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Reference documentation for deal.II version 9.0.0
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Reference documentation for deal.II version 9.0.0
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#include <deal.II/lac/precondition_block.h>
Classes | |
| class | AdditionalData |
Public Types | |
| typedef types::global_dof_index | size_type |
Public Member Functions | |
| PreconditionBlock (bool store_diagonals=false) | |
| ~PreconditionBlock ()=default | |
| void | initialize (const MatrixType &A, const AdditionalData parameters) |
| void | clear () |
| bool | empty () const |
| value_type | el (size_type i, size_type j) const |
| void | invert_diagblocks () |
| template<typename number2 > | |
| void | forward_step (Vector< number2 > &dst, const Vector< number2 > &prev, const Vector< number2 > &src, const bool transpose_diagonal) const |
| template<typename number2 > | |
| void | backward_step (Vector< number2 > &dst, const Vector< number2 > &prev, const Vector< number2 > &src, const bool transpose_diagonal) const |
| size_type | block_size () const |
| std::size_t | memory_consumption () const |
 Public 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 |
| void | list_subscribers () const |
| template<class Archive > | |
| void | serialize (Archive &ar, const unsigned int version) |
Static Public Member Functions | |
| static ::ExceptionBase & | ExcWrongBlockSize (int arg1, int arg2) |
| static ::ExceptionBase & | ExcInverseMatricesAlreadyExist () |
| Static Public 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) |
Protected Member Functions | |
| void | initialize (const MatrixType &A, const std::vector< size_type > &permutation, const std::vector< size_type > &inverse_permutation, const AdditionalData parameters) |
| void | set_permutation (const std::vector< size_type > &permutation, const std::vector< size_type > &inverse_permutation) |
| void | invert_permuted_diagblocks () |
| Protected Member Functions inherited from PreconditionBlockBase< inverse_type > | |
| PreconditionBlockBase (bool store_diagonals=false, Inversion method=gauss_jordan) | |
| ~PreconditionBlockBase ()=default | |
| void | clear () |
| void | reinit (unsigned int nblocks, size_type blocksize, bool compress, Inversion method=gauss_jordan) |
| void | inverses_computed (bool are_they) |
| bool | same_diagonal () const |
| bool | store_diagonals () const |
| bool | inverses_ready () const |
| unsigned int | size () const |
| void | inverse_vmult (size_type i, Vector< number2 > &dst, const Vector< number2 > &src) const |
| void | inverse_Tvmult (size_type i, Vector< number2 > &dst, const Vector< number2 > &src) const |
| FullMatrix< inverse_type > & | inverse (size_type i) |
| const FullMatrix< inverse_type > & | inverse (size_type i) const |
| Householder< inverse_type > & | inverse_householder (size_type i) |
| const Householder< inverse_type > & | inverse_householder (size_type i) const |
| LAPACKFullMatrix< inverse_type > & | inverse_svd (size_type i) |
| const LAPACKFullMatrix< inverse_type > & | inverse_svd (size_type i) const |
| FullMatrix< inverse_type > & | diagonal (size_type i) |
| const FullMatrix< inverse_type > & | diagonal (size_type i) const |
| void | log_statistics () const |
| std::size_t | memory_consumption () const |
Protected Attributes | |
| size_type | blocksize |
| SmartPointer< const MatrixType, PreconditionBlock< MatrixType, inverse_type > > | A |
| double | relaxation |
| std::vector< size_type > | permutation |
| std::vector< size_type > | inverse_permutation |
| Protected Attributes inherited from PreconditionBlockBase< inverse_type > | |
| Inversion | inversion |
Private Types | |
| typedef MatrixType::value_type | number |
| typedef inverse_type | value_type |
Additional Inherited Members | |
| Protected Types inherited from PreconditionBlockBase< inverse_type > | |
| enum | Inversion |
| typedef types::global_dof_index | size_type |
| Static Protected Member Functions inherited from PreconditionBlockBase< inverse_type > | |
| static ::ExceptionBase & | ExcDiagonalsNotStored () |
| static ::ExceptionBase & | ExcInverseNotAvailable () |
Base class for actual block preconditioners. This class assumes the MatrixType consisting of invertible blocks of blocksize on the diagonal and provides the inversion of the diagonal blocks of the matrix. It is not necessary for this class that the matrix be block diagonal; rather, it applies to matrices of arbitrary structure with the minimal property of having invertible blocks on the diagonal. Still the matrix must have access to single matrix entries. Therefore, BlockMatrixArray and similar classes are not a possible matrix class template arguments.
The block matrix structure used by this class is given, e.g., for the DG method for the transport equation. For a downstream numbering the matrices even have got a block lower left matrix structure, i.e. the matrices are empty above the diagonal blocks.
For all matrices that are empty above and below the diagonal blocks (i.e. for all block diagonal matrices) the BlockJacobi preconditioner is a direct solver. For all matrices that are empty only above the diagonal blocks (e.g. the matrices one gets by the DG method with downstream numbering) BlockSOR is a direct solver.
This first implementation of the PreconditionBlock assumes the matrix has blocks each of the same block size. Varying block sizes within the matrix must still be implemented if needed.
The first template parameter denotes the type of number representation in the sparse matrix, the second denotes the type of number representation in which the inverted diagonal block matrices are stored within this class by invert_diagblocks(). If you don't want to use the block inversion as an exact solver, but rather as a preconditioner, you may probably want to store the inverted blocks with less accuracy than the original matrix; for example, number==double, inverse_type=float might be a viable choice.
Definition at line 81 of file precondition_block.h.
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private |
Define number type of matrix.
Definition at line 89 of file precondition_block.h.
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Value type for inverse matrices.
Definition at line 94 of file precondition_block.h.
| typedef types::global_dof_index PreconditionBlock< MatrixType, inverse_type >::size_type |
Declare type for container size.
Definition at line 100 of file precondition_block.h.
| PreconditionBlock< MatrixType, inverse_type >::PreconditionBlock | ( | bool | store_diagonals = false | ) |
Constructor.
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default |
Destructor.
| void PreconditionBlock< MatrixType, inverse_type >::initialize | ( | const MatrixType & | A, |
| const AdditionalData | parameters | ||
| ) |
Initialize matrix and block size. We store the matrix and the block size in the preconditioner object. In a second step, the inverses of the diagonal blocks may be computed.
Additionally, a relaxation parameter for derived classes may be provided.
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Initialize matrix and block size for permuted preconditioning. Additionally to the parameters of the other initialize() function, we hand over two index vectors with the permutation and its inverse. For the meaning of these vectors see PreconditionBlockSOR.
In a second step, the inverses of the diagonal blocks may be computed. Make sure you use invert_permuted_diagblocks() to yield consistent data.
Additionally, a relaxation parameter for derived classes may be provided.
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Set either the permutation of rows or the permutation of blocks, depending on the size of the vector.
If the size of the permutation vectors is equal to the dimension of the linear system, it is assumed that rows are permuted individually. In this case, set_permutation() must be called before initialize(), since the diagonal blocks are built from the permuted entries of the matrix.
If the size of the permutation vector is not equal to the dimension of the system, the diagonal blocks are computed from the unpermuted entries. Instead, the relaxation methods step() and Tstep() are executed applying the blocks in the order given by the permutation vector. They will throw an exception if length of this vector is not equal to the number of blocks.
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Replacement of invert_diagblocks() for permuted preconditioning.
| void PreconditionBlock< MatrixType, inverse_type >::clear | ( | ) |
Deletes the inverse diagonal block matrices if existent, sets the blocksize to 0, hence leaves the class in the state that it had directly after calling the constructor.
| bool PreconditionBlock< MatrixType, inverse_type >::empty | ( | ) | const |
Check whether the object is empty.
| value_type PreconditionBlock< MatrixType, inverse_type >::el | ( | size_type | i, |
| size_type | j | ||
| ) | const |
Read-only access to entries. This function is only possible if the inverse diagonal blocks are stored.
| void PreconditionBlock< MatrixType, inverse_type >::invert_diagblocks | ( | ) |
Stores the inverse of the diagonal blocks in inverse. This costs some additional memory - for DG methods about 1/3 (for double inverses) or 1/6 (for float inverses) of that used for the matrix - but it makes the preconditioning much faster.
It is not allowed to call this function twice (will produce an error) before a call of clear(...) because at the second time there already exist the inverse matrices.
After this function is called, the lock on the matrix given through the use_matrix function is released, i.e. you may overwrite of delete it. You may want to do this in case you use this matrix to precondition another matrix.
| void PreconditionBlock< MatrixType, inverse_type >::forward_step | ( | Vector< number2 > & | dst, |
| const Vector< number2 > & | prev, | ||
| const Vector< number2 > & | src, | ||
| const bool | transpose_diagonal | ||
| ) | const |
Perform one block relaxation step in forward numbering.
Depending on the arguments dst and pref, this performs an SOR step (both reference the same vector) of a Jacobi step (both different vectors). For the Jacobi step, the calling function must copy dst to pref after this.
| void PreconditionBlock< MatrixType, inverse_type >::backward_step | ( | Vector< number2 > & | dst, |
| const Vector< number2 > & | prev, | ||
| const Vector< number2 > & | src, | ||
| const bool | transpose_diagonal | ||
| ) | const |
Perform one block relaxation step in backward numbering.
Depending on the arguments dst and pref, this performs an SOR step (both reference the same vector) of a Jacobi step (both different vectors). For the Jacobi step, the calling function must copy dst to pref after this.
| size_type PreconditionBlock< MatrixType, inverse_type >::block_size | ( | ) | const |
Return the size of the blocks.
| std::size_t PreconditionBlock< MatrixType, inverse_type >::memory_consumption | ( | ) | const |
Determine an estimate for the memory consumption (in bytes) of this object.
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Size of the blocks. Each diagonal block is assumed to be of the same size.
Definition at line 326 of file precondition_block.h.
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Pointer to the matrix. Make sure that the matrix exists as long as this class needs it, i.e. until calling invert_diagblocks, or (if the inverse matrices should not be stored) until the last call of the preconditoining vmult function of the derived classes.
Definition at line 334 of file precondition_block.h.
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Relaxation parameter to be used by derived classes.
Definition at line 338 of file precondition_block.h.
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The permutation vector
Definition at line 343 of file precondition_block.h.
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The inverse permutation vector
Definition at line 348 of file precondition_block.h.
1.8.14