Reference documentation for deal.II version 9.1.1
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Classes | Public Member Functions | Protected Member Functions | Protected Attributes | Private Member Functions | List of all members
SolverBicgstab< VectorType > Class Template Reference

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

Inheritance diagram for SolverBicgstab< VectorType >:
[legend]

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 ()
 
Subscriptoroperator= (const Subscriptor &)
 
Subscriptoroperator= (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), StateCombineriteration_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 ::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 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.

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.

◆ 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 &  preconditioner 
)
private

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

Member Data Documentation

◆ Vx

template<typename VectorType = Vector<double>>
VectorType* SolverBicgstab< VectorType >::Vx
protected

Auxiliary vector.

Definition at line 194 of file solver_bicgstab.h.

◆ Vr

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

Auxiliary vector.

Definition at line 199 of file solver_bicgstab.h.

◆ Vrbar

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

Auxiliary vector.

Definition at line 204 of file solver_bicgstab.h.

◆ Vp

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

Auxiliary vector.

Definition at line 209 of file solver_bicgstab.h.

◆ Vy

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

Auxiliary vector.

Definition at line 214 of file solver_bicgstab.h.

◆ Vz

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

Auxiliary vector.

Definition at line 219 of file solver_bicgstab.h.

◆ Vt

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

Auxiliary vector.

Definition at line 224 of file solver_bicgstab.h.

◆ Vv

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

Auxiliary vector.

Definition at line 229 of file solver_bicgstab.h.

◆ Vb

template<typename VectorType = Vector<double>>
const VectorType* SolverBicgstab< VectorType >::Vb
protected

Right hand side vector.

Definition at line 234 of file solver_bicgstab.h.

◆ additional_data

template<typename VectorType = Vector<double>>
AdditionalData SolverBicgstab< VectorType >::additional_data
protected

Additional parameters.

Definition at line 257 of file solver_bicgstab.h.


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