Conjugate gradient solver for MAC grid linear algebra. More...

#include <macpcgsolver.hpp>

Public Member Functions
	MACPCGSolver (int nx, int ny, int nz)
	Allocate scratch space for linear system with given MAC dimensions.
	MACPCGSolver (const MACPCGSolver< scalar_t > &S)
	Copy constructor.
virtual void	resize (int nx, int ny, int nz)
	Reallocate solver space for given MAC dimensions.
int	xdim () const
int	ydim () const
int	zdim () const
void	setTolerance (scalar_t tol)
void	setMaxIter (unsigned max)
scalar_t	getTolerance () const
unsigned	getMaxIter () const
unsigned	LastIter () const
	Number of iterations that cgsolve() has performed.
scalar_t	ResNorm () const
	$\ell^2$ -norm of
void	pcgsolve (MACPrecond< scalar_t > &A, const MACVector< scalar_t > &b, MACVector< scalar_t > &x)
	Conjugate gradient for .
Protected Member Functions
scalar_t	macheps ()
	Estimate "machine epsilon.".
Protected Attributes
int	nx_
int	ny_
int	nz_
MACVector< scalar_t >	res
	Residue vector in iterative linear solver.
MACVector< scalar_t >	p0
MACVector< scalar_t >	p1
MACVector< scalar_t >	q
MACVector< scalar_t >	z
scalar_t	tol_
	Stopping tolerance.
unsigned	maxiter_
	Iteration bound.
scalar_t	rnorm_
	Current residue norm.
unsigned	iter_
	Iteration counter.

Detailed Description

template<typename scalar_t>
class fdl::MACPCGSolver< scalar_t >

Conjugate gradient solver for MAC grid linear algebra.

The main utility of the class is to encapsulate (and manage) the scratch vectors used in the iterative algorithm. Hence the salient constructor parameters are the MAC grid dimensions. However dimension checking for all terms is performed at the outset of each call to of cgsolve(). Dimension mismatch will throw a standar error.

Convergence is measured by the usual criterion

$\|\rho_n\|_{\ell^2} \leq \epsilon_{\mathrm{tol}}$

where $\rho_n$ denotes the residue vector of the n-th iteration, and $\epsilon_{\mathrm{tol}}$ is set by setTolerance. Failure to converge is handled in one of two ways:

do nothing (default),
throw a standard exception. The latter behavior is enforced by passing the definition -DABORT_ON_DIVERGENCE when compiling the solver.

The tolerance $\epsilon_{\mathrm{tol}}$ is initialized in dependence on "machine epsilon," specifically

$\epsilon_{\mathrm{tol}} = \sqrt{\epsilon_{\mathrm{mach}}},$

for the template paramter.

Definition at line 58 of file macpcgsolver.hpp.

Member Function Documentation

template<typename scalar_t>

void fdl::MACPCGSolver< scalar_t >::pcgsolve	(	MACPrecond< scalar_t > &	A,
		const MACVector< scalar_t > &	rhs,
		MACVector< scalar_t > &	soln
	)

Conjugate gradient for $Ax = b$ .

Follows structure of Algorithm 10.2.1 from Matrix Computations.

Definition at line 159 of file macpcgsolver.hpp.

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

macpcgsolver.hpp

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

template<typename scalar_t> class fdl::MACPCGSolver< scalar_t >

Member Function Documentation

template<typename scalar_t>
class fdl::MACPCGSolver< scalar_t >