patches</tt>: if not true, patches containing a
* single cell are eliminated.
*/
template <typename DoFHandlerType>
void make_vertex_patches(SparsityPattern &block_list,
const DoFHandlerType &dof_handler,
const unsigned int level,
const bool interior_dofs_only,
const bool boundary_patches = false,
const bool level_boundary_patches = false,
const bool single_cell_patches = false);
/**
* Create an incidence matrix that for every cell on a given level of a
* multilevel DoFHandler flags which degrees of freedom are associated with
* children of this cell. This data structure is conveniently represented by
* a SparsityPattern object.
*
* The function thus creates a sparsity pattern which in each row (with rows
* corresponding to the cells on this level) lists the degrees of freedom
* associated to the cells that are the children of this cell. The DoF
* indices used here are level dof indices of a multilevel hierarchy, i.e.,
* they may be associated with children that are not themselves active. The
* sparsity pattern may be empty when entering this function and will be
* reinitialized to the correct size.
*
* The function has some boolean arguments (listed below) controlling
* details of the generated patches. The default settings are those for
* Arnold-Falk-Winther type smoothers for divergence and curl conforming
* finite elements with essential boundary conditions. Other applications
* are possible, in particular changing <tt>boundary_dofs</tt> for non-
* essential boundary conditions.
*
* @arg <tt>block_list</tt>: the SparsityPattern into which the patches will
* be stored.
*
* @arg <tt>dof_handler</tt>: The multilevel dof handler providing the
* topology operated on.
*
* @arg <tt>interior_dofs_only</tt>: for each patch of cells around a
* vertex, collect only the interior degrees of freedom of the patch and
* disregard those on the boundary of the patch. This is for instance the
* setting for smoothers of Arnold-Falk-Winther type.
*
* @arg <tt>boundary_dofs</tt>: include degrees of freedom, which would have
* excluded by <tt>interior_dofs_only</tt>, but are lying on the boundary of
* the domain, and thus need smoothing. This parameter has no effect if
* <tt>interior_dofs_only</tt> is false.
*/
template <typename DoFHandlerType>
void make_child_patches(SparsityPattern &block_list,
const DoFHandlerType &dof_handler,
const unsigned int level,
const bool interior_dofs_only,
const bool boundary_dofs = false);
/**
* Create a block list with only a single patch, which in turn contains all
* degrees of freedom on the given level.
*
* This function is mostly a closure on level 0 for functions like
* make_child_patches() and make_vertex_patches(), which may produce an
* empty patch list.
*
* @arg <tt>block_list</tt>: the SparsityPattern into which the patches will
* be stored.
*
* @arg <tt>dof_handler</tt>: The multilevel dof handler providing the
* topology operated on.
*
* @arg <tt>level</tt> The grid level used for building the list.
*
* @arg <tt>interior_dofs_only</tt>: if true, exclude degrees of freedom on
* the boundary of the domain.
*/
template <typename DoFHandlerType>
void make_single_patch(SparsityPattern &block_list,
const DoFHandlerType &dof_handler,
const unsigned int level,
const bool interior_dofs_only = false);
/**
* @}
*/
/**
* @name Counting degrees of freedom and related functions
* @{
*/
/**
* Count how many degrees of freedom out of the total number belong to each
* component. If the number of components the finite element has is one
* (i.e. you only have one scalar variable), then the number in this
* component obviously equals the total number of degrees of freedom.
* Otherwise, the sum of the DoFs in all the components needs to equal the
* total number.
*
* However, the last statement does not hold true if the finite element is
* not primitive, i.e. some or all of its shape functions are non-zero in
* more than one vector component. This applies, for example, to the Nedelec
* or Raviart-Thomas elements. In this case, a degree of freedom is counted
* in each component in which it is non-zero, so that the sum mentioned
* above is greater than the total number of degrees of freedom.
*
* This behavior can be switched off by the optional parameter
* <tt>vector_valued_once</tt>. If this is <tt>true</tt>, the number of
* components of a nonprimitive vector valued element is collected only in
* the first component. All other components will have a count of zero.
*
* The additional optional argument @p target_component allows for a re-
* sorting and grouping of components. To this end, it contains for each
* component the component number it shall be counted as. Having the same
* number entered several times sums up several components as the same. One
* of the applications of this argument is when you want to form block
* matrices and vectors, but want to pack several components into the same
* block (for example, when you have @p dim velocities and one pressure, to
* put all velocities into one block, and the pressure into another).
*
* The result is returned in @p dofs_per_component. Note that the size of @p
* dofs_per_component needs to be enough to hold all the indices specified
* in @p target_component. If this is not the case, an assertion is thrown.
* The indices not targeted by target_components are left untouched.
*/
template <typename DoFHandlerType>
void
count_dofs_per_component (const DoFHandlerType &dof_handler,
std::vector<types::global_dof_index> &dofs_per_component,
const bool vector_valued_once = false,
std::vector<unsigned int> target_component
= std::vector<unsigned int>());
/**
* Count the degrees of freedom in each block. This function is similar to
* count_dofs_per_component(), with the difference that the counting is done
* by blocks. See
* @ref GlossBlock "blocks"
* in the glossary for details. Again the vectors are assumed to have the
* correct size before calling this function. If this is not the case, an
* assertion is thrown.
*
* This function is used in the step-22, step-31, and step-32 tutorial
* programs.
*
* @pre The dofs_per_block variable has as many components as the finite
* element used by the dof_handler argument has blocks, or alternatively as
* many blocks as are enumerated in the target_blocks argument if given.
*/
template <typename DoFHandlerType>
void
count_dofs_per_block (const DoFHandlerType &dof,
std::vector<types::global_dof_index> &dofs_per_block,
const std::vector<unsigned int> &target_block
= std::vector<unsigned int>());
/**
* For each active cell of a DoFHandler or hp::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 non-hp DoFHandler objects given as first argument, the returned
* vector will consist of only zeros, indicating that all cells use the same
* finite element. For a hp::DoFHandler, the values may be different,
* though.
*/
template <typename DoFHandlerType>
void
get_active_fe_indices (const DoFHandlerType &dof_handler,
std::vector<unsigned int> &active_fe_indices);
/**
* Count how many degrees of freedom live on a set of cells (i.e., a patch)
* described by the argument.
*
* Patches are often used in defining error estimators that require the
* solution of a local problem on the patch surrounding each of the cells of
* the mesh. You can get a list of cells that form the patch around a given
* cell using GridTools::get_patch_around_cell(). This function is then
* useful in setting up the size of the linear system used to solve the
* local problem on the patch around a cell. The function
* DoFTools::get_dofs_on_patch() will then help to make the connection
* between global degrees of freedom and the local ones.
*
* @tparam DoFHandlerType A type that is either DoFHandler or
* hp::DoFHandler. In C++, the compiler can not determine the type of
* <code>DoFHandlerType</code> from the function call. You need to specify
* it as an explicit template argument following the function name.
*
* @param patch A collection of cells within an object of type
* DoFHandlerType
*
* @return The number of degrees of freedom associated with the cells of
* this patch.
*
* @note In the context of a parallel distributed computation, it only makes
* sense to call this function on patches around locally owned cells. This
* is because the neighbors of locally owned cells are either locally owned
* themselves, or ghost cells. For both, we know that these are in fact the
* real cells of the complete, parallel triangulation. We can also query the
* degrees of freedom on these. In other words, this function can only work
* if all cells in the patch are either locally owned or ghost cells.
*
* @author Arezou Ghesmati, Wolfgang Bangerth, 2014
*/
template <typename DoFHandlerType>
unsigned int
count_dofs_on_patch (const std::vector<typename DoFHandlerType::active_cell_iterator> &patch);
/**
* Return the set of degrees of freedom that live on a set of cells (i.e., a
* patch) described by the argument.
*
* Patches are often used in defining error estimators that require the
* solution of a local problem on the patch surrounding each of the cells of
* the mesh. You can get a list of cells that form the patch around a given
* cell using GridTools::get_patch_around_cell(). While
* DoFTools::count_dofs_on_patch() can be used to determine the size of
* these local problems, so that one can assemble the local system and then
* solve it, it is still necessary to provide a mapping between the global
* indices of the degrees of freedom that live on the patch and a local
* enumeration. This function provides such a local enumeration by returning
* the set of degrees of freedom that live on the patch.
*
* Since this set is returned in the form of a std::vector, one can also
* think of it as a mapping
* @code
* i -> global_dof_index
* @endcode
* where <code>i</code> is an index into the returned vector (i.e., a the
* <i>local</i> index of a degree of freedom on the patch) and
* <code>global_dof_index</code> is the global index of a degree of freedom
* located on the patch. The array returned has size equal to
* DoFTools::count_dofs_on_patch().
*
* @note The array returned is sorted by global DoF index. Consequently, if
* one considers the index into this array a local DoF index, then the local
* system that results retains the block structure of the global system.
*
* @tparam DoFHandlerType A type that is either DoFHandler or
* hp::DoFHandler. In C++, the compiler can not determine the type of
* <code>DoFHandlerType</code> from the function call. You need to specify
* it as an explicit template argument following the function name.
*
* @param patch A collection of cells within an object of type
* DoFHandlerType
*
* @return A list of those global degrees of freedom located on the patch,
* as defined above.
*
* @note In the context of a parallel distributed computation, it only makes
* sense to call this function on patches around locally owned cells. This
* is because the neighbors of locally owned cells are either locally owned
* themselves, or ghost cells. For both, we know that these are in fact the
* real cells of the complete, parallel triangulation. We can also query the
* degrees of freedom on these. In other words, this function can only work
* if all cells in the patch are either locally owned or ghost cells.
*
* @author Arezou Ghesmati, Wolfgang Bangerth, 2014
*/
template <typename DoFHandlerType>
std::vector<types::global_dof_index>
get_dofs_on_patch (const std::vector<typename DoFHandlerType::active_cell_iterator> &patch);
/**
* @}
*/
/**
* Create a mapping from degree of freedom indices to the index of that
* degree of freedom on the boundary. After this operation,
* <tt>mapping[dof]</tt> gives the index of the degree of freedom with
* global number @p dof in the list of degrees of freedom on the boundary.
* If the degree of freedom requested is not on the boundary, the value of
* <tt>mapping[dof]</tt> is @p invalid_dof_index. This function is mainly
* used when setting up matrices and vectors on the boundary from the trial
* functions, which have global numbers, while the matrices and vectors use
* numbers of the trial functions local to the boundary.
*
* Prior content of @p mapping is deleted.
*/
template <typename DoFHandlerType>
void
map_dof_to_boundary_indices (const DoFHandlerType &dof_handler,
std::vector<types::global_dof_index> &mapping);
/**
* Same as the previous function, except that only those parts of the
* boundary are considered for which the boundary indicator is listed in the
* second argument.
*
* See the general doc of this class for more information.
*
* @see
* @ref GlossBoundaryIndicator "Glossary entry on boundary indicators"
*/
template <typename DoFHandlerType>
void
map_dof_to_boundary_indices (const DoFHandlerType &dof_handler,
const std::set<types::boundary_id> &boundary_ids,
std::vector<types::global_dof_index> &mapping);
/**
* Return a list of support points (see this
* @ref GlossSupport "glossary entry")
* for all the degrees of freedom handled by this DoF handler object. This
* function, of course, only works if the finite element object used by the
* DoF handler object actually provides support points, i.e. no edge
* elements or the like. Otherwise, an exception is thrown.
*
* @pre The given array must have a length of as many elements as there are
* degrees of freedom.
*
* @note The precondition to this function that the output argument needs to
* have size equal to the total number of degrees of freedom makes this
* function unsuitable for the case that the given DoFHandler object derives
* from a parallel::distributed::Triangulation object. Consequently, this
* function will produce an error if called with such a DoFHandler.
*/
template <int dim, int spacedim>
void
map_dofs_to_support_points (const Mapping<dim,spacedim> &mapping,
const DoFHandler<dim,spacedim> &dof_handler,
std::vector<Point<spacedim> > &support_points);
/**
* Same as the previous function but for the hp case.
*/
template <int dim, int spacedim>
void
map_dofs_to_support_points (const dealii::hp::MappingCollection<dim,spacedim> &mapping,
const hp::DoFHandler<dim,spacedim> &dof_handler,
std::vector<Point<spacedim> > &support_points);
/**
* This function is a version of the above map_dofs_to_support_points
* function that doesn't simply return a vector of support points (see this
* @ref GlossSupport "glossary entry")
* with one entry for each global degree of freedom, but instead a map that
* maps from the DoFs index to its location. The point of this function is
* that it is also usable in cases where the DoFHandler is based on a
* parallel::distributed::Triangulation object. In such cases, each
* processor will not be able to determine the support point location of all
* DoFs, and worse no processor may be able to hold a vector that would
* contain the locations of all DoFs even if they were known. As a
* consequence, this function constructs a map from those DoFs for which we
* can know the locations (namely, those DoFs that are locally relevant (see
* @ref GlossLocallyRelevantDof "locally relevant DoFs")
* to their locations.
*
* For non-distributed triangulations, the map returned as @p support_points
* is of course dense, i.e., every DoF is to be found in it.
*
* @param mapping The mapping from the reference cell to the real cell on
* which DoFs are defined.
* @param dof_handler The object that describes which DoF indices live on
* which cell of the triangulation.
* @param support_points A map that for every locally relevant DoF index
* contains the corresponding location in real space coordinates. Previous
* content of this object is deleted in this function.
*/
template <int dim, int spacedim>
void
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);
/**
* Same as the previous function but for the hp case.
*/
template <int dim, int spacedim>
void
map_dofs_to_support_points (const dealii::hp::MappingCollection<dim,spacedim> &mapping,
const hp::DoFHandler<dim,spacedim> &dof_handler,
std::map<types::global_dof_index, Point<spacedim> > &support_points);
/**
* 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
* @ref GlossSupport "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.
*/
template <typename DoFHandlerType, class Comp>
void
map_support_points_to_dofs
(const Mapping<DoFHandlerType::dimension, DoFHandlerType::space_dimension> &mapping,
const DoFHandlerType &dof_handler,
std::map<Point<DoFHandlerType::space_dimension>, types::global_dof_index, Comp> &point_to_index_map);
/**
* Map a coupling table from the user friendly organization by components to
* the organization by blocks. Specializations of this function for
* DoFHandler and hp::DoFHandler are required due to the different results
* of their finite element access.
*
* The return vector will be initialized to the correct length inside this
* function.
*/
template <int dim, int spacedim>
void
convert_couplings_to_blocks (const hp::DoFHandler<dim,spacedim> &dof_handler,
const Table<2, Coupling> &table_by_component,
std::vector<Table<2,Coupling> > &tables_by_block);
/**
* Make a constraint matrix for the constraints that result from zero
* boundary values on the given boundary indicator.
*
* This function constrains all degrees of freedom on the given part of the
* boundary.
*
* A variant of this function with different arguments is used in step-36.
*
* @param dof The DoFHandler to work on.
* @param boundary_id The indicator of that part of the boundary for which
* constraints should be computed. If this number equals
* numbers::invalid_boundary_id then all boundaries of the domain will be
* treated.
* @param zero_boundary_constraints The constraint object into which the
* constraints will be written. The new constraints due to zero boundary
* values will simply be added, preserving any other constraints previously
* present. However, this will only work if the previous content of that
* object consists of constraints on degrees of freedom that are not located
* on the boundary treated here. If there are previously existing
* constraints for degrees of freedom located on the boundary, then this
* would constitute a conflict. See the
* @ref constraints
* module for handling the case where there are conflicting constraints on
* individual degrees of freedom.
* @param component_mask An optional component mask that restricts the
* functionality of this function to a subset of an FESystem. For non-
* @ref GlossPrimitive "primitive"
* shape functions, any degree of freedom is affected that belongs to a
* shape function where at least one of its nonzero components is affected
* by the component mask (see
* @ref GlossComponentMask).
* If this argument is omitted, all components of the finite element with
* degrees of freedom at the boundary will be considered.
*
* @ingroup constraints
*
* @see
* @ref GlossBoundaryIndicator "Glossary entry on boundary indicators"
*/
template <int dim, int spacedim, template <int, int> class DoFHandlerType>
void
make_zero_boundary_constraints (const DoFHandlerType<dim,spacedim> &dof,
const types::boundary_id boundary_id,
ConstraintMatrix &zero_boundary_constraints,
const ComponentMask &component_mask = ComponentMask());
/**
* Do the same as the previous function, except do it for all parts of the
* boundary, not just those with a particular boundary indicator. This
* function is then equivalent to calling the previous one with
* numbers::invalid_boundary_id as second argument.
*
* This function is used in step-36, for example.
*
* @ingroup constraints
*/
template <int dim, int spacedim, template <int, int> class DoFHandlerType>
void
make_zero_boundary_constraints (const DoFHandlerType<dim,spacedim> &dof,
ConstraintMatrix &zero_boundary_constraints,
const ComponentMask &component_mask = ComponentMask());
/**
* Map a coupling table from the user friendly organization by components to
* the organization by blocks. Specializations of this function for
* DoFHandler and hp::DoFHandler are required due to the different results
* of their finite element access.
*
* The return vector will be initialized to the correct length inside this
* function.
*/
template <int dim, int spacedim>
void
convert_couplings_to_blocks (const DoFHandler<dim,spacedim> &dof_handler,
const Table<2, Coupling> &table_by_component,
std::vector<Table<2,Coupling> > &tables_by_block);
/**
* Given a finite element and a table how the vector components of it couple
* with each other, compute and return a table that describes how the
* individual shape functions couple with each other.
*/
template <int dim, int spacedim>
Table<2,Coupling>
dof_couplings_from_component_couplings (const FiniteElement<dim,spacedim> &fe,
const Table<2,Coupling> &component_couplings);
/**
* Same function as above for a collection of finite elements, returning a
* collection of tables.
*
* The function currently treats DoFTools::Couplings::nonzero the same as
* DoFTools::Couplings::always .
*/
template <int dim, int spacedim>
std::vector<Table<2,Coupling> >
dof_couplings_from_component_couplings (const hp::FECollection<dim,spacedim> &fe,
const Table<2,Coupling> &component_couplings);
/**
* @todo Write description
*
* @ingroup Exceptions
*/
DeclException0 (ExcFiniteElementsDontMatch);
/**
* @todo Write description
*
* @ingroup Exceptions
*/
DeclException0 (ExcGridNotCoarser);
/**
* @todo Write description
*
* Exception
* @ingroup Exceptions
*/
DeclException0 (ExcGridsDontMatch);
/**
* The ::DoFHandler or hp::DoFHandler was not initialized with a finite
* element. Please call DoFHandler::distribute_dofs() etc. first.
*
* @ingroup Exceptions
*/
DeclException0 (ExcNoFESelected);
/**
* @todo Write description
*
* @ingroup Exceptions
*/
DeclException0 (ExcInvalidBoundaryIndicator);
}
/* ------------------------- inline functions -------------- */
#ifndef DOXYGEN
namespace DoFTools
{
/**
* Operator computing the maximum coupling out of two.
*
* @relates DoFTools
*/
inline
Coupling operator |= (Coupling &c1,
const Coupling c2)
{
if (c2 == always)
c1 = always;
else if (c1 != always && c2 == nonzero)
return c1 = nonzero;
return c1;
}
/**
* Operator computing the maximum coupling out of two.
*
* @relates DoFTools
*/
inline
Coupling operator | (const Coupling c1,
const Coupling c2)
{
if (c1 == always || c2 == always)
return always;
if (c1 == nonzero || c2 == nonzero)
return nonzero;
return none;
}
// ---------------------- inline and template functions --------------------
template <int dim, int spacedim>
inline
unsigned int
max_dofs_per_cell (const DoFHandler<dim,spacedim> &dh)
{
return dh.get_fe().dofs_per_cell;
}
template <int dim, int spacedim>
inline
unsigned int
max_dofs_per_face (const DoFHandler<dim,spacedim> &dh)
{
return dh.get_fe().dofs_per_face;
}
template <int dim, int spacedim>
inline
unsigned int
max_dofs_per_vertex (const DoFHandler<dim,spacedim> &dh)
{
return dh.get_fe().dofs_per_vertex;
}
template <int dim, int spacedim>
inline
unsigned int
n_components (const DoFHandler<dim,spacedim> &dh)
{
return dh.get_fe().n_components();
}
template <int dim, int spacedim>
inline
bool
fe_is_primitive (const DoFHandler<dim,spacedim> &dh)
{
return dh.get_fe().is_primitive();
}
template <int dim, int spacedim>
inline
unsigned int
max_dofs_per_cell (const hp::DoFHandler<dim,spacedim> &dh)
{
return dh.get_fe().max_dofs_per_cell ();
}
template <int dim, int spacedim>
inline
unsigned int
max_dofs_per_face (const hp::DoFHandler<dim,spacedim> &dh)
{
return dh.get_fe().max_dofs_per_face ();
}
template <int dim, int spacedim>
inline
unsigned int
max_dofs_per_vertex (const hp::DoFHandler<dim,spacedim> &dh)
{
return dh.get_fe().max_dofs_per_vertex ();
}
template <int dim, int spacedim>
inline
unsigned int
n_components (const hp::DoFHandler<dim,spacedim> &dh)
{
return dh.get_fe()[0].n_components();
}
template <int dim, int spacedim>
inline
bool
fe_is_primitive (const hp::DoFHandler<dim,spacedim> &dh)
{
return dh.get_fe()[0].is_primitive();
}
template <typename DoFHandlerType, class Comp>
void
map_support_points_to_dofs
(
const Mapping<DoFHandlerType::dimension,DoFHandlerType::space_dimension> &mapping,
const DoFHandlerType &dof_handler,
std::map<Point<DoFHandlerType::space_dimension>, types::global_dof_index, Comp> &point_to_index_map)
{
// let the checking of arguments be
// done by the function first
// called
std::vector<Point<DoFHandlerType::space_dimension> > support_points (dof_handler.n_dofs());
map_dofs_to_support_points (mapping, dof_handler, support_points);
// now copy over the results of the
// previous function into the
// output arg
point_to_index_map.clear ();
for (types::global_dof_index i=0; i<dof_handler.n_dofs(); ++i)
point_to_index_map[support_points[i]] = i;
}
}
#endif
DEAL_II_NAMESPACE_CLOSE
#endif
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