#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 ()

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

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

	Solver (SolverControl &solver_control)

boost::signals2::connection	connect (const std_cxx11::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 &&)

virtual	~Subscriptor ()

Subscriptor &	operator= (const Subscriptor &)

Subscriptor &	operator= (Subscriptor &&)

void	subscribe (const char *identifier=0) const

void	unsubscribe (const char *identifier=0) const

unsigned int	n_subscriptions () 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 Attributes
VectorType *	Vx

VectorType *	Vr

VectorType *	Vrbar

VectorType *	Vp

VectorType *	Vy

VectorType *	Vz

VectorType *	Vt

VectorType *	Vv

const VectorType *	Vb

double	alpha

double	beta

double	omega

double	rho

double	rhobar

unsigned int	step

double	res

AdditionalData	additional_data

Protected Attributes inherited from Solver< 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

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

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

Additional Inherited Members
Public Types inherited from Solver< VectorType >
typedef VectorType	vector_type

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

static ::ExceptionBase &	ExcNoSubscriber (char arg1, char 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 73 of file solver_bicgstab.h.

Constructor & Destructor Documentation

◆ SolverBicgstab() [1/2]

template<typename VectorType = Vector<double>>

SolverBicgstab< VectorType >::SolverBicgstab	(	SolverControl &	cn,
		VectorMemory< VectorType > &	mem,
		const AdditionalData &	data = `AdditionalData()`
	)

Constructor.

◆ SolverBicgstab() [2/2]

template<typename VectorType = Vector<double>>

SolverBicgstab< VectorType >::SolverBicgstab	(	SolverControl &	cn,
		const AdditionalData &	data = `AdditionalData()`
	)

Constructor. Use an object of type GrowingVectorMemory as a default to allocate memory.

◆ ~SolverBicgstab()

template<typename VectorType = Vector<double>>

virtual SolverBicgstab< VectorType >::~SolverBicgstab ( )

virtual

Virtual destructor.

Member Function Documentation

◆ solve()

template<typename VectorType = Vector<double>>

template<typename MatrixType , typename PreconditionerType >

void SolverBicgstab< VectorType >::solve	(	const MatrixType &	A,
		VectorType &	x,
		const VectorType &	b,
		const PreconditionerType &	precondition
	)

Solve primal problem only.

◆ criterion()

template<typename VectorType = Vector<double>>

template<typename MatrixType >

double SolverBicgstab< VectorType >::criterion	(	const MatrixType &	A,
		const VectorType &	x,
		const VectorType &	b
	)

protected

Computation of the stopping criterion.

◆ print_vectors()

template<typename VectorType = Vector<double>>

virtual void SolverBicgstab< VectorType >::print_vectors	(	const unsigned int	step,
		const VectorType &	x,
		const VectorType &	r,
		const VectorType &	d
	)		const

protectedvirtual

Interface for derived class. This function gets the current iteration vector, the residual and the update vector in each step. It can be used for a graphical output of the convergence history.

◆ start()

template<typename VectorType = Vector<double>>

template<typename MatrixType >

SolverControl::State SolverBicgstab< VectorType >::start ( const MatrixType & A )

private

Everything before the iteration loop.

◆ iterate()

template<typename VectorType = Vector<double>>

template<typename MatrixType , typename PreconditionerType >

IterationResult SolverBicgstab< VectorType >::iterate	(	const MatrixType &	A,
		const PreconditionerType &	precondition
	)

protected

Residual.

Definition at line 222 of file solver_bicgstab.h.

◆ additional_data

template<typename VectorType = Vector<double>>

AdditionalData SolverBicgstab< VectorType >::additional_data

protected

Additional parameters.

Definition at line 227 of file solver_bicgstab.h.

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

deal.II/lac/solver_bicgstab.h

Classes

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Additional Inherited Members

Detailed Description

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

Observing the progress of linear solver iterations

Constructor & Destructor Documentation

◆ SolverBicgstab() [1/2]

◆ SolverBicgstab() [2/2]

◆ ~SolverBicgstab()

Member Function Documentation

◆ solve()

◆ criterion()

◆ print_vectors()

◆ start()

◆ iterate()

Member Data Documentation

◆ Vx

◆ Vr

◆ Vrbar

◆ Vp

◆ Vy

◆ Vz

◆ Vt

◆ Vv

◆ Vb

◆ alpha

◆ beta

◆ omega

◆ rho

◆ rhobar

◆ step

◆ res

◆ additional_data

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