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Reference documentation for deal.II version 9.1.1
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#include <deal.II/lac/precondition.h>
Public Types | |
using | AdditionalData = typename PreconditionRelaxation< MatrixType >::AdditionalData |
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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 |
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void | initialize (const MatrixType &A, const AdditionalData ¶meters=AdditionalData()) |
void | clear () |
size_type | m () const |
size_type | n () const |
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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) |
Additional Inherited Members | |
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static ::ExceptionBase & | ExcInUse (int arg1, std::string arg2, std::string arg3) |
static ::ExceptionBase & | ExcNoSubscriber (std::string arg1, std::string arg2) |
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SmartPointer< const MatrixType, PreconditionRelaxation< MatrixType > > | A |
double | relaxation |
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 594 of file precondition.h.
using PreconditionSOR< MatrixType >::AdditionalData = typename PreconditionRelaxation<MatrixType>::AdditionalData |
An alias to the base class AdditionalData.
Definition at line 601 of file precondition.h.
void PreconditionSOR< MatrixType >::vmult | ( | VectorType & | , |
const VectorType & | |||
) | const |
Apply preconditioner.
void PreconditionSOR< MatrixType >::Tvmult | ( | VectorType & | , |
const VectorType & | |||
) | const |
Apply transpose preconditioner.
void PreconditionSOR< MatrixType >::step | ( | VectorType & | x, |
const VectorType & | rhs | ||
) | const |
Perform one step of the preconditioned Richardson iteration.
void PreconditionSOR< MatrixType >::Tstep | ( | VectorType & | x, |
const VectorType & | rhs | ||
) | const |
Perform one transposed step of the preconditioned Richardson iteration.