Reference documentation for deal.II version 9.3.3
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#include <deal.II/lac/precondition.h>
Public Types | |
using | AdditionalData = typename PreconditionRelaxation< MatrixType >::AdditionalData |
using | size_type = typename MatrixType::size_type |
Public Member Functions | |
template<class VectorType > | |
void | vmult (VectorType &, const VectorType &) const |
template<class VectorType > | |
void | Tvmult (VectorType &, const VectorType &) const |
template<class VectorType > | |
void | step (VectorType &x, const VectorType &rhs) const |
template<class VectorType > | |
void | Tstep (VectorType &x, const VectorType &rhs) const |
void | initialize (const SparseMatrix< double > &A, const AdditionalData ¶meters=AdditionalData()) |
void | clear () |
size_type | m () const |
size_type | n () const |
Protected Attributes | |
SmartPointer< const SparseMatrix< double >, PreconditionRelaxation< SparseMatrix< double > > > | A |
double | relaxation |
Subscriptor functionality | |
Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class. | |
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) |
using | map_value_type = decltype(counter_map)::value_type |
using | map_iterator = decltype(counter_map)::iterator |
std::atomic< unsigned int > | counter |
std::map< std::string, unsigned int > | counter_map |
std::vector< std::atomic< bool > * > | validity_pointers |
const std::type_info * | object_info |
static std::mutex | mutex |
static ::ExceptionBase & | ExcInUse (int arg1, std::string arg2, std::string arg3) |
static ::ExceptionBase & | ExcNoSubscriber (std::string arg1, std::string arg2) |
void | check_no_subscribers () const noexcept |
SOR preconditioner using matrix built-in function.
Assuming the matrix A = D + L + U is split into its diagonal D as well as the strict lower and upper triangles L and U, then the SOR preconditioner with relaxation parameter r is
\[ P^{-1} = r (D+rL)^{-1}. \]
It is this operator P-1, which is implemented by vmult() through forward substitution. Analogously, Tvmult() implements the operation of r(D+rU)-1.
The SOR iteration itself can be directly written as
\[ x^{k+1} = x^k - r D^{-1} \bigl(L x^{k+1} + U x^k - b\bigr). \]
Using the right hand side b and the previous iterate x, this is the operation implemented by step().
The MatrixType class used is required to have functions precondition_SOR(VectorType&, const VectorType&, double)
and precondition_TSOR(VectorType&, const VectorType&, double)
. This class satisfies the relaxation concept.
Definition at line 583 of file precondition.h.
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inherited |
Declare type for container size.
Definition at line 408 of file precondition.h.
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inherited |
Initialize matrix and relaxation parameter. The matrix is just stored in the preconditioner object. The relaxation parameter should be larger than zero and smaller than 2 for numerical reasons. It defaults to 1.
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inherited |
Release the matrix and reset its pointer.
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inherited |
Return the dimension of the codomain (or range) space. Note that the matrix is of dimension \(m \times n\).
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inherited |
Return the dimension of the domain space. Note that the matrix is of dimension \(m \times n\).
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protectedinherited |
Pointer to the matrix object.
Definition at line 460 of file precondition.h.
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protectedinherited |
Relaxation parameter.
Definition at line 465 of file precondition.h.