Reference documentation for deal.II version 9.4.0
SolverBicgstab< VectorType > Class Template Reference

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

Inheritance diagram for SolverBicgstab< VectorType >:
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## Classes

struct  IterationResult

## Public Types

using vector_type = Vector< double >

## Public Member Functions

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 Vector< double > &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

GrowingVectorMemory< Vector< double > > static_vector_memory

VectorMemory< Vector< double > > & memory

boost::signals2::signal< SolverControl::State(const unsigned int iteration, const double check_value, const Vector< double > &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 intcounter

std::map< std::string, unsigned intcounter_map

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

const std::type_info * object_info

static std::mutex mutex

static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)

static ::ExceptionBaseExcNoSubscriber (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.

## ◆ vector_type

 using SolverBase< Vector< double > >::vector_type = Vector< double >
inherited

An alias for the underlying vector type

Definition at line 346 of file solver.h.

## ◆ 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.

## ◆ 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()

 boost::signals2::connection SolverBase< Vector< double > >::connect ( const std::function< SolverControl::State(const unsigned int iteration, const double check_value, const Vector< double > ¤t_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.

## ◆ 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::Pointer SolverBicgstab< VectorType >::Vr
protected

Auxiliary vector.

Definition at line 202 of file solver_bicgstab.h.

## ◆ Vrbar

template<typename VectorType = Vector<double>>
 VectorMemory::Pointer SolverBicgstab< VectorType >::Vrbar
protected

Auxiliary vector.

Definition at line 207 of file solver_bicgstab.h.

## ◆ Vp

template<typename VectorType = Vector<double>>
 VectorMemory::Pointer SolverBicgstab< VectorType >::Vp
protected

Auxiliary vector.

Definition at line 212 of file solver_bicgstab.h.

## ◆ Vy

template<typename VectorType = Vector<double>>
 VectorMemory::Pointer SolverBicgstab< VectorType >::Vy
protected

Auxiliary vector.

Definition at line 217 of file solver_bicgstab.h.

## ◆ Vz

template<typename VectorType = Vector<double>>
 VectorMemory::Pointer SolverBicgstab< VectorType >::Vz
protected

Auxiliary vector.

Definition at line 222 of file solver_bicgstab.h.

## ◆ Vt

template<typename VectorType = Vector<double>>
 VectorMemory::Pointer SolverBicgstab< VectorType >::Vt
protected

Auxiliary vector.

Definition at line 227 of file solver_bicgstab.h.

## ◆ Vv

template<typename VectorType = Vector<double>>
 VectorMemory::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.

template<typename VectorType = Vector<double>>
protected

Definition at line 260 of file solver_bicgstab.h.

## ◆ static_vector_memory

 GrowingVectorMemory > SolverBase< Vector< double > >::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

 VectorMemory >& SolverBase< Vector< double > >::memory
protectedinherited

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

Definition at line 419 of file solver.h.

## ◆ iteration_status

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