BlockTrianglePrecondition< number, BlockVectorType > Class Template Reference

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

Inheritance diagram for BlockTrianglePrecondition< number, BlockVectorType >:

Public Types
using	size_type = types::global_dof_index

Public Member Functions
	BlockTrianglePrecondition ()
	BlockTrianglePrecondition (const unsigned int n_blocks)
void	reinit (const unsigned int n_block_rows)
template<typename MatrixType >
void	enter (const MatrixType &matrix, const size_type row, const size_type col, const number prefix=1., const bool transpose=false)
void	vmult (BlockVectorType &dst, const BlockVectorType &src) const
void	vmult_add (BlockVectorType &dst, const BlockVectorType &src) const
void	Tvmult (BlockVectorType &dst, const BlockVectorType &src) const
void	Tvmult_add (BlockVectorType &dst, const BlockVectorType &src) const

Static Public Member Functions
static::ExceptionBase &	ExcNoDiagonal (size_type arg1)
static::ExceptionBase &	ExcMultipleDiagonal (size_type arg1)

Private Member Functions
void	do_row (BlockVectorType &dst, size_type row_num) const
Private Member Functions inherited from BlockMatrixArray< number, BlockVectorType >
	BlockMatrixArray ()
	BlockMatrixArray (const unsigned int n_block_rows, const unsigned int n_block_cols)
void	initialize (const unsigned int n_block_rows, const unsigned int n_block_cols)
void	reinit (const unsigned int n_block_rows, const unsigned int n_block_cols)
template<typename MatrixType >
void	enter (const MatrixType &matrix, const unsigned int row, const unsigned int col, const number prefix=1., const bool transpose=false)
void	clear ()
unsigned int	n_block_rows () const
unsigned int	n_block_cols () const
void	vmult (BlockVectorType &dst, const BlockVectorType &src) const
void	vmult_add (BlockVectorType &dst, const BlockVectorType &src) const
void	Tvmult (BlockVectorType &dst, const BlockVectorType &src) const
void	Tvmult_add (BlockVectorType &dst, const BlockVectorType &src) const
number	matrix_scalar_product (const BlockVectorType &u, const BlockVectorType &v) const
number	matrix_norm_square (const BlockVectorType &u) const
template<class StreamType >
void	print_latex (StreamType &out) const
Private Member Functions inherited from Subscriptor
	Subscriptor ()
	Subscriptor (const Subscriptor &)
	Subscriptor (Subscriptor &&) noexcept
virtual	~Subscriptor ()
Subscriptor &	operator= (const Subscriptor &)
Subscriptor &	operator= (Subscriptor &&) noexcept
void	subscribe (const char *identifier=nullptr) const
void	unsubscribe (const char *identifier=nullptr) const
unsigned int	n_subscriptions () const
template<typename StreamType >
void	list_subscribers (StreamType &stream) const
void	list_subscribers () const
template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

Private Attributes
bool	backward
Private Attributes inherited from BlockMatrixArray< number, BlockVectorType >
std::vector< Entry >	entries

Additional Inherited Members
Private Types inherited from BlockMatrixArray< number, BlockVectorType >
using	size_type = types::global_dof_index
Static Private Member Functions inherited from Subscriptor
static::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)
static::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string arg2)

Detailed Description

template<typename number = double, typename BlockVectorType = BlockVector<number>>
class BlockTrianglePrecondition< number, BlockVectorType >

Inversion of a block-triangular matrix.

In this block matrix, the inverses of the diagonal blocks are stored together with the off-diagonal blocks of a block matrix. Then, forward or backward insertion is performed block-wise. The diagonal blocks are NOT inverted for this purpose!

Like for all preconditioners, the preconditioning operation is performed by the vmult() member function.

Note

While block indices may be duplicated (see BlockMatrixArray) to add blocks, this has to be used with caution, since summing up the inverse of two blocks does not yield the inverse of the sum. While the latter would be desirable, we can only perform the first.

The implementation may be a little clumsy, but it should be sufficient as long as the block sizes are much larger than the number of blocks.

Example

Here, we document the second part of examples/doxygen/block_matrix_array.cc. For the beginning of this file, see BlockMatrixArray.

In order to set up the preconditioner, we have to compute the inverses of the diagonal blocks ourselves. Since we used FullMatrix objects, this is fairly easy.

  deallog << "Error " << x.l2_norm() << std::endl;

  deallog << "Error A-norm " << std::sqrt(matrix.matrix_norm_square(x))
          << std::endl;

  FullMatrix<float> Ainv(4, 4);
  Ainv.invert(A);
  FullMatrix<float> Cinv(2, 2);
  Cinv.invert(C);

After creating a 2x2 BlockTrianglePrecondition object, we only fill its diagonals. The scaling factor 1/2 used for A is the reciprocal of the scaling factor used for the matrix itself. Remember, this preconditioner actually multiplies with the diagonal blocks.

  BlockTrianglePrecondition<double> precondition(2);
  precondition.enter(Ainv, 0, 0, .5);
  precondition.enter(Cinv, 1, 1);

Now, we have a block Jacobi preconditioner, which is still symmetric, since the blocks are symmetric. Therefore, we can still use the preconditioned conjugate gradient method.

  cg.solve(matrix, x, y, precondition);
  x.add(-1., result);
  deallog << "Error " << x.l2_norm() << std::endl;

Now, we enter the subdiagonal block. This is the same as in matrix.

  precondition.enter(B1, 1, 0, -1., true);
  precondition.enter(B2, 1, 0, 1.);

Since the preconditioner is not symmetric anymore, we use the GMRES method for solving.

  SolverGMRES<BlockVector<double>> gmres(control);
  gmres.solve(matrix, x, y, precondition);
  x.add(-1., result);
  deallog << "Error " << x.l2_norm() << std::endl;

Deprecated:

This class has been superseded by block_back_substitution and block_forward_substitution, which build on BlockLinearOperator.

Author

Guido Kanschat, 2001, 2005

Definition at line 421 of file block_matrix_array.h.

Member Typedef Documentation

template<typename number = double, typename BlockVectorType = BlockVector<number>>

using BlockTrianglePrecondition< number, BlockVectorType >::size_type = types::global_dof_index

Declare type for container size.

Definition at line 428 of file block_matrix_array.h.

Constructor & Destructor Documentation

template<typename number , typename BlockVectorType >

BlockTrianglePrecondition< number, BlockVectorType >::BlockTrianglePrecondition

(

)

Default constructor creating a useless object. initialize() must be called before using it.

Definition at line 258 of file block_matrix_array.cc.

template<typename number , typename BlockVectorType >

BlockTrianglePrecondition< number, BlockVectorType >::BlockTrianglePrecondition

(

const unsigned int

n_blocks

)

Constructor. This matrix must be block-quadratic, and n_blocks is the number of blocks in each direction.

Definition at line 265 of file block_matrix_array.cc.

Member Function Documentation

template<typename number , typename BlockVectorType >

void BlockTrianglePrecondition< number, BlockVectorType >::reinit

(

const unsigned int

n_block_rows

)

Resize preconditioner to a new size and clear all blocks.

Definition at line 274 of file block_matrix_array.cc.

template<typename number = double, typename BlockVectorType = BlockVector<number>>

template<typename MatrixType >

void BlockTrianglePrecondition< number, BlockVectorType >::enter	(	const MatrixType &	matrix,
		const size_type	row,
		const size_type	col,
		const number	prefix = 1.,
		const bool	transpose = false
	)

Enter a block. This calls BlockMatrixArray::enter(). Remember that the diagonal blocks should actually be inverse matrices or preconditioners.

template<typename number , typename BlockVectorType >

void BlockTrianglePrecondition< number, BlockVectorType >::vmult	(	BlockVectorType &	dst,
		const BlockVectorType &	src
	)		const

Preconditioning.

Definition at line 387 of file block_matrix_array.cc.

template<typename number , typename BlockVectorType >

void BlockTrianglePrecondition< number, BlockVectorType >::vmult_add	(	BlockVectorType &	dst,
		const BlockVectorType &	src
	)		const

Preconditioning adding to dst.

Definition at line 368 of file block_matrix_array.cc.

template<typename number , typename BlockVectorType >

void BlockTrianglePrecondition< number, BlockVectorType >::Tvmult	(	BlockVectorType &	dst,
		const BlockVectorType &	src
	)		const

Transposed preconditioning

Definition at line 412 of file block_matrix_array.cc.

template<typename number , typename BlockVectorType >

void BlockTrianglePrecondition< number, BlockVectorType >::Tvmult_add	(	BlockVectorType &	dst,
		const BlockVectorType &	src
	)		const

Transposed preconditioning adding to dst.

Definition at line 422 of file block_matrix_array.cc.

template<typename number , typename BlockVectorType >

void BlockTrianglePrecondition< number, BlockVectorType >::do_row ( BlockVectorType &  dst, size_type  row_num  ) const

private

Add all off-diagonal contributions and return the entry of the diagonal element for one row.

Definition at line 282 of file block_matrix_array.cc.

Member Data Documentation

template<typename number = double, typename BlockVectorType = BlockVector<number>>

bool BlockTrianglePrecondition< number, BlockVectorType >::backward

private

Flag for backward insertion.

Definition at line 536 of file block_matrix_array.h.

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The documentation for this class was generated from the following files:

• deal.II/lac/block_matrix_array.h
• /mnt/data/darndt/Sources/dealii-clang-6.0.0/source/lac/block_matrix_array.cc