Reference documentation for deal.II version Git 27fb7ec 2016-07-13 12:46:58 -0400
Public Types | Public Member Functions | Static Public Member Functions | Private Member Functions | Private Attributes | List of all members
BlockTrianglePrecondition< number, BlockVectorType > Class Template Reference

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

Inheritance diagram for BlockTrianglePrecondition< number, BlockVectorType >:
[legend]

Public Types

typedef types::global_dof_index size_type
 

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 &&)
 
virtual ~Subscriptor ()
 
Subscriptoroperator= (const Subscriptor &)
 
Subscriptoroperator= (Subscriptor &&)
 
void subscribe (const char *identifier=0) const
 
void unsubscribe (const char *identifier=0) const
 
unsigned int n_subscriptions () 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< Entryentries
 

Additional Inherited Members

- Private Types inherited from BlockMatrixArray< number, BlockVectorType >
typedef types::global_dof_index size_type
 
- Static Private Member Functions inherited from Subscriptor
static::ExceptionBase & ExcInUse (int arg1, char *arg2, std::string &arg3)
 
static::ExceptionBase & ExcNoSubscriber (char *arg1, char *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.

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.

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

Author
Guido Kanschat, 2001, 2005

Definition at line 397 of file block_matrix_array.h.

Member Typedef Documentation

template<typename number = double, typename BlockVectorType = BlockVector<number>>
typedef types::global_dof_index BlockTrianglePrecondition< number, BlockVectorType >::size_type

Declare type for container size.

Definition at line 404 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 266 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 276 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 386 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 367 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 285 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 510 of file block_matrix_array.h.


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