Reference documentation for deal.II version 8.4.2
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PreconditionChebyshev< MatrixType, VectorType > Class Template Reference
Linear algebra classesLinear algebra classes » | Matrix classes » Preconditioners and Relaxation Operators

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

Inheritance diagram for PreconditionChebyshev< MatrixType, VectorType >:
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Classes

struct  AdditionalData
 

Public Types

typedef types::global_dof_index size_type
 

Public Member Functions

void initialize (const MatrixType &matrix, const AdditionalData &additional_data=AdditionalData())
 
void vmult (VectorType &dst, const VectorType &src) const
 
void Tvmult (VectorType &dst, const VectorType &src) const
 
void clear ()
 
size_type m () const
 
size_type n () const
 
- Public Member Functions inherited from Subscriptor
 Subscriptor ()
 
 Subscriptor (const Subscriptor &)
 
virtual ~Subscriptor ()
 
Subscriptor & operator= (const Subscriptor &)
 
void subscribe (const char *identifier=0) const
 
void unsubscribe (const char *identifier=0) const
 
unsigned int n_subscriptions () const
 
void list_subscribers () const
 
 DeclException3 (ExcInUse, int, char *, std::string &,<< "Object of class "<< arg2<< " is still used by "<< arg1<< " other objects."<< "\"<< "(Additional information: "<< arg3<< ")\"<< "See the entry in the Frequently Asked Questions of "<< "deal.II (linked to from http://www.dealii.org/) for "<< "a lot more information on what this error means and "<< "how to fix programs in which it happens.")
 
 DeclException2 (ExcNoSubscriber, char *, char *,<< "No subscriber with identifier <"<< arg2<< "> subscribes to this object of class "<< arg1<< ". Consequently, it cannot be unsubscribed.")
 
template<class Archive >
void serialize (Archive &ar, const unsigned int version)
 

Private Attributes

SmartPointer< const MatrixType, PreconditionChebyshev< MatrixType, VectorType > > matrix_ptr
 
VectorType update1
 
VectorType update2
 
AdditionalData data
 
double theta
 
double delta
 
bool is_initialized
 

Detailed Description

template<typename MatrixType = SparseMatrix<double>, class VectorType = Vector<double>>
class PreconditionChebyshev< MatrixType, VectorType >

Preconditioning with a Chebyshev polynomial for symmetric positive definite matrices. This preconditioner is similar to a Jacobi preconditioner if the degree variable is set to one, otherwise some higher order polynomial corrections are used. This preconditioner needs access to the diagonal of the matrix it acts on and needs a respective vmult implementation. However, it does not need to explicitly know the matrix entries.

This class is useful e.g. in multigrid smoother objects, since it is trivially parallel (assuming that matrix-vector products are parallel).

Author
Martin Kronbichler, 2009; extension for full compatibility with LinearOperator class: Jean-Paul Pelteret, 2015

Definition at line 812 of file precondition.h.

Member Typedef Documentation

§ size_type

template<typename MatrixType = SparseMatrix<double>, class VectorType = Vector<double>>
typedef types::global_dof_index PreconditionChebyshev< MatrixType, VectorType >::size_type

Declare type for container size.

Definition at line 818 of file precondition.h.

Member Function Documentation

§ initialize()

template<typename MatrixType = SparseMatrix<double>, class VectorType = Vector<double>>
void PreconditionChebyshev< MatrixType, VectorType >::initialize ( const MatrixType &  matrix,
const AdditionalData &  additional_data = AdditionalData() 
)

Initialize function. Takes the matrix which is used to form the preconditioner, and additional flags if there are any. This function works only if the input matrix has an operator el(i,i) for accessing all the elements in the diagonal. Alternatively, the diagonal can be supplied with the help of the AdditionalData field.

This function calculates an estimate of the eigenvalue range of the matrix weighted by its diagonal using a modified CG iteration in case the given number of iterations is positive.

§ vmult()

template<typename MatrixType = SparseMatrix<double>, class VectorType = Vector<double>>
void PreconditionChebyshev< MatrixType, VectorType >::vmult ( VectorType &  dst,
const VectorType &  src 
) const

Computes the action of the preconditioner on src, storing the result in dst.

§ Tvmult()

template<typename MatrixType = SparseMatrix<double>, class VectorType = Vector<double>>
void PreconditionChebyshev< MatrixType, VectorType >::Tvmult ( VectorType &  dst,
const VectorType &  src 
) const

Computes the action of the transposed preconditioner on src, storing the result in dst.

§ clear()

template<typename MatrixType = SparseMatrix<double>, class VectorType = Vector<double>>
void PreconditionChebyshev< MatrixType, VectorType >::clear ( )

Resets the preconditioner.

§ m()

template<typename MatrixType = SparseMatrix<double>, class VectorType = Vector<double>>
size_type PreconditionChebyshev< MatrixType, VectorType >::m ( ) const

Return the dimension of the codomain (or range) space. To remember: the matrix is of dimension $m \times n$.

§ n()

template<typename MatrixType = SparseMatrix<double>, class VectorType = Vector<double>>
size_type PreconditionChebyshev< MatrixType, VectorType >::n ( ) const

Return the dimension of the domain space. To remember: the matrix is of dimension $m \times n$.

Member Data Documentation

§ matrix_ptr

template<typename MatrixType = SparseMatrix<double>, class VectorType = Vector<double>>
SmartPointer<const MatrixType,PreconditionChebyshev<MatrixType,VectorType> > PreconditionChebyshev< MatrixType, VectorType >::matrix_ptr
private

A pointer to the underlying matrix.

Definition at line 946 of file precondition.h.

§ update1

template<typename MatrixType = SparseMatrix<double>, class VectorType = Vector<double>>
VectorType PreconditionChebyshev< MatrixType, VectorType >::update1
mutableprivate

Internal vector used for the vmult operation.

Definition at line 951 of file precondition.h.

§ update2

template<typename MatrixType = SparseMatrix<double>, class VectorType = Vector<double>>
VectorType PreconditionChebyshev< MatrixType, VectorType >::update2
mutableprivate

Internal vector used for the vmult operation.

Definition at line 956 of file precondition.h.

§ data

template<typename MatrixType = SparseMatrix<double>, class VectorType = Vector<double>>
AdditionalData PreconditionChebyshev< MatrixType, VectorType >::data
private

Stores the additional data provided to the initialize function.

Definition at line 961 of file precondition.h.

§ theta

template<typename MatrixType = SparseMatrix<double>, class VectorType = Vector<double>>
double PreconditionChebyshev< MatrixType, VectorType >::theta
private

Average of the largest and smallest eigenvalue under consideration.

Definition at line 966 of file precondition.h.

§ delta

template<typename MatrixType = SparseMatrix<double>, class VectorType = Vector<double>>
double PreconditionChebyshev< MatrixType, VectorType >::delta
private

Half the interval length between the largest and smallest eigenvalue under consideration.

Definition at line 972 of file precondition.h.

§ is_initialized

template<typename MatrixType = SparseMatrix<double>, class VectorType = Vector<double>>
bool PreconditionChebyshev< MatrixType, VectorType >::is_initialized
private

Stores whether the preconditioner has been set up.

Definition at line 977 of file precondition.h.

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