solvers.hpp File Reference

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Functions
void	CG (const Operator &A, const Vector &b, Vector &x, int print_iter=0, int max_num_iter=1000, double RTOLERANCE=10e-12, double ATOLERANCE=10e-24)
void	PCG (const Operator &A, const Operator &B, const Vector &b, Vector &x, int print_iter=0, int max_num_iter=1000, double RTOLERANCE=10e-12, double ATOLERANCE=10e-24, int save=0)
int	GMRES (const Operator &A, Vector &x, const Vector &b, const Operator &M, int &max_iter, int m, double &tol, double &atol, int printit)
	A GMRES solver.
int	aGMRES (const Operator &A, Vector &x, const Vector &b, const Operator &M, int &max_iter, int m_max, int m_min, int m_step, double cf, double &tol, double &atol, int printit)
int	BiCGSTAB (const Operator &A, Vector &x, const Vector &b, const Operator &M, int &max_iter, double &tol, double atol, int printit)
	A BiCG-Stab solver.
void	SLI (const Operator &A, const Operator &B, const Vector &b, Vector &x, int print_iter=0, int max_num_iter=1000, double RTOLERANCE=10e-12, double ATOLERANCE=10e-24)
	Stationary linear iteration: x <- x + B (b - A x)

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Function Documentation

int aGMRES	(	const Operator &	A,
		Vector &	x,
		const Vector &	b,
		const Operator &	M,
		int &	max_iter,
		int	m_max,
		int	m_min,
		int	m_step,
		double	cf,
		double &	tol,
		double &	atol,
		int	printit
	)

Adaptive restarted GMRES. m_max and m_min(=1) are the maximal and minimal restart parameters. m_step(=1) is the step to use for going from m_max and m_min. cf(=0.4) is a desired convergance factor.

Definition at line 200 of file gmres.cpp.

References DenseMatrix::Add(), Add(), ApplyPlaneRotation(), GeneratePlaneRotation(), Operator::Mult(), norm(), Operator::Size(), subtract(), and Update().

int BiCGSTAB	(	const Operator &	A,
		Vector &	x,
		const Vector &	b,
		const Operator &	M,
		int &	max_iter,
		double &	tol,
		double	atol,
		int	printit
	)

A BiCG-Stab solver.

Definition at line 39 of file bicgstab.cpp.

References Vector::Add(), add(), Operator::Mult(), Operator::Size(), and subtract().

void CG	(	const Operator &	A,
		const Vector &	b,
		Vector &	x,
		int	print_iter = 0,
		int	max_num_iter = 1000,
		double	RTOLERANCE = 10e-12,
		double	ATOLERANCE = 10e-24
	)

Conjugate gradient method. Given Matrix A, vector b and initial guess x, iteratively solve A x = b. When the default arguments are used CG doesn't print current residual and number of iterations, maximum number of iterations is 1000, the relative tolerance is 10e-12 and the absolute tolerance is 10e-24.

Definition at line 20 of file cgsolver.cpp.

References add(), Operator::Mult(), Vector::Size(), and subtract().

int GMRES	(	const Operator &	A,
		Vector &	x,
		const Vector &	b,
		const Operator &	M,
		int &	max_iter,
		int	m,
		double &	tol,
		double &	atol,
		int	printit
	)

A GMRES solver.

Definition at line 84 of file gmres.cpp.

References DenseMatrix::Add(), Add(), ApplyPlaneRotation(), GeneratePlaneRotation(), Operator::Mult(), norm(), Operator::Size(), subtract(), and Update().

void PCG	(	const Operator &	A,
		const Operator &	B,
		const Vector &	b,
		Vector &	x,
		int	print_iter = 0,
		int	max_num_iter = 1000,
		double	RTOLERANCE = 10e-12,
		double	ATOLERANCE = 10e-24,
		int	save = 0
	)

Preconditioned conjugate gradient method. Given Matrix A, preconditioner Matrix B, vector b and initial guess x, iteratively solve A x = b. When the default arguments are used PCG doesn't print current residuals and number of iterations, maximum number of iterations is 1000, the relative tolerance is 10e-12 and the absolute tolerance is 10e-24. Remark : if no better initial guess is available, the user may set it as B b (since not done in PCG routine).

Definition at line 22 of file pcgsolver.cpp.

References add(), Operator::Mult(), Vector::Print(), Vector::Size(), and subtract().

Referenced by main().

void SLI	(	const Operator &	A,
		const Operator &	B,
		const Vector &	b,
		Vector &	x,
		int	print_iter = 0,
		int	max_num_iter = 1000,
		double	RTOLERANCE = 10e-12,
		double	ATOLERANCE = 10e-24
	)

Stationary linear iteration: x <- x + B (b - A x)

Definition at line 115 of file pcgsolver.cpp.

References add(), Operator::Mult(), Vector::Size(), and subtract().