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

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

Public Types
enum class	EigenvalueAlgorithm { lanczos , power_iteration }
enum class	PolynomialType { first_kind , fourth_kind }

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)
AdditionalData &	operator= (const AdditionalData &other_data)

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

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 1944 of file precondition.h.

Member Enumeration Documentation

EigenvalueAlgorithm

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

enum class PreconditionChebyshev::AdditionalData::EigenvalueAlgorithm

strong

An enum to define the available types of eigenvalue estimation algorithms.

Enumerator
lanczos	This option runs the conjugate gradient solver and computes an eigenvalue estimation from the underlying Lanczos space. This only works for symmetric positive definite matrices.
power_iteration	This option runs a power iteration to estimate the largest eigenvalue. This algorithm also works for non-symmetric matrices, but typically gives less accurate estimates than the option 'lanczos' because it does not take the relation between vectors in the iterations into account (roughly speaking the off-diagonal entries in the tri-diagonal matrix of the Lanczos iteration).

Definition at line 1950 of file precondition.h.

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 [125] and [147].

Definition at line 1972 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
	)

Constructor.

Member Function Documentation

operator=()

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

AdditionalData & PreconditionChebyshev< MatrixType, VectorType, PreconditionerType >::AdditionalData::operator=

(

const AdditionalData &

other_data

)

Copy assignment operator.

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 2016 of file precondition.h.

smoothing_range

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

double PreconditionChebyshev< MatrixType, VectorType, PreconditionerType >::AdditionalData::smoothing_range

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 Chebyshev polynomial 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 2029 of file precondition.h.

eig_cg_n_iterations

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

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

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 PreconditionChebyshev::AdditionalData::max_eigenvalue.

Definition at line 2037 of file precondition.h.

eig_cg_residual

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

double PreconditionChebyshev< MatrixType, VectorType, PreconditionerType >::AdditionalData::eig_cg_residual

Tolerance for CG iterations performed for finding the maximum eigenvalue.

Definition at line 2043 of file precondition.h.

max_eigenvalue

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

double PreconditionChebyshev< MatrixType, VectorType, PreconditionerType >::AdditionalData::max_eigenvalue

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 2050 of file precondition.h.

constraints

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

AffineConstraints<double> PreconditionChebyshev< MatrixType, VectorType, PreconditionerType >::AdditionalData::constraints

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 2056 of file precondition.h.

preconditioner

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

std::shared_ptr<PreconditionerType> PreconditionChebyshev< MatrixType, VectorType, PreconditionerType >::AdditionalData::preconditioner

Stores the preconditioner object that the Chebyshev is wrapped around.

Definition at line 2061 of file precondition.h.

eigenvalue_algorithm

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

EigenvalueAlgorithm PreconditionChebyshev< MatrixType, VectorType, PreconditionerType >::AdditionalData::eigenvalue_algorithm

Specifies the underlying eigenvalue estimation algorithm.

Definition at line 2066 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 2071 of file precondition.h.

---

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

• include/deal.II/lac/precondition.h