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

Richardson iterative solver for linear systems. Satisfies the SolverLike concept (see solver.hpp). Implements the update rule: More...

#include <richardson.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.

Public Member Functions
	Richardson (const int iterations, const double omega, const RHSVectorType &r_tmp)
	Construct a Richardson solver.
void	solve_impl (OperatorType &A, SolutionVectorType &x, const RHSVectorType &b)
	Solve the linear system using Richardson iteration. Applies the update rule for the specified number of iterations.

Detailed Description

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

Richardson iterative solver for linear systems. Satisfies the SolverLike concept (see solver.hpp). Implements the update rule:

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

where \( \omega \) is the relaxation parameter.

Template Parameters

OperatorT

Operator type (must satisfy OperatorLike).

Member Typedef Documentation

OperatorType

template<OperatorLike OperatorT>

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

Operator type to be solved.

RHSVectorType

template<OperatorLike OperatorT>

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

Right-hand side vector type.

SolutionVectorType

template<OperatorLike OperatorT>

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

Solution vector type.

Constructor & Destructor Documentation

Richardson()

template<OperatorLike OperatorT>

terra::linalg::solvers::Richardson< OperatorT >::Richardson ( const int  iterations, const double  omega, const RHSVectorType &  r_tmp  )

inline

Construct a Richardson solver.

Parameters

iterations	Number of Richardson iterations to perform.
omega	Relaxation parameter.
r_tmp	Temporary vector for workspace.

Member Function Documentation

solve_impl()

template<OperatorLike OperatorT>

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

inline

Solve the linear system using Richardson 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:

• richardson.hpp