Reference documentation for deal.II version 9.4.1
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Public Types | Public Member Functions | Protected Attributes | Private Types | List of all members

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

Inheritance diagram for PreconditionSOR< MatrixType >:

Public Types

using AdditionalData = typename BaseClass::AdditionalData
using size_type = types::global_dof_index

Public Member Functions

void initialize (const MatrixType &A, const AdditionalData &parameters=AdditionalData())
void clear ()
size_type m () const
size_type n () const
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

Protected Attributes

SmartPointer< const MatrixType, PreconditionRelaxation< MatrixType > > A
double relaxation
unsigned int n_iterations
std::shared_ptr< PreconditionerTypepreconditioner

Private Types

using PreconditionerType = internal::PreconditionRelaxation::PreconditionSORImpl< MatrixType >
using BaseClass = PreconditionRelaxation< MatrixType, PreconditionerType >

Subscriptor functionality

Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.

using map_value_type = decltype(counter_map)::value_type
using map_iterator = decltype(counter_map)::iterator
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)
std::atomic< unsigned intcounter
std::map< std::string, unsigned intcounter_map
std::vector< std::atomic< bool > * > validity_pointers
const std::type_info * object_info
static std::mutex mutex
static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)
static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string arg2)
void check_no_subscribers () const noexcept

Detailed Description

template<typename MatrixType = SparseMatrix<double>>
class PreconditionSOR< MatrixType >

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.

// Declare related objects
SolverCG<> solver(...);
//...initialize and build A
// Define and initialize preconditioner
solver.solve (A, x, b, precondition);
Definition: vector.h:109
SmartPointer< const MatrixType, PreconditionRelaxation< MatrixType > > A
Definition: precondition.h:503
typename BaseClass::AdditionalData AdditionalData
void initialize(const MatrixType &A, const AdditionalData &parameters=AdditionalData())

Definition at line 1202 of file precondition.h.

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