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
void	subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
void	unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") 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 (std::atomic< bool > *const validity, const std::string &identifier="") const
void	unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") 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 Function Documentation

subscribe()

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

void Subscriptor::subscribe

Subscribes a user of the object by storing the pointer validity. The subscriber may be identified by text supplied as identifier.

Definition at line 130 of file subscriptor.cc.

unsubscribe()

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

void Subscriptor::unsubscribe

Unsubscribes a user from the object.

Note

The identifier and the validity pointer must be the same as the one supplied to subscribe().

Definition at line 150 of file subscriptor.cc.

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

• deal.II/lac/block_matrix_array.h
• /build/deal.ii-Kzz1m0/deal.ii-9.1.1/source/lac/block_matrix_array.cc