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

Inheritance diagram for SolverBicgstab< VectorType >:

Classes
struct	AdditionalData

struct	IterationResult

Public Types
using	vector_type = VectorType

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)

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

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

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

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

double	alpha

double	beta

double	omega

double	rho

double	rhobar

unsigned int	step

double	res

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

Subscriptor functionality
Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.
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)

void	check_no_subscribers () const noexcept

using	map_value_type = decltype(counter_map)::value_type

using	map_iterator = decltype(counter_map)::iterator

std::atomic< unsigned int >	counter

std::map< std::string, unsigned int >	counter_map

std::vector< std::atomic< bool > * >	validity_pointers

const std::type_info *	object_info

static std::mutex	mutex

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 SolverBase 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 found in the SolverBicgstab::AdditionalData struct: the first, exact_residual 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 breakdown 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.

Member Typedef Documentation

◆ vector_type

template<class VectorType = Vector<double>>

using SolverBase< VectorType >::vector_type = VectorType

inherited

An alias for the underlying vector type

Definition at line 346 of file solver.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 ( )

overridevirtualdefault

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 &	preconditioner
	)

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 graphical output of the convergence history.

◆ iterate()

template<typename VectorType = Vector<double>>

template<typename MatrixType , typename PreconditionerType >

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

private

The iteration loop itself. The function returns a structure indicating what happened in this function.

◆ connect()

template<class VectorType = Vector<double>>

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

inherited

Connect a function object that will be called periodically within iterative solvers. This function is used to attach monitors to iterative solvers, either to determine when convergence has happened, or simply to observe the progress of an iteration. See the documentation of this class for more information.

Parameters

slot A function object specified here will, with each call, receive the number of the current iteration, the value that is used to check for convergence (typically the residual of the current iterate with respect to the linear system to be solved) and the currently best available guess for the current iterate. Note that some solvers do not update the approximate solution in every iteration but only after convergence or failure has been determined (GMRES is an example); in such cases, the vector passed as the last argument to the signal is simply the best approximate at the time the signal is called, but not the vector that will be returned if the signal's return value indicates that the iteration should be terminated. The function object must return a SolverControl::State value that indicates whether the iteration should continue, has failed, or has succeeded. The results of all connected functions will then be combined to determine what should happen with the iteration.

Returns: A connection object that represents the connection from the signal to the function object. It can be used to disconnect the function object again from the signal. See the documentation of the BOOST Signals2 library for more information on connection management.

Member Data Documentation

◆ Vx

template<typename VectorType = Vector<double>>

VectorType* SolverBicgstab< VectorType >::Vx

protected

A pointer to the solution vector passed to solve().

Definition at line 197 of file solver_bicgstab.h.

◆ Vr

template<typename VectorType = Vector<double>>

VectorMemory<VectorType>::Pointer SolverBicgstab< VectorType >::Vr

protected

Auxiliary vector.

Definition at line 202 of file solver_bicgstab.h.

◆ Vrbar

template<typename VectorType = Vector<double>>

VectorMemory<VectorType>::Pointer SolverBicgstab< VectorType >::Vrbar

protected

Auxiliary vector.

Definition at line 207 of file solver_bicgstab.h.

◆ Vp

template<typename VectorType = Vector<double>>

VectorMemory<VectorType>::Pointer SolverBicgstab< VectorType >::Vp

protected

Auxiliary vector.

Definition at line 212 of file solver_bicgstab.h.

◆ Vy

template<typename VectorType = Vector<double>>

VectorMemory<VectorType>::Pointer SolverBicgstab< VectorType >::Vy

protected

Auxiliary vector.

Definition at line 217 of file solver_bicgstab.h.

◆ Vz

template<typename VectorType = Vector<double>>

VectorMemory<VectorType>::Pointer SolverBicgstab< VectorType >::Vz

protected

Auxiliary vector.

Definition at line 222 of file solver_bicgstab.h.

◆ Vt

template<typename VectorType = Vector<double>>

VectorMemory<VectorType>::Pointer SolverBicgstab< VectorType >::Vt

protected

Auxiliary vector.

Definition at line 227 of file solver_bicgstab.h.

◆ Vv

template<typename VectorType = Vector<double>>

VectorMemory<VectorType>::Pointer SolverBicgstab< VectorType >::Vv

protected

Auxiliary vector.

Definition at line 232 of file solver_bicgstab.h.

◆ Vb

template<typename VectorType = Vector<double>>

const VectorType* SolverBicgstab< VectorType >::Vb

protected

A pointer to the right hand side vector passed to solve().

Definition at line 237 of file solver_bicgstab.h.

◆ additional_data

template<typename VectorType = Vector<double>>

AdditionalData SolverBicgstab< VectorType >::additional_data

protected

Additional parameters.

Definition at line 260 of file solver_bicgstab.h.

◆ static_vector_memory

template<class VectorType = Vector<double>>

GrowingVectorMemory<VectorType> SolverBase< VectorType >::static_vector_memory

mutableprotectedinherited

A static vector memory object to be used whenever no such object has been given to the constructor.

Definition at line 414 of file solver.h.

◆ memory

template<class VectorType = Vector<double>>

VectorMemory<VectorType>& SolverBase< VectorType >::memory

protectedinherited

A reference to an object that provides memory for auxiliary vectors.

Definition at line 419 of file solver.h.

◆ iteration_status

template<class VectorType = Vector<double>>

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

protectedinherited

A signal that iterative solvers can execute at the end of every iteration (or in an otherwise periodic fashion) to find out whether we should continue iterating or not. The signal may call one or more slots that each will make this determination by themselves, and the result over all slots (function calls) will be determined by the StateCombiner object.

The arguments passed to the signal are (i) the number of the current iteration; (ii) the value that is used to determine convergence (oftentimes the residual, but in other cases other quantities may be used as long as they converge to zero as the iterate approaches the solution of the linear system); and (iii) a vector that corresponds to the current best guess for the solution at the point where the signal is called. Note that some solvers do not update the approximate solution in every iteration but only after convergence or failure has been determined (GMRES is an example); in such cases, the vector passed as the last argument to the signal is simply the best approximate at the time the signal is called, but not the vector that will be returned if the signal's return value indicates that the iteration should be terminated.

Definition at line 470 of file solver.h.

◆ alpha

double internal::SolverBicgstabData::alpha

protectedinherited

Auxiliary value.

Definition at line 48 of file solver_bicgstab.h.

◆ beta

double internal::SolverBicgstabData::beta

protectedinherited

Auxiliary value.

Definition at line 52 of file solver_bicgstab.h.

◆ omega

double internal::SolverBicgstabData::omega

protectedinherited

Auxiliary value.

Definition at line 56 of file solver_bicgstab.h.

◆ rho

double internal::SolverBicgstabData::rho

protectedinherited

Auxiliary value.

Definition at line 60 of file solver_bicgstab.h.

◆ rhobar

double internal::SolverBicgstabData::rhobar

protectedinherited

Auxiliary value.

Definition at line 64 of file solver_bicgstab.h.

◆ step

unsigned int internal::SolverBicgstabData::step

protectedinherited

Current iteration step.

Definition at line 69 of file solver_bicgstab.h.

◆ res

double internal::SolverBicgstabData::res

protectedinherited

Residual.

Definition at line 74 of file solver_bicgstab.h.

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

include/deal.II/lac/solver_bicgstab.h

Classes

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Subscriptor functionality

Detailed Description

Observing the progress of linear solver iterations

Member Typedef Documentation

◆ vector_type

Constructor & Destructor Documentation

◆ SolverBicgstab() [1/2]

◆ SolverBicgstab() [2/2]

◆ ~SolverBicgstab()

Member Function Documentation

◆ solve()

◆ criterion()

◆ print_vectors()

◆ iterate()

◆ connect()

Member Data Documentation

◆ Vx

◆ Vr

◆ Vrbar

◆ Vp

◆ Vy

◆ Vz

◆ Vt

◆ Vv

◆ Vb

◆ additional_data

◆ static_vector_memory

◆ memory

◆ iteration_status

◆ alpha

◆ beta

◆ omega

◆ rho

◆ rhobar

◆ step

◆ res