terra::linalg::solvers::Jacobi< OperatorT > Class Template Reference

Jacobi iterative solver for linear systems. More...

#include <jacobi.hpp>

Public Types
using	OperatorType = OperatorT
	Operator type to be solved.
using	SolutionVectorType = SrcOf< OperatorType >
	Solution vector type.
using	RHSVectorType = DstOf< OperatorType >
	Right-hand side vector type.
using	ScalarType = SolutionVectorType::ScalarType
	Scalar type for computations.

Public Member Functions
	Jacobi (const SolutionVectorType &inverse_diagonal, const int iterations, const SolutionVectorType &tmp, const ScalarType omega=1.0)
	Construct a Jacobi solver.
void	solve_impl (OperatorType &A, SolutionVectorType &x, const RHSVectorType &b)
	Solve the linear system using Jacobi iteration. Applies the update rule for the specified number of iterations.
SolutionVectorType &	get_inverse_diagonal ()

Detailed Description

template<OperatorLike OperatorT>
class terra::linalg::solvers::Jacobi< OperatorT >

Jacobi iterative solver for linear systems.

Satisfies the SolverLike concept (see solver.hpp). Uses a diagonal preconditioner and supports relaxation. The update rule is:

\[ x^{(k+1)} = x^{(k)} + \omega D^{-1} (b - Ax^{(k)}) \]

where \( D \) is the diagonal of \( A \) and \( \omega \) is the relaxation parameter.

Template Parameters

OperatorT

Operator type (must satisfy OperatorLike).

Member Typedef Documentation

OperatorType

template<OperatorLike OperatorT>

using terra::linalg::solvers::Jacobi< OperatorT >::OperatorType = OperatorT

Operator type to be solved.

RHSVectorType

template<OperatorLike OperatorT>

using terra::linalg::solvers::Jacobi< OperatorT >::RHSVectorType = DstOf< OperatorType >

Right-hand side vector type.

ScalarType

template<OperatorLike OperatorT>

using terra::linalg::solvers::Jacobi< OperatorT >::ScalarType = SolutionVectorType::ScalarType

Scalar type for computations.

SolutionVectorType

template<OperatorLike OperatorT>

using terra::linalg::solvers::Jacobi< OperatorT >::SolutionVectorType = SrcOf< OperatorType >

Solution vector type.

Constructor & Destructor Documentation

Jacobi()

template<OperatorLike OperatorT>

terra::linalg::solvers::Jacobi< OperatorT >::Jacobi ( const SolutionVectorType &  inverse_diagonal, const int  iterations, const SolutionVectorType &  tmp, const ScalarType  omega = 1.0  )

inline

Construct a Jacobi solver.

Parameters

inverse_diagonal	Inverse of the diagonal of the operator.
iterations	Number of Jacobi iterations to perform.
tmp	Temporary vector for workspace.
omega	Relaxation parameter (default 1.0).

Member Function Documentation

get_inverse_diagonal()

template<OperatorLike OperatorT>

SolutionVectorType & terra::linalg::solvers::Jacobi< OperatorT >::get_inverse_diagonal ( )

inline

solve_impl()

template<OperatorLike OperatorT>

void terra::linalg::solvers::Jacobi< OperatorT >::solve_impl ( OperatorType &  A, SolutionVectorType &  x, const RHSVectorType &  b  )

inline

Solve the linear system using Jacobi iteration. Applies the update rule for the specified number of iterations.

Parameters

A	Operator (matrix).
x	Solution vector (output).
b	Right-hand side vector (input).

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

• jacobi.hpp