Schur.cpp File Reference

Implementation of Schur Complement. More...

Go to the source code of this file.

Classes
struct	MoFEM::OpSchurAssembleBaseImpl
struct	MoFEM::OpSchurAssembleBegin
	Clear Schur complement internal data. More...
struct	MoFEM::OpSchurZeroRowsAndCols
struct	MoFEM::OpSchurAssembleEndImpl< OP_SCHUR_ASSEMBLE_BASE >
	Assemble Schur complement (Implementation) More...
struct	MoFEM::OpSchurAssembleEnd< SchurDSYSV >
struct	MoFEM::OpSchurAssembleEnd< SchurDGESV >
struct	MoFEM::SchurElemMats
	Schur complement data storage. More...
struct	MoFEM::SchurElemMats::uid_mi_tag
struct	MoFEM::SchurElemMats::col_mi_tag
struct	MoFEM::BlockStorage
	Storage of block matrix, shared by block matrix and its nested (Schur) sub-matrices. More...
struct	MoFEM::BlockStorage::Indexes
	block data indexes More...
struct	MoFEM::BlockStorage::ElemEntity
	DOFs on one entity (node) of A00 element. More...
struct	MoFEM::BlockStorage::Pattern
	Block pattern of A00 element and layout of element buffer. More...
struct	MoFEM::BlockStorage::Elem
	A00 element. More...
struct	MoFEM::BlockStorage::RowUIdLess
struct	MoFEM::BlockStructure
	Context of block matrix shell. More...
struct	MoFEM::BlockStructure::Block
	block in numbering of this matrix (blocks not stored in element buffers) More...
struct	MoFEM::SchurDSYSV
struct	MoFEM::SchurDGESV
struct	MoFEM::SchurElemMatsBlock
struct	MoFEM::SchurElemMatsPreconditionedBlock

Namespaces
namespace	MoFEM
	implementation of Data Operators for Forces and Sources

Typedefs
using	MoFEM::BlockPattern = BlockStorage::Pattern

Functions
static void	MoFEM::apply_lu_factors (int n, const double *lu, const __CLPK_integer *ipiv, double *t, bool trans)
	Apply in place LU factors of element matrix.
static void	MoFEM::copy_block (double *dst, int ld_dst, int ridx, int cidx, const double *src, int ld_src, int nb_rows, int nb_cols)
	copy row-major block into row-major matrix at (ridx, cidx)
static bool	MoFEM::is_zero_matrix (const double *ptr, size_t size)
void	MoFEM::dgecon_ (char *norm, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *anorm, __CLPK_doublereal *rcond, __CLPK_doublereal *work, __CLPK_integer *iwork, __CLPK_integer *info)
static double	MoFEM::norm1_block (int m, int n, const double *a, int ld)
	1-norm of column-major m x n block, infinity if block is not finite
static void	MoFEM::add_gemv (bool trans_a, int m, int kk, const double *a, int lda, const double *x, double *y)
	y += op(A) x, op(A) is m x kk, A is column-major
static void	MoFEM::sub_gemm (bool trans_a, int m, int kk, int nrhs, const double *a, int lda, const double *b, int ldb, double *c, int ldc)
	C -= op(A) B, op(A) is m x kk, A, B and C are column-major.
static bool	MoFEM::factorise_pivot_block (int n, double *d, int ld, __CLPK_integer *piv, double coupling, double u, double rcond_min, std::vector< double > &work, std::vector< __CLPK_integer > &iwork, double *rcond_out=nullptr, double *anorm_out=nullptr)
	Factorise diagonal block in place and test it as block pivot.
static std::vector< int >	MoFEM::natural_offsets (const BlockPattern &p)
	offsets of nodes in element vector in order of nodes
static size_t	MoFEM::listed_size (const BlockPattern &p)
	doubles in listed blocks of one element
static void	MoFEM::make_listed_layout (BlockPattern &p)
	layout with listed blocks only
static std::vector< char >	MoFEM::symbolic_elimination (const BlockPattern &p, const std::vector< int > &order)
	Blocks of M = A^T present after eliminating nodes in given order.
static void	MoFEM::make_block_layout (BlockPattern &p, const std::vector< int > &order)
	Layout for block elimination of nodes in order, followed by dense core of remaining nodes.
static std::vector< int >	MoFEM::structural_order (const BlockPattern &p)
	elimination order by structure only (minimal fill, diagonal present)
static std::vector< int >	MoFEM::analyse_pattern (const BlockPattern &p, double *w, double u, double rcond_min)
	Decide elimination order on probe element.
static void	MoFEM::copy_listed (const BlockPattern &from, const double *src, const BlockPattern &to, double *dst)
	copy listed blocks of element buffer from one layout to another
static void	MoFEM::elem_gather_dense (const BlockPattern &p, const double *buf, double *dense)
	dense element matrix (row-major A, size x size) from listed blocks
static void	MoFEM::elem_mult_listed (const BlockPattern &p, const double *buf, const double *x, double *y, bool trans)
	y += A x (trans false) or y += A^T x (trans true) from listed blocks
static int	MoFEM::elem_factorise (const BlockPattern &p, double *buf, __CLPK_integer *piv, double u, double rcond_min, std::vector< double > &work, std::vector< __CLPK_integer > &iwork)
	Factorise element buffer in place.
static MoFEMErrorCode	MoFEM::elem_solve (const BlockPattern &p, const double *buf, const __CLPK_integer *piv, double *r, int ldr, int nrhs, bool trans, const std::vector< char > *nz_in)
	Solve with factorised element buffer.
static void	MoFEM::elem_mult_factors (const BlockPattern &p, const double *buf, const __CLPK_integer *piv, double *v, bool trans)
	Product with factorised element buffer, in place.
static double	MoFEM::backward_error_rhs (int i)
	right-hand side used to measure backward error
static double	MoFEM::elem_backward_error (const BlockPattern &p, const double *orig, const double *lu, const __CLPK_integer *piv, std::vector< double > &x, std::vector< double > &r, std::vector< double > &rs)
	Normwise backward error of solve with factors of element.
static double	MoFEM::accepted_backward_error (double be_dense, double be_tol)
	backward error accepted for block factors, given dense backward error
static bool	MoFEM::backward_error_accepted (double be, double be_dense, double be_tol)
	true if backward error is finite and not larger than accepted
static bool	MoFEM::verify_probe (const BlockPattern &nl, const std::vector< double > &mat, double u, double rcond_min, double be_tol, double &be_block, double &be_dense)
	Verify block layout on probe element.
static std::string	MoFEM::describe_nodes (const BlockPattern &p, const std::vector< int > &nodes)
static void	MoFEM::relayout_pattern (BlockStorage &s, int pi, BlockPattern nl)
	Relayout element buffers of pattern pi, element by element, in place.
static MoFEMErrorCode	MoFEM::factorise_elems (BlockStorage &storage, BlockStorage::FactorStorage where)
	Factorise A00 elements in place.
static void	MoFEM::set_block_orders (BlockStorage &storage)
	set orders of blocks by finite element and by column entity
static void	MoFEM::set_parent_blocks (BlockStructure &s)
	set blocks of block matrix (parent numbering)
template<typename FUN >
static void	MoFEM::for_each_block (const BlockStructure &ctx, FUN &&fun)
	Iterate all blocks of matrix, including listed blocks of A00 elements.
boost::shared_ptr< BlockStructure >	MoFEM::createBlockMatStructure (DM dm, SchurFEOpsFEandFields schur_fe_op_vec)
	Create block matrix structure.
static MoFEMErrorCode	MoFEM::mult_block_structure (Mat mat, Vec x, Vec y, InsertMode iora, bool trans)
	Matrix-vector product of block matrix.
static MoFEMErrorCode	MoFEM::solve_block_structure (Mat mat, Vec f, Vec x, InsertMode iora, bool trans)
	Solve with A00, i.e. x = A00^{-1} f, element by element.
static PetscErrorCode	MoFEM::mult (Mat mat, Vec x, Vec y)
static PetscErrorCode	MoFEM::mult_add (Mat mat, Vec x, Vec y)
static PetscErrorCode	MoFEM::mult_transpose (Mat mat, Vec x, Vec y)
static PetscErrorCode	MoFEM::mult_transpose_add (Mat mat, Vec x, Vec y)
static PetscErrorCode	MoFEM::solve (Mat mat, Vec x, Vec y)
static PetscErrorCode	MoFEM::solve_add (Mat mat, Vec x, Vec y)
static PetscErrorCode	MoFEM::solve_transpose (Mat mat, Vec x, Vec y)
static PetscErrorCode	MoFEM::solve_transpose_add (Mat mat, Vec x, Vec y)
static PetscErrorCode	MoFEM::zero_rows_columns (Mat A, PetscInt N, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
static PetscErrorCode	MoFEM::mat_zero (Mat m)
static MoFEMErrorCode	MoFEM::setSchurBlockMatOps (Mat mat_raw)
SchurShellMatData	MoFEM::createBlockMat (DM dm, boost::shared_ptr< BlockStructure > data)
	Create a Schur Mat object.
MoFEMErrorCode	MoFEM::assembleBlockMatSchur (MoFEM::Interface &m_field, Mat B, Mat S, std::vector< std::string > fields_name, std::vector< boost::shared_ptr< Range > > field_ents, SmartPetscObj< AO > ao)
	Assemble Schur complement S = A11 - A10 A00^{-1} A01 from block matrix.
boost::shared_ptr< std::vector< double > >	MoFEM::getBlockMatStorageMat (Mat B)
	Get block values storage.
boost::shared_ptr< std::vector< double > >	MoFEM::getBlockMatPrconditionerStorageMat (Mat B)
	Get preconditioner blocks storage.
MoFEMErrorCode	MoFEM::shell_block_mat_asmb_wrap_impl (BlockStructure *ctx, const EntitiesFieldData::EntData &row_data, const EntitiesFieldData::EntData &col_data, const MatrixDouble &mat, InsertMode iora, bool is_preconditioner)
MoFEMErrorCode	MoFEM::shell_block_mat_asmb_wrap (Mat M, const EntitiesFieldData::EntData &row_data, const EntitiesFieldData::EntData &col_data, const MatrixDouble &mat, InsertMode iora)
MoFEMErrorCode	MoFEM::shell_block_preconditioner_mat_asmb_wrap (Mat M, const EntitiesFieldData::EntData &row_data, const EntitiesFieldData::EntData &col_data, const MatrixDouble &mat, InsertMode iora)
boost::shared_ptr< NestSchurData >	MoFEM::createSchurNestedMatrixStruture (std::pair< SmartPetscObj< DM >, SmartPetscObj< DM > > dms, boost::shared_ptr< BlockStructure > block_mat_data, std::vector< std::string > fields_name, std::vector< boost::shared_ptr< Range > > field_ents, bool add_preconditioner_block=false)
	Create structure of nested matrix [A11 A10; A01 A00].
std::pair< SmartPetscObj< Mat >, boost::shared_ptr< NestSchurData > >	MoFEM::createSchurNestedMatrix (boost::shared_ptr< NestSchurData > schur_net_data_ptr)
	Create a Mat Diag Blocks object.
OpSchurAssembleBase *	MoFEM::createOpSchurAssembleBegin ()
OpSchurAssembleBase *	MoFEM::createOpSchurAssembleEnd (std::vector< std::string > fields_name, std::vector< boost::shared_ptr< Range > > field_ents, SmartPetscObj< AO > ao=SmartPetscObj< AO >(), SmartPetscObj< Mat > schur=SmartPetscObj< Mat >(), bool sym_schur=false, bool symm_op=false)
	Construct a new Op Schur Assemble End object.
OpSchurAssembleBase *	MoFEM::createOpSchurZeroRowsAndCols (boost::shared_ptr< std::vector< unsigned char > > marker_ptr, double diag_val)
	Create a Op Schur Zero Rows And Cols object.
OpSchurAssembleBase *	MoFEM::createOpSchurAssembleEnd (std::vector< std::string > fields_name, std::vector< boost::shared_ptr< Range > > field_ents, std::vector< SmartPetscObj< AO > > sequence_of_aos, std::vector< SmartPetscObj< Mat > > sequence_of_mats, std::vector< bool > sym_schur, bool symm_op, boost::shared_ptr< BlockStructure > diag_blocks)
OpSchurAssembleBase *	MoFEM::createOpSchurAssembleEnd (std::vector< std::string > fields_name, std::vector< boost::shared_ptr< Range > > field_ents, std::vector< SmartPetscObj< AO > > sequence_of_aos, std::vector< SmartPetscObj< Mat > > sequence_of_mats, std::vector< bool > sym_schur, std::vector< double > diag_eps, bool symm_op, boost::shared_ptr< BlockStructure > diag_blocks)
MoFEMErrorCode	MoFEM::setSchurA00MatSolvePC (SmartPetscObj< PC > pc)
	Set PC for A00 block.
template<>
MoFEMErrorCode	MoFEM::MatSetValues< SchurElemMats > (Mat M, const EntitiesFieldData::EntData &row_data, const EntitiesFieldData::EntData &col_data, const MatrixDouble &mat, InsertMode iora)
MoFEMErrorCode	MoFEM::schur_mat_set_values_wrap (Mat M, const EntitiesFieldData::EntData &row_data, const EntitiesFieldData::EntData &col_data, const MatrixDouble &mat, InsertMode iora)
template<>
MoFEMErrorCode	MoFEM::MatSetValues< AssemblyTypeSelector< SCHUR > > (Mat M, const EntitiesFieldData::EntData &row_data, const EntitiesFieldData::EntData &col_data, const MatrixDouble &mat, InsertMode iora)
template<>
MoFEMErrorCode	MoFEM::MatSetValues< BlockStructure > (Mat M, const EntitiesFieldData::EntData &row_data, const EntitiesFieldData::EntData &col_data, const MatrixDouble &mat, InsertMode iora)
template<>
MoFEMErrorCode	MoFEM::MatSetValues< SchurElemMatsBlock > (Mat M, const EntitiesFieldData::EntData &row_data, const EntitiesFieldData::EntData &col_data, const MatrixDouble &mat, InsertMode iora)
template<>
MoFEMErrorCode	MoFEM::MatSetValues< SchurElemMatsPreconditionedBlock > (Mat M, const EntitiesFieldData::EntData &row_data, const EntitiesFieldData::EntData &col_data, const MatrixDouble &mat, InsertMode iora)
MoFEMErrorCode	MoFEM::schurSwitchPreconditioner (boost::shared_ptr< BlockStructure > block_mat_data)
	Switch preconditioner.
MoFEMErrorCode	MoFEM::schurSaveBlockMesh (boost::shared_ptr< BlockStructure > block_mat_data, std::string filename)
	Save block matrix as a mesh.

Variables
constexpr bool	MoFEM::debug_schur = false
constexpr double	MoFEM::backward_error_factor = 100
	factor of dense backward error accepted for block factors

Detailed Description

Implementation of Schur Complement.

Date

2023-02-03

Copyright

Copyright (c) 2023

Definition in file Schur.cpp.