The cell will be or was refined.
\nThe children of this cell will be or were coarsened into this cell.
\nInvalid status. Will not occur for the user.
\nDefinition at line 30 of file cell_status.h.
\n \n \n \n"}, {"source1": "./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classAffineConstraints.html", "source2": "./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/classAffineConstraints.html", "unified_diff": "@@ -636,15 +636,15 @@\nConstructor. The supplied IndexSet defines for which indices this object will store constraints. In a calculation with a DoFHandler object based on parallel::distributed::Triangulation or parallel::shared::Triangulation, one should use the set of locally relevant DoFs (see GlossLocallyRelevantDof).
\nThe given IndexSet allows the AffineConstraints container to save memory by just not caring about degrees of freedom that are not of importance to the current processor. In contrast, in parallel computations, if you do not provide such an index set (here, or using the reinit() function that takes such an argument), the current object will allocate memory proportional to the total number of degrees of freedom (accumulated over all processes), which is clearly wasteful and not efficient – and should be considered a bug.
\n-Definition at line 2312 of file affine_constraints.h.
\n \nclear() the AffineConstraints object and supply an IndexSet that describes for which degrees of freedom this object can store constraints. See the discussion in the documentation of the constructor of this class that takes a single index set as argument.
\n-This function copies the content of constraints_in with DoFs that are element of the IndexSet filter. Elements that are not present in the IndexSet are ignored. All DoFs will be transformed to local index space of the filter, both the constrained DoFs and the other DoFs these entries are constrained to. The local index space of the filter is a contiguous numbering of all (global) DoFs that are elements in the filter.
If, for example, the filter represents the range [10,20), and the constraints object constraints_in includes the global indices {7,13,14}, the indices {3,4} are added to the calling constraints object (since 13 and 14 are elements in the filter and element 13 is the fourth element in the index, and 14 is the fifth).
This function provides an easy way to create a AffineConstraints for certain vector components in a vector-valued problem from a full AffineConstraints, i.e. extracting a diagonal subblock from a larger AffineConstraints. The block is specified by the IndexSet argument.
\n-This is the base class for block versions of the sparsity pattern and dynamic sparsity pattern classes. It has not much functionality, but only administrates an array of sparsity pattern objects and delegates work to them. It has mostly the same interface as has the SparsityPattern, and DynamicSparsityPattern, and simply transforms calls to its member functions to calls to the respective member functions of the member sparsity patterns.
\nThe largest difference between the SparsityPattern and DynamicSparsityPattern classes and this class is that mostly, the matrices have different properties and you will want to work on the blocks making up the matrix rather than the whole matrix. You can access the different blocks using the block(row,col) function.
Attention: this object is not automatically notified if the size of one of its subobjects' size is changed. After you initialize the sizes of the subobjects, you will therefore have to call the collect_sizes() function of this class! Note that, of course, all sub-matrices in a (block-)row have to have the same number of rows, and that all sub-matrices in a (block-)column have to have the same number of columns.
You will in general not want to use this class, but one of the derived classes.
\n-Definition at line 79 of file block_sparsity_pattern.h.
\n| using DoFHandler< dim, spacedim >::active_fe_index_type = types::fe_index | \n
The type in which we store the active FE index.
\n-Definition at line 536 of file dof_handler.h.
\n \nFor each locally owned cell, set the active finite element index to the corresponding value given in active_fe_indices.
The vector active_fe_indices needs to have as many entries as there are active cells. The FE indices must be in the order in which we iterate over active cells. Vector entries corresponding to active cells that are not locally owned are ignored.
Active FE indices will only be set for locally owned cells. Ghost and artificial cells will be ignored; no active FE index will be assigned to them. To exchange active FE indices on ghost cells, call distribute_dofs() afterwards.
\n-For each locally relevant cell, extract the active finite element index and fill the vector active_fe_indices in the order in which we iterate over active cells. This vector is resized, if necessary.
As we do not know the active FE index on artificial cells, they are set to the invalid value numbers::invalid_fe_index.
\nFor DoFHandler objects without hp-capabilities, the vector will consist of zeros, indicating that all cells use the same finite element. In hp-mode, the values may be different, though.
\nThe returned vector has as many entries as there are active cells.
\n-Invalid index of the finite element to be used on a given cell.
\n-Definition at line 528 of file dof_handler.h.
\n \nInvalid active FE index which will be used as a default value to determine whether a future FE index has been set or not.
\n-Definition at line 549 of file dof_handler.h.
\n \nThe same as above.
\n-The same as above.
\n-The same as above.
\n-Implementation of Arnold-Boffi-Falk (ABF) elements, conforming with the space Hdiv. These elements generate vector fields with normal components continuous between mesh cells.
\nThese elements are based on an article from Arnold, Boffi and Falk: Quadrilateral H(div) finite elements, SIAM J. Numer. Anal. Vol.42, No.6, pp.2429-2451
\nIn this article, the authors demonstrate that the usual RT elements and also BDM and other proposed finite dimensional subspaces of H(div) do not work properly on arbitrary FE grids. I.e. the convergence rates deteriorate on these meshes. As a solution the authors propose the ABF elements, which are implemented in this class.
\nThis class is not implemented for the codimension one case (spacedim != dim).
The interpolation operators associated with the RT element are constructed such that interpolation and computing the divergence are commuting operations. We require this from interpolating arbitrary functions as well as the restriction matrices. It can be achieved by two interpolation schemes, the simplified one in FE_RaviartThomasNodal and the original one here:
\nOn edges or faces, the node values are the moments of the normal component of the interpolated function with respect to the traces of the RT polynomials. Since the normal trace of the RT space of degree k on an edge/face is the space Qk, the moments are taken with respect to this space.
\nHigher order RT spaces have interior nodes. These are moments taken with respect to the gradient of functions in Qk on the cell (this space is the matching space for RTk in a mixed formulation).
\nThe Brezzi-Douglas-Marini element.
\nThe matching pressure space for FE_BDM of order k is the element FE_DGP of order k-1.
\nThe BDM element of order p has p+1 degrees of freedom on each face. These are implemented as the function values in the p+1 Gauss points on each face.
Additionally, for order greater or equal 2, we have additional p(p-1), the number of vector valued polynomials in Pp, interior degrees of freedom. These are the vector function values in the first p(p-1)/2 of the p2 Gauss points in the cell.
\n \n \nGinkgo matrix data structure. First template parameter is for storing the array of the non-zeros of the matrix. The second is for the row pointers and the column indices.
\n-Definition at line 195 of file ginkgo_solver.h.
\n \nGinkgo matrix data structure. First template parameter is for storing the array of the non-zeros of the matrix. The second is for the row pointers and the column indices.
\n-Definition at line 195 of file ginkgo_solver.h.
\n \nGinkgo matrix data structure. First template parameter is for storing the array of the non-zeros of the matrix. The second is for the row pointers and the column indices.
\n-Definition at line 195 of file ginkgo_solver.h.
\n \nGinkgo matrix data structure. First template parameter is for storing the array of the non-zeros of the matrix. The second is for the row pointers and the column indices.
\n-Definition at line 195 of file ginkgo_solver.h.
\n \nGinkgo matrix data structure. First template parameter is for storing the array of the non-zeros of the matrix. The second is for the row pointers and the column indices.
\n-Definition at line 195 of file ginkgo_solver.h.
\n \nGinkgo matrix data structure. First template parameter is for storing the array of the non-zeros of the matrix. The second is for the row pointers and the column indices.
\n-Definition at line 195 of file ginkgo_solver.h.
\n \nGinkgo matrix data structure. First template parameter is for storing the array of the non-zeros of the matrix. The second is for the row pointers and the column indices.
\n-Definition at line 195 of file ginkgo_solver.h.
\n \nDefinition at line 150 of file cuda_vector.h.
\n \nDefinition at line 345 of file trilinos_epetra_vector.h.
\n \nDefinition at line 312 of file read_write_vector.h.
\n \nDefinition at line 341 of file read_write_vector.h.
\n \nDefinition at line 371 of file read_write_vector.h.
\n \nDefinition at line 403 of file read_write_vector.h.
\n \nDefinition at line 435 of file read_write_vector.h.
\n \nDefinition at line 464 of file read_write_vector.h.
\n \nDefinition at line 493 of file read_write_vector.h.
\n \nDefinition at line 514 of file trilinos_tpetra_vector.h.
\n \nDefinition at line 573 of file la_parallel_block_vector.h.
\n \nDefinition at line 717 of file la_parallel_vector.h.
\n \nDefinition at line 776 of file la_parallel_vector.h.
\n \nBase class used to declare the operations needed by a concrete class implementing prolongation and restriction of vectors in the multigrid context. This class is abstract and has no implementation of these operations.
\nThere are several derived classes, reflecting the fact that vector types and numbering of the fine-grid discretization and of the multi-level implementation are independent.
\nIf you use multigrid for a single PDE or for your complete system of equations, you will use MGTransferPrebuilt together with Multigrid. The vector types used on the fine grid as well as for the multilevel operations may be Vector or BlockVector. In both cases, MGTransferPrebuilt will operate on all components of the solution.
\nFor mixed systems, it may be required to do multigrid only for a single component or for some components. The classes MGTransferSelect and MGTransferBlock handle these cases.
\nMGTransferSelect is used if you use multigrid (on Vector objects) for a single component, possibly grouped using mg_target_component.
The class MGTransferBlock handles the case where your multigrid method operates on BlockVector objects. These can contain all or a consecutive set of the blocks of the complete system. Since most smoothers cannot operate on block structures, it is not clear whether this case is really useful. Therefore, a tested implementation of this case will be supplied when needed.
\n \n \nAdd all elements in a FullMatrix into global locations given by row_indices and col_indices, respectively. The global locations are translated into locations in this block and ExcBlockIndexMismatch is thrown, if the global index does not point into the block referred to by row and column.
elide_zero_values is currently ignored.elide_zero_values is currently ignored.The optional parameter elide_zero_values can be used to specify whether zero values should be added anyway or these should be filtered away and only non-zero data is added. The default value is true, i.e., zero values won't be added into the matrix.
Definition at line 695 of file matrix_block.h.
\n \nSet several elements in the specified row of the matrix with column indices as given by col_indices to the respective value. This is the function doing the actual work for the ones adding full matrices. The global locations row_index and col_indices are translated into locations in this block and ExcBlockIndexMismatch is thrown, if the global index does not point into the block referred to by row and column.
elide_zero_values is currently ignored.elide_zero_values is currently ignored.The optional parameter elide_zero_values can be used to specify whether zero values should be added anyway or these should be filtered away and only non-zero data is added. The default value is true, i.e., zero values won't be added into the matrix.
Definition at line 780 of file matrix_block.h.
\n \nAssemble local matrices into level matrices without using block structure.
\n-Assemble local residuals into global residuals.
\nThe global residuals are expected as an FEVectors object. The local residuals are block vectors.
\nDepending on whether the BlockInfo object was initialize with BlockInfo::initialize_local(), the comprehensive or block data model is used locally.
\nIn the block model, each of the blocks of the local vectors corresponds to the restriction of a single block of the system to this cell (see GlossBlock). Thus, the size of this local block is the number of degrees of freedom of the corresponding base element of the FESystem.
\n-Definition at line 110 of file assembler.h.
\nA class bundling the MeshWorker::DoFInfo objects used on a cell.
\n-Definition at line 220 of file dof_info.h.
\nWrite input for ParameterHandler without comments or changed default values.
\nKeep the order of the parameters as they have been declared.
\nWrite human readable output suitable to be read by ParameterHandler::parse_input() again.
\nWrite human readable output suitable to be read by ParameterHandler::parse_input() again.
\n-PRM instead of Text. PRM instead of Text. Write parameters as a LaTeX table.
\nWrite out declared parameters with description and possible values.
\nWrite out everything as an XML file suitable to be read by ParameterHandler::parse_input_from_xml() again.
\nSee the general documentation of this class for an example of output.
\nWrite out everything as a JSON file suitable to be read by ParameterHandler::parse_input_from_json() again.
\nWrite the content of ParameterHandler without comments or changed default values.
\nWrite the content of ParameterHandler without comments or changed default values.
\n-ShortPRM instead of ShortText. ShortPRM instead of ShortText. Write the content of ParameterHandler without comments or changed default values as a XML file.
\nWrite the content of ParameterHandler without comments or changed default values as a JSON file.
\nWrite the content of ParameterHandler without comments or changed default values as a LaTeX file.
\nConstructor, selecting the solver and other parameters specified in additional_data.
Definition at line 495 of file nonlinear.h.
\n \n| std::function<void(const real_type t, VectorType &y)> PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::distribute | \n
update_constrained_components, but is deprecated. Use update_constrained_components instead. update_constrained_components, but is deprecated. Use update_constrained_components instead. Definition at line 621 of file petsc_ts.h.
\n \n| std::function<void(const real_type t, const unsigned int step, const VectorType &y, bool &resize)> PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::decide_for_coarsening_and_refinement | \n
decide_and_prepare_for_remeshing except that it returns the decision whether or not to stop operations via the last reference argument of the function object instead of a plain return value. This callback is deprecated. Use decide_and_prepare_for_remeshing instead. decide_and_prepare_for_remeshing except that it returns the decision whether or not to stop operations via the last reference argument of the function object instead of a plain return value. This callback is deprecated. Use decide_and_prepare_for_remeshing instead. Definition at line 656 of file petsc_ts.h.
\n \n| std::function<void(const std::vector<VectorType> &all_in, std::vector<VectorType> &all_out)> PETScWrappers::TimeStepper< VectorType, PMatrixType, AMatrixType >::interpolate | \n
transfer_solution_vectors_to_new_mesh, but is deprecated. Use transfer_solution_vectors_to_new_mesh instead. transfer_solution_vectors_to_new_mesh, but is deprecated. Use transfer_solution_vectors_to_new_mesh instead. Definition at line 688 of file petsc_ts.h.
\n \nWrite input for ParameterHandler without comments or changed default values.
\nKeep the order of the parameters as they have been declared.
\nWrite human readable output suitable to be read by ParameterHandler::parse_input() again.
\nWrite human readable output suitable to be read by ParameterHandler::parse_input() again.
\n-PRM instead of Text. PRM instead of Text. Write parameters as a LaTeX table.
\nWrite out declared parameters with description and possible values.
\nWrite out everything as an XML file suitable to be read by ParameterHandler::parse_input_from_xml() again.
\nSee the general documentation of this class for an example of output.
\nWrite out everything as a JSON file suitable to be read by ParameterHandler::parse_input_from_json() again.
\nWrite the content of ParameterHandler without comments or changed default values.
\nWrite the content of ParameterHandler without comments or changed default values.
\n-ShortPRM instead of ShortText. ShortPRM instead of ShortText. Write the content of ParameterHandler without comments or changed default values as a XML file.
\nWrite the content of ParameterHandler without comments or changed default values as a JSON file.
\nWrite the content of ParameterHandler without comments or changed default values as a LaTeX file.
\nTell the particle where to store its properties (even if it does not own properties). Usually this is only done once per particle, but since the particle generator does not know about the properties we want to do it not at construction time. Another use for this function is after particle transfer to a new process.
\n-Definition at line 835 of file particle_accessor.h.
\n \nCallback function that should be called before every refinement and when writing checkpoints. This function is used to register pack_callback() with the triangulation. This function is used in step-70.
\n-Definition at line 2186 of file particle_handler.cc.
\n \nCallback function that should be called after every refinement and after resuming from a checkpoint. This function is used to register unpack_callback() with the triangulation. This function is used in step-70.
\n-Definition at line 2233 of file particle_handler.cc.
\n \nFill a vector with all tensor elements.
\nThis function unrolls all tensor entries into a single, linearly numbered vector. As usual in C++, the rightmost index of the tensor marches fastest.
\n-| const Point<spacedim> PolarManifold< dim, spacedim >::center | \n
The center of the spherical coordinate system.
\n-Definition at line 150 of file manifold_lib.h.
\n \nStatic function to generate an offset object for a given face of a cell with the given face orientation, flip and rotation. This function of course is only allowed if dim>=2, and the face orientation, flip and rotation are ignored if the space dimension equals 2.
The last argument denotes the number of quadrature points the lower-dimensional face quadrature formula (the one that has been projected onto the faces) has.
\n-Definition at line 1349 of file qprojector.cc.
\n \nCompute an offset object for the given face number and orientation, taking into account the possibility of different quadrature rules being used on each face.
\n-Definition at line 1421 of file qprojector.cc.
\n \nStatic function to generate an offset object for a given subface of a cell with the given face orientation, flip and rotation. This function of course is only allowed if dim>=2, and the face orientation, flip and rotation are ignored if the space dimension equals 2.
The last but one argument denotes the number of quadrature points the lower-dimensional face quadrature formula (the one that has been projected onto the faces) has.
\nThrough the last argument anisotropic refinement can be respected.
\n-Definition at line 1541 of file qprojector.cc.
\n \nDetermine the orientation of the current entity described by its vertices vertices_1 relative to an entity described by vertices_0. The two arrays given as arguments can be arrays of global vertex indices or local vertex indices, arrays of vertex locations, or arrays of any other objects identifying the vertices and the order in which they are encountered in a cell.
The size of the arrays, i.e., the template argument N, must be equal to or larger than the number of vertices of the current entity. If it is larger, only those elements of the input and output arrays are read from or written to that correspond to valid vertex indices.
Definition at line 3183 of file reference_cell.h.
\n \nInverse function of compute_orientation(): Given a set of vertex-associated objects (such as vertex indices, locations, etc.) and a desired orientation permutation, return the permuted vertex information.
\nThe size of the input and output arrays, i.e., the template argument N, must be equal to or larger than the number of vertices of the current entity. If it is larger, only those elements of the input and output arrays are read from or written to that correspond to valid vertex indices.
Definition at line 3259 of file reference_cell.h.
\n \nAn implementation of the transformation interface using the SLEPc Spectrum Folding. This transformation type has been removed in SLEPc 3.5.0 and thus cannot be used in the newer versions.
\n-Definition at line 211 of file slepc_spectral_transformation.h.
\n| std::function<VectorType &()> SUNDIALS::KINSOL< VectorType >::get_solution_scaling | \n
A function object that users may supply and that is intended to return a vector whose components are the weights used by KINSOL to compute the vector norm of the solution. The implementation of this function is optional, and it is used only if implemented.
\n-The intent for this scaling factor is for problems in which the different components of a solution have vastly different numerical magnitudes – typically because they have different physical units and represent different things. For example, if one were to solve a nonlinear Stokes problem, the solution vector has components that correspond to velocities and other components that correspond to pressures. These have different physical units and depending on which units one chooses, they may have roughly comparable numerical sizes or maybe they don't. To give just one example, in simulations of flow in the Earth's interior, one has velocities on the order of maybe ten centimeters per year, and pressures up to around 100 GPa. If one expresses this in SI units, this corresponds to velocities of around \\(0.000,000,003=3 \\times 10^{-9}\\) m/s, and pressures around \\(10^9 \\text{kg}/\\text{m}/\\text{s}^2\\), i.e., vastly different. In such cases, computing the \\(l_2\\) norm of a solution-type vector (e.g., the difference between the previous and the current solution) makes no sense because the norm will either be dominated by the velocity components or the pressure components. The scaling vector this function returns is intended to provide each component of the solution with a scaling factor that is generally chosen as the inverse of a \"typical velocity\" or \"typical pressure\" so that upon multiplication of a vector component by the corresponding scaling vector component, one obtains a number that is of order of magnitude of one (i.e., a reasonably small multiple of one times the typical velocity/pressure). The KINSOL manual states this as follows: \"The user should supply values \\_form#2621,\n-which are diagonal elements of the scaling matrix such that \\_form#2640 has\n-all components roughly the same magnitude when \\_form#304 is close to a\n+
The intent for this scaling factor is for problems in which the different components of a solution have vastly different numerical magnitudes – typically because they have different physical units and represent different things. For example, if one were to solve a nonlinear Stokes problem, the solution vector has components that correspond to velocities and other components that correspond to pressures. These have different physical units and depending on which units one chooses, they may have roughly comparable numerical sizes or maybe they don't. To give just one example, in simulations of flow in the Earth's interior, one has velocities on the order of maybe ten centimeters per year, and pressures up to around 100 GPa. If one expresses this in SI units, this corresponds to velocities of around \\(0.000,000,003=3 \\times 10^{-9}\\) m/s, and pressures around \\(10^9 \\text{kg}/\\text{m}/\\text{s}^2\\), i.e., vastly different. In such cases, computing the \\(l_2\\) norm of a solution-type vector (e.g., the difference between the previous and the current solution) makes no sense because the norm will either be dominated by the velocity components or the pressure components. The scaling vector this function returns is intended to provide each component of the solution with a scaling factor that is generally chosen as the inverse of a \"typical velocity\" or \"typical pressure\" so that upon multiplication of a vector component by the corresponding scaling vector component, one obtains a number that is of order of magnitude of one (i.e., a reasonably small multiple of one times the typical velocity/pressure). The KINSOL manual states this as follows: \"The user should supply values \\_form#2626,\n+which are diagonal elements of the scaling matrix such that \\_form#2645 has\n+all components roughly the same magnitude when \\_form#239 is close to a\n solution\".
\nIf no function is provided to a KINSOL object, then this is interpreted as implicitly saying that all of these scaling factors should be considered as one.
\n| const Point<spacedim> SphericalManifold< dim, spacedim >::center | \n
The center of the spherical coordinate system.
\n-Definition at line 356 of file manifold_lib.h.
\n \nReturn a pointer to the first element of the underlying storage.
\n-Return a const pointer to the first element of the underlying storage.
\n-Return a pointer to the element past the end of the underlying storage.
\n-Return a const pointer to the element past the end of the underlying storage.
\n-Fill a vector with all tensor elements.
\nThis function unrolls all tensor entries into a single, linearly numbered vector. As usual in C++, the rightmost index of the tensor marches fastest.
\n-Definition at line 767 of file trilinos_vector.h.
\n \nDefinition at line 61 of file mpi_remote_point_evaluation.cc.
\n \n \n \n \nReturn an iterator to the next free slot for a single object. This function is only used by Triangulation::execute_refinement() in 3d.
\nReturn an iterator to the next free slot for a pair of objects. This function is only used by Triangulation::execute_refinement() in 3d.
\nLoad the triangulation saved with save() back in. The mesh must be empty before calling this function.
\nYou need to load with the same number of MPI processes that you saved with, hence autopartition is disabled.
\nCell-based data that was saved with register_data_attach() can be read in with notify_ready_to_unpack() after calling load().
\n-Implements parallel::DistributedTriangulationBase< dim, spacedim >.
\n \nDefinition at line 741 of file fully_distributed_tria.cc.
\n \nstd::map instead. std::map instead. std::map instead. std_cxx20::type_identity instead. std_cxx20::type_identity instead. ShortPRM instead of ShortText. ShortPRM instead of ShortText. PRM instead of Text. PRM instead of Text. decide_and_prepare_for_remeshing except that it returns the decision whether or not to stop operations via the last reference argument of the function object instead of a plain return value. This callback is deprecated. Use decide_and_prepare_for_remeshing instead. decide_and_prepare_for_remeshing except that it returns the decision whether or not to stop operations via the last reference argument of the function object instead of a plain return value. This callback is deprecated. Use decide_and_prepare_for_remeshing instead. update_constrained_components, but is deprecated. Use update_constrained_components instead. update_constrained_components, but is deprecated. Use update_constrained_components instead. transfer_solution_vectors_to_new_mesh, but is deprecated. Use transfer_solution_vectors_to_new_mesh instead. transfer_solution_vectors_to_new_mesh, but is deprecated. Use transfer_solution_vectors_to_new_mesh instead. vtu: .vtu svg: .svg deal_II_intermediate: .d2. Definition at line 2496 of file data_out_base.cc.
\n \nExtract the set of global DoF indices that are active on the current DoFHandler. For regular DoFHandlers, these are all DoF indices, but for DoFHandler objects built on parallel::distributed::Triangulation this set is a superset of DoFHandler::locally_owned_dofs() and contains all DoF indices that live on all locally owned cells (including on the interface to ghost cells). However, it does not contain the DoF indices that are exclusively defined on ghost or artificial cells (see the glossary).
\nThe 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.
\n-Definition at line 1105 of file dof_tools.cc.
\n \nSame function as above but for a certain (multigrid-)level. This function returns all DoF indices that live on all locally owned cells (including on the interface to ghost cells) on the given level.
\n-Definition at line 1152 of file dof_tools.cc.
\n \nExtract the set of global DoF indices that are active on the current DoFHandler. For regular DoFHandlers, these are all DoF indices, but for DoFHandler objects built on parallel::distributed::Triangulation this set is the union of DoFHandler::locally_owned_dofs() and the DoF indices on all ghost cells. In essence, it is the DoF indices on all cells that are not artificial (see the glossary).
\n-Definition at line 1202 of file dof_tools.cc.
\n \nSame as extract_locally_relevant_dofs() but for multigrid DoFs for the given level.
Definition at line 1258 of file dof_tools.cc.
\n \nFor each active cell of a DoFHandler, extract the active finite element index and fill the vector given as second argument. This vector is assumed to have as many entries as there are active cells.
\nFor DoFHandler objects without hp-capabilities given as first argument, the returned vector will consist of only zeros, indicating that all cells use the same finite element. In hp-mode, the values may be different, though.
\nAs we do not know the active FE index on artificial cells, we set them to the invalid value numbers::invalid_fe_index.
\n-Definition at line 1499 of file dof_tools.cc.
\n \nA version of the function of same name that returns the map via its third argument. This function is deprecated.
std::map instead. A version of the function of same name that returns the map via its third argument. This function is deprecated.
std::map instead. Definition at line 2430 of file dof_tools.cc.
\n \nA version of the function of same name that returns the map via its third argument. This function is deprecated.
std::map instead. A version of the function of same name that returns the map via its third argument. This function is deprecated.
std::map instead. Definition at line 2451 of file dof_tools.cc.
\n \nThis is the opposite function to the one above. It generates a map where the keys are the support points of the degrees of freedom, while the values are the DoF indices. For a definition of support points, see this glossary entry.
\nSince 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.
\nJust 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.
\n-Same as above but for a specific number of sub-elements.
\n-Take a FiniteElement object and return a boolean vector describing the restriction_is_additive_flags (see the documentation of the FiniteElement class) for each shape function of the mixed element consisting of N1, N2, ... copies of the sub-elements fe1, fe2, ...
The \"restriction is additive\" flags are properties of individual shape functions that do not depend on whether the composed element uses the tensor product or combination strategy outlined in the documentation of the FETools::Composition namespace. Consequently, this function does not have a do_tensor_product argument.
Compute the non-zero vector components of a composed finite element. This function is similar to the previous one, except that the pointers indicate the elements to be composed, and the arguments N1, N2, ... the multiplicities. Null pointers indicate that an argument is to be skipped.
If do_tensor_product is true, the number of components (and thus the size of the ComponentMask objects) is the sum over the product of the number of components in each of the finite elements times the corresponding multiplicity. Otherwise the number of components is taken from the first finite element with non-zero multiplicity, and all other elements with non-zero multiplicities need to have the same number of vector components.
See the documentation of namespace FETools::Compositing for more information about the do_tensor_product argument.
Definition at line 241 of file grid_tools.cc.
\n \nIf the library is configured to use multithreading, this function works in parallel.
\nweight: an optional weight for the computation of the mass matrix. If no weight is given, it is set to one. In case you want to specify component_mapping and use the default argument for the coefficient you have to specify the (unused) coefficient argument as (const Function <spacedim,number> *const)nullptr.component_mapping: if the components in boundary_functions and dof do not coincide, this vector allows them to be remapped. If the vector is not empty, it has to have one entry for each component in dof. This entry is the component number in boundary_functions that should be used for this component in dof. By default, no remapping is applied.| [in] | axis | A unit vector that defines the axis of rotation |
| [in] | angle | The rotation angle in radians |
Definition at line 1092 of file sparsity_tools.cc.
\n \nThe same trick with the mixed system does not work here, because we would end up with both Dirichlet and Neumann boundary conditions for \\(u\\), but none for \\(v\\).
\nThe solution to this conundrum arrived with the Discontinuous Galerkin method wave in the 1990s and early 2000s: In much the same way as one can use discontinuous shape functions for the Laplace equation by penalizing the size of the discontinuity to obtain a scheme for an equation that has one derivative on each shape function, we can use a scheme that uses continuous (but not \\(C^1\\) continuous) shape functions and penalize the jump in the derivative to obtain a scheme for an equation that has two derivatives on each shape function. In analogy to the Interior Penalty (IP) method for the Laplace equation, this scheme for the biharmonic equation is typically called the \\(C^0\\) IP (or C0IP) method, since it uses \\(C^0\\) (continuous but not continuously differentiable) shape functions with an interior penalty formulation.
\nIt is worth noting that the C0IP method is not the only one that has been developed for the biharmonic equation. step-82 shows an alternative method.
\nWe base this program on the \\(C^0\\) IP method presented by Susanne Brenner and Li-Yeng Sung in the paper \"C \\_form#3735 Interior Penalty Method\n+
We base this program on the \\(C^0\\) IP method presented by Susanne Brenner and Li-Yeng Sung in the paper \"C \\_form#4537 Interior Penalty Method\n for Linear Fourth Order Boundary Value Problems on polygonal\n domains\" [Brenner2005] where the method is derived for the biharmonic equation with \"clamped\" boundary conditions.
\nAs mentioned, this method relies on the use of \\(C^0\\) Lagrange finite elements where the \\(C^1\\) continuity requirement is relaxed and has been replaced with interior penalty techniques. To derive this method, we consider a \\(C^0\\) shape function \\(v_h\\) which vanishes on \\(\\partial\\Omega\\). We introduce notation \\( \\mathbb{F} \\) as the set of all faces of \\(\\mathbb{T}\\), \\( \\mathbb{F}^b \\) as the set of boundary faces, and \\( \\mathbb{F}^i \\) as the set of interior faces for use further down below. Since the higher order derivatives of \\(v_h\\) have two values on each interface \\(e\\in \\mathbb{F}\\) (shared by the two cells \\(K_{+},K_{-} \\in \\mathbb{T}\\)), we cope with this discontinuity by defining the following single-valued functions on \\(e\\):
\n \\begin{align*}\n \\jump{\\frac{\\partial^k v_h}{\\partial \\mathbf n^k}}\n &=\n \\frac{\\partial^k v_h|_{K_+}}{\\partial \\mathbf n^k} \\bigg |_e\n", "details": [{"source1": "html2text {}", "source2": "html2text {}", "unified_diff": "@@ -175,15 +175,15 @@\n (C^0\\) IP (or C0IP) method, since it uses \\(C^0\\) (continuous but not\n continuously differentiable) shape functions with an interior penalty\n formulation.\n It is worth noting that the C0IP method is not the only one that has been\n developed for the biharmonic equation. _\bs_\bt_\be_\bp_\b-_\b8_\b2 shows an alternative method.\n *\b**\b**\b**\b* D\bDe\ber\bri\biv\bva\bat\bti\bio\bon\bn o\bof\bf t\bth\bhe\be C\bC0\b0I\bIP\bP m\bme\bet\bth\bho\bod\bd *\b**\b**\b**\b*\n We base this program on the \\(C^0\\) IP method presented by Susanne Brenner and\n-Li-Yeng Sung in the paper \"C \\_form#3735 Interior Penalty Method for Linear\n+Li-Yeng Sung in the paper \"C \\_form#4537 Interior Penalty Method for Linear\n Fourth Order Boundary Value Problems on polygonal domains\" [\b[B\bBr\bre\ben\bnn\bne\ber\br2\b20\b00\b05\b5]\b] where\n the method is derived for the biharmonic equation with \"clamped\" boundary\n conditions.\n As mentioned, this method relies on the use of \\(C^0\\) Lagrange finite elements\n where the \\(C^1\\) continuity requirement is relaxed and has been replaced with\n interior penalty techniques. To derive this method, we consider a \\(C^0\\) shape\n function \\(v_h\\) which vanishes on \\(\\partial\\Omega\\). We introduce notation \\\n"}]}, {"source1": "./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/step_58.html", "source2": "./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/step_58.html", "unified_diff": "@@ -567,15 +567,15 @@\n +\n V \\left[\\frac 12 \\left(\\psi^{(n,2)}+\\psi^{(n,1)}\\right)\\right] = 0.\n \\end{align*}\n
\nHere, the \"previous\" solution \\(\\psi^{(n,1)}\\) (or the \"initial\n condition\" for this part of the time step) is the output of the first phase rotation half-step; the output of the current step will be denoted by \\(\\psi^{(n,2)}\\). \\(k_{n+1}=t_{n+1}-t_n\\) is the length of the time step. (One could argue whether \\(\\psi^{(n,1)}\\) and \\(\\psi^{(n,1)}\\) live at time step \\(n\\) or \\(n+1\\) and what their upper indices should be. This is a philosophical discussion without practical impact, and one might think of \\(\\psi^{(n,1)}\\) as something like \\(\\psi^{(n+\\tfrac 13)}\\), and \\(\\psi^{(n,2)}\\) as \\(\\psi^{(n+\\tfrac 23)}\\) if that helps clarify things – though, again \\(n+\\frac 13\\) is not to be understood as \"one third time step after\n \\_form#375\" but more like \"we've already done one third of the work necessary\n-for time step \\_form#3193\".)
\n+for time step \\_form#2972\".)\nIf we multiply the whole equation with \\(k_{n+1}\\) and sort terms with the unknown \\(\\psi^{(n+1,2)}\\) to the left and those with the known \\(\\psi^{(n,2)}\\) to the right, then we obtain the following (spatial) partial differential equation that needs to be solved in each time step:
\n \\begin{align*}\n -i\\psi^{(n,2)}\n -\n \\frac 14 k_{n+1} \\Delta \\psi^{(n,2)}\n +\n \\frac 12 k_{n+1} V \\psi^{(n,2)}\n", "details": [{"source1": "html2text {}", "source2": "html2text {}", "unified_diff": "@@ -379,15 +379,15 @@\n {n+1}=t_{n+1}-t_n\\) is the length of the time step. (One could argue whether \\\n (\\psi^{(n,1)}\\) and \\(\\psi^{(n,1)}\\) live at time step \\(n\\) or \\(n+1\\) and\n what their upper indices should be. This is a philosophical discussion without\n practical impact, and one might think of \\(\\psi^{(n,1)}\\) as something like \\\n (\\psi^{(n+\\tfrac 13)}\\), and \\(\\psi^{(n,2)}\\) as \\(\\psi^{(n+\\tfrac 23)}\\) if\n that helps clarify things \u2013 though, again \\(n+\\frac 13\\) is not to be\n understood as \"one third time step after \\_form#375\" but more like \"we've\n-already done one third of the work necessary for time step \\_form#3193\".)\n+already done one third of the work necessary for time step \\_form#2972\".)\n If we multiply the whole equation with \\(k_{n+1}\\) and sort terms with the\n unknown \\(\\psi^{(n+1,2)}\\) to the left and those with the known \\(\\psi^{\n (n,2)}\\) to the right, then we obtain the following (spatial) partial\n differential equation that needs to be solved in each time step:\n \\begin{align*} -i\\psi^{(n,2)} - \\frac 14 k_{n+1} \\Delta \\psi^{(n,2)} + \\frac 12\n k_{n+1} V \\psi^{(n,2)} = -i\\psi^{(n,1)} + \\frac 14 k_{n+1} \\Delta \\psi^{(n,1)}\n - \\frac 12 k_{n+1} V \\psi^{(n,1)}. \\end{align*}\n"}]}, {"source1": "./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/structCellData.html", "source2": "./usr/share/doc/libdeal.ii-doc/html/doxygen/deal.II/structCellData.html", "unified_diff": "@@ -126,22 +126,22 @@\n
\n Public Attributes | ||
| std::vector< unsigned int > | vertices | |
| union { | ||
| union { | ||
| types::material_id material_id | ||
| types::boundary_id boundary_id | ||
| }; | ||
| types::material_id material_id | ||
| types::boundary_id boundary_id | ||
| }; | ||
| types::manifold_id | manifold_id | |
The CellData class (and the related SubCellData class) is used to provide a comprehensive, but minimal, description of the cells when creating a triangulation via Triangulation::create_triangulation(). Specifically, each CellData object – describing one cell in a triangulation – has member variables for indices of the \\(2^d\\) vertices (the actual coordinates of the vertices are described in a separate vector passed to Triangulation::create_triangulation(), so the CellData object only needs to store indices into that vector), the material id of the cell that can be used in applications to describe which part of the domain a cell belongs to (see the glossary entry on material ids), and a manifold id that is used to describe the geometry object that is responsible for this cell (see the glossary entry on manifold ids) to describe the manifold this object belongs to.
\nThis structure is also used to represent data for faces and edges when used as a member of the SubCellData class. In this case, the template argument structdim of an object will be less than the dimension dim of the triangulation. If this is so, then vertices array represents the indices of the vertices of one face or edge of one of the cells passed to Triangulation::create_triangulation(). Furthermore, for faces the material id has no meaning, and the material_id field is reused to store a boundary_id instead to designate which part of the boundary the face or edge belongs to (see the glossary entry on boundary ids).
The boundary id of a face or edge being described. See the documentation of the CellData class for examples of how to use this field.
\nThis variable can only be used if the current object is used to describe a face or edge, i.e., if structdim is less than the dimension dim of a triangulation. In this case, the CellData object this variable belongs to will be part of a SubCellData object.
Definition at line 129 of file tria_description.h.
\n \n| union { ... } CellData< structdim > | \n
| using DataOutBase::VtkFlags::ZlibCompressionLevel = DataOutBase::CompressionLevel | \n
A data type providing the different possible zlib compression levels. These map directly to constants defined by zlib.
\n-Definition at line 1166 of file data_out_base.h.
\n \nA data type providing the different possible zlib compression levels. These map directly to constants defined by zlib.
\n-Definition at line 1166 of file data_out_base.h.
\n \nA data type providing the different possible zlib compression levels. These map directly to constants defined by zlib.
\n-Definition at line 1166 of file data_out_base.h.
\n \n| unsigned int SolverGMRES< VectorType >::AdditionalData::max_n_tmp_vectors | \n
Maximum number of temporary vectors. Together with max_basis_size, this parameter controls the size of the Arnoldi basis, which corresponds to max_n_tmp_vectors-2 as used in previous versions of the deal.II library. SolverGMRES assumes that there are at least three temporary vectors, so this value must be greater than or equal to three. If both this variable and max_basis_size are set to a non-zero value, the choice in max_basis_size takes precedence.
\n-Definition at line 391 of file solver_gmres.h.
\n \n\n Public Attributes | ||
| union { | ||
| union { | ||
| types::boundary_id boundary_id | ||
| types::material_id material_id | ||
| }; | ||
| types::boundary_id boundary_id | ||
| types::material_id material_id | ||
| }; | ||
We use this union to store boundary and material data. Because only one out of these two is actually needed here, we use an union.
\n \nDefinition at line 135 of file tria_objects.h.
\nDefinition at line 140 of file tria_objects.h.
\n \n| union { ... } internal::TriangulationImplementation::TriaObjects::BoundaryOrMaterialId | \n|
| template<class Archive > | |
| void | serialize (Archive &ar, const unsigned int version) |
\n Public Attributes | ||
| union { | ||
| union { | ||
| void * p | ||
| unsigned int i | ||
| }; | ||
| void * p | ||
| unsigned int i | ||
| }; | ||
The data type storing user pointers or user indices.
\n \nDefinition at line 312 of file tria_objects.h.
\nThe entry used as user index.
\n \nDefinition at line 321 of file tria_objects.h.
\n \n| union { ... } internal::TriangulationImplementation::TriaObjects::UserData | \n
| using identity = std_cxx20::type_identity<T> | \n
A using declaration to make the std::identity_type class available under the name that deal.II has used for a long time.
std_cxx20::type_identity instead. std_cxx20::type_identity instead. Definition at line 322 of file template_constraints.h.
\n \nmapping argument should be replaced by a hp::MappingCollection in case of a DoFHandler with hp-capabilities. The 3d version exhibits some numerical instabilities, in particular for higher order
\n-Restriction matrices are missing.
\n+Restriction matrices are missing.
\n+The 3d version exhibits some numerical instabilities, in particular for higher order
\nelide_zero_values is currently ignored. elide_zero_values is currently ignored. elide_zero_values is currently ignored. elide_zero_values is currently ignored. elide_zero_values is currently ignored.