PreconditionChebyshev< MatrixType, VectorType, PreconditionerType >::AdditionalData Struct Reference

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

Detailed Description

template<typename MatrixType = SparseMatrix<double>, typename VectorType = Vector<double>, typename PreconditionerType = DiagonalMatrix<VectorType>>
struct PreconditionChebyshev< MatrixType, VectorType, PreconditionerType >::AdditionalData

Standardized data struct to pipe additional parameters to the preconditioner.

Definition at line 2121 of file precondition.h.

Inheritance diagram for PreconditionChebyshev< MatrixType, VectorType, PreconditionerType >::AdditionalData:

Public Types
enum class	PolynomialType { first_kind , fourth_kind }
using	EigenvalueAlgorithm = internal::EigenvalueAlgorithm

Public Member Functions
	AdditionalData (const unsigned int degree=1, const double smoothing_range=0., const unsigned int eig_cg_n_iterations=8, const double eig_cg_residual=1e-2, const double max_eigenvalue=1, const EigenvalueAlgorithm eigenvalue_algorithm=EigenvalueAlgorithm::lanczos, const PolynomialType polynomial_type=PolynomialType::first_kind, const double safety_factor=1.2)

Public Attributes
unsigned int	degree
PolynomialType	polynomial_type
double	smoothing_range
unsigned int	eig_cg_n_iterations
double	eig_cg_residual
double	max_eigenvalue
::AffineConstraints< double >	constraints
EigenvalueAlgorithm	eigenvalue_algorithm
double	safety_factor
std::shared_ptr< PreconditionerType >	preconditioner

Member Typedef Documentation

EigenvalueAlgorithm

template<typename MatrixType = SparseMatrix<double>, typename VectorType = Vector<double>, typename PreconditionerType = DiagonalMatrix<VectorType>>

using PreconditionChebyshev< MatrixType, VectorType, PreconditionerType >::AdditionalData::EigenvalueAlgorithm = internal::EigenvalueAlgorithm

Definition at line 2124 of file precondition.h.

Member Enumeration Documentation

PolynomialType

template<typename MatrixType = SparseMatrix<double>, typename VectorType = Vector<double>, typename PreconditionerType = DiagonalMatrix<VectorType>>

enum class PreconditionChebyshev::AdditionalData::PolynomialType

strong

An enum to define the available types of polynomial types.

Enumerator
first_kind	First-kind Chebyshev polynomials.
fourth_kind	Fourth-kind Chebyshev polynomials according to [167] and [200].

Definition at line 2129 of file precondition.h.

Constructor & Destructor Documentation

AdditionalData()

template<typename MatrixType = SparseMatrix<double>, typename VectorType = Vector<double>, typename PreconditionerType = DiagonalMatrix<VectorType>>

PreconditionChebyshev< MatrixType, VectorType, PreconditionerType >::AdditionalData::AdditionalData	(	const unsigned int	degree = 1,
		const double	smoothing_range = 0.,
		const unsigned int	eig_cg_n_iterations = 8,
		const double	eig_cg_residual = 1e-2,
		const double	max_eigenvalue = 1,
		const EigenvalueAlgorithm	eigenvalue_algorithm = EigenvalueAlgorithm::lanczos,
		const PolynomialType	polynomial_type = PolynomialType::first_kind,
		const double	safety_factor = 1.2
	)

Constructor.

Member Data Documentation

degree

template<typename MatrixType = SparseMatrix<double>, typename VectorType = Vector<double>, typename PreconditionerType = DiagonalMatrix<VectorType>>

unsigned int PreconditionChebyshev< MatrixType, VectorType, PreconditionerType >::AdditionalData::degree

This determines the degree of the Chebyshev polynomial. The degree of the polynomial gives the number of matrix-vector products to be performed for one application of the step() operation. During vmult(), the method performs (degree-1) matrix-vector products. Degree one corresponds to a damped Jacobi method.

If the degree is set to numbers::invalid_unsigned_int, the algorithm will automatically determine the number of necessary iterations based on the usual Chebyshev error formula as mentioned in the discussion of the main class.

Definition at line 2168 of file precondition.h.

polynomial_type

template<typename MatrixType = SparseMatrix<double>, typename VectorType = Vector<double>, typename PreconditionerType = DiagonalMatrix<VectorType>>

PolynomialType PreconditionChebyshev< MatrixType, VectorType, PreconditionerType >::AdditionalData::polynomial_type

Specifies the polynomial type to be used.

Definition at line 2173 of file precondition.h.

smoothing_range

template<typename PreconditionerType >

double internal::EigenvalueAlgorithmAdditionalData< PreconditionerType >::smoothing_range

inherited

This sets the range between the largest eigenvalue in the matrix and the smallest eigenvalue to be treated. If the parameter is set to a number less than 1, an estimate for the largest and for the smallest eigenvalue will be calculated internally. For a smoothing range larger than one, the preconditioner will act in the interval \([\lambda_\mathrm{max}/ \tt{smoothing\_range}, \lambda_\mathrm{max}]\), where \(\lambda_\mathrm{max}\) is an estimate of the maximum eigenvalue of the matrix. A choice of smoothing_range between 5 and 20 is useful in case the preconditioner is used as a smoother in multigrid.

Definition at line 158 of file precondition.h.

eig_cg_n_iterations

template<typename PreconditionerType >

unsigned int internal::EigenvalueAlgorithmAdditionalData< PreconditionerType >::eig_cg_n_iterations

inherited

Maximum number of CG iterations performed for finding the maximum eigenvalue. If set to zero, no computations are performed. Instead, the user must supply a largest eigenvalue via the variable PreconditionRelaxation::AdditionalData::max_eigenvalue.

Definition at line 166 of file precondition.h.

eig_cg_residual

template<typename PreconditionerType >

double internal::EigenvalueAlgorithmAdditionalData< PreconditionerType >::eig_cg_residual

inherited

Tolerance for iterations performed for finding the maximum eigenvalue by the eigenvalue algorithm (Lanczos or power iteration).

Definition at line 172 of file precondition.h.

max_eigenvalue

template<typename PreconditionerType >

double internal::EigenvalueAlgorithmAdditionalData< PreconditionerType >::max_eigenvalue

inherited

Maximum eigenvalue to work with. Only in effect if eig_cg_n_iterations is set to zero, otherwise this parameter is ignored.

Definition at line 179 of file precondition.h.

constraints

template<typename PreconditionerType >

::AffineConstraints<double> internal::EigenvalueAlgorithmAdditionalData< PreconditionerType >::constraints

inherited

Constraints to be used for the operator given. This variable is used to zero out the correct entries when creating an initial guess.

Definition at line 185 of file precondition.h.

eigenvalue_algorithm

template<typename PreconditionerType >

EigenvalueAlgorithm internal::EigenvalueAlgorithmAdditionalData< PreconditionerType >::eigenvalue_algorithm

inherited

Stores the preconditioner object that the Chebyshev is wrapped around.

Definition at line 190 of file precondition.h.

safety_factor

template<typename PreconditionerType >

double internal::EigenvalueAlgorithmAdditionalData< PreconditionerType >::safety_factor

inherited

Safety factor that is multiplied to the estimated maximum eigenvalue before it is used in the preconditioner. This should be larger than 1 (default: 1.2) to ensure that the maximum eigenvalue is not underestimated.

Definition at line 198 of file precondition.h.

preconditioner

template<typename PreconditionerType >

std::shared_ptr<PreconditionerType> internal::EigenvalueAlgorithmAdditionalData< PreconditionerType >::preconditioner

inherited

Preconditioner.

Definition at line 203 of file precondition.h.

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

• include/deal.II/lac/precondition.h