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

Inheritance diagram for SolverBicgstab< VectorType >:

Classes
struct	AdditionalData

struct	IterationResult

Public Member Functions
	SolverBicgstab (SolverControl &cn, VectorMemory< VectorType > &mem, const AdditionalData &data=AdditionalData())

	SolverBicgstab (SolverControl &cn, const AdditionalData &data=AdditionalData())

virtual	~SolverBicgstab () override=default

template<typename MatrixType , typename PreconditionerType >
void	solve (const MatrixType &A, VectorType &x, const VectorType &b, const PreconditionerType &preconditioner)

Public Member Functions inherited from SolverBase< VectorType >
	SolverBase (SolverControl &solver_control, VectorMemory< VectorType > &vector_memory)

	SolverBase (SolverControl &solver_control)

boost::signals2::connection	connect (const std::function< SolverControl::State(const unsigned int iteration, const double check_value, const VectorType &current_iterate)> &slot)

Public Member Functions inherited from Subscriptor
	Subscriptor ()

	Subscriptor (const Subscriptor &)

	Subscriptor (Subscriptor &&) noexcept

virtual	~Subscriptor ()

Subscriptor &	operator= (const Subscriptor &)

Subscriptor &	operator= (Subscriptor &&) noexcept

void	subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const

void	unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const

unsigned int	n_subscriptions () const

template<typename StreamType >
void	list_subscribers (StreamType &stream) const

void	list_subscribers () const

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

Protected Member Functions
template<typename MatrixType >
double	criterion (const MatrixType &A, const VectorType &x, const VectorType &b)

virtual void	print_vectors (const unsigned int step, const VectorType &x, const VectorType &r, const VectorType &d) const

Protected Member Functions inherited from internal::SolverBicgstabData
	SolverBicgstabData ()

Protected Attributes
VectorType *	Vx

VectorMemory< VectorType >::Pointer	Vr

VectorMemory< VectorType >::Pointer	Vrbar

VectorMemory< VectorType >::Pointer	Vp

VectorMemory< VectorType >::Pointer	Vy

VectorMemory< VectorType >::Pointer	Vz

VectorMemory< VectorType >::Pointer	Vt

VectorMemory< VectorType >::Pointer	Vv

const VectorType *	Vb

AdditionalData	additional_data

Protected Attributes inherited from SolverBase< VectorType >
GrowingVectorMemory< VectorType >	static_vector_memory

VectorMemory< VectorType > &	memory

boost::signals2::signal< SolverControl::State(const unsigned int iteration, const double check_value, const VectorType &current_iterate), StateCombiner >	iteration_status

Protected Attributes inherited from internal::SolverBicgstabData
double	alpha

double	beta

double	omega

double	rho

double	rhobar

unsigned int	step

double	res

Private Member Functions
template<typename MatrixType >
SolverControl::State	start (const MatrixType &A)

template<typename MatrixType , typename PreconditionerType >
IterationResult	iterate (const MatrixType &A, const PreconditionerType &preconditioner)

Additional Inherited Members
Public Types inherited from SolverBase< VectorType >
using	vector_type = VectorType

Static Public Member Functions inherited from Subscriptor
static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

static ::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string arg2)

Detailed Description

template<typename VectorType = Vector<double>>
class SolverBicgstab< VectorType >

Bicgstab algorithm by van der Vorst.

For the requirements on matrices and vectors in order to work with this class, see the documentation of the Solver base class.

Like all other solver classes, this class has a local structure called AdditionalData which is used to pass additional parameters to the solver, like damping parameters or the number of temporary vectors. We use this additional structure instead of passing these values directly to the constructor because this makes the use of the SolverSelector and other classes much easier and guarantees that these will continue to work even if number or type of the additional parameters for a certain solver changes.

The Bicgstab-method has two additional parameters: the first is a boolean, deciding whether to compute the actual residual in each step (true) or to use the length of the computed orthogonal residual (false). Note that computing the residual causes a third matrix-vector-multiplication, though no additional preconditioning, in each step. The reason for doing this is, that the size of the orthogonalized residual computed during the iteration may be larger by orders of magnitude than the true residual. This is due to numerical instabilities related to badly conditioned matrices. Since this instability results in a bad stopping criterion, the default for this parameter is true. Whenever the user knows that the estimated residual works reasonably as well, the flag should be set to false in order to increase the performance of the solver.

The second parameter is the size of a breakdown criterion. It is difficult to find a general good criterion, so if things do not work for you, try to change this value.

Observing the progress of linear solver iterations

The solve() function of this class uses the mechanism described in the Solver base class to determine convergence. This mechanism can also be used to observe the progress of the iteration.

Definition at line 124 of file solver_bicgstab.h.