Reference documentation for deal.II version SVN Revision 32790
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SolverBicgstab< VECTOR > Class Template Reference

#include <solver_bicgstab.h>

Inheritance diagram for SolverBicgstab< VECTOR >:
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Classes

struct  AdditionalData
 

Public Member Functions

 SolverBicgstab (SolverControl &cn, VectorMemory< VECTOR > &mem, const AdditionalData &data=AdditionalData())
 
 SolverBicgstab (SolverControl &cn, const AdditionalData &data=AdditionalData())
 
virtual ~SolverBicgstab ()
 
template<class MATRIX , class PRECONDITIONER >
void solve (const MATRIX &A, VECTOR &x, const VECTOR &b, const PRECONDITIONER &precondition)
 
- Public Member Functions inherited from Solver< VECTOR >
 Solver (SolverControl &solver_control, VectorMemory< VECTOR > &vector_memory)
 
 Solver (SolverControl &solver_control)
 
SolverControlcontrol () const
 
- Public Member Functions inherited from Subscriptor
 Subscriptor ()
 
 Subscriptor (const Subscriptor &)
 
virtual ~Subscriptor ()
 
Subscriptoroperator= (const Subscriptor &)
 
void subscribe (const char *identifier=0) const
 
void unsubscribe (const char *identifier=0) const
 
unsigned int n_subscriptions () const
 
void list_subscribers () const
 
 DeclException3 (ExcInUse, int, char *, std::string &,<< "Object of class "<< arg2<< " is still used by "<< arg1<< " other objects.\n"<< "(Additional information: "<< arg3<< ")\n"<< "Note the entry in the Frequently Asked Questions of "<< "deal.II (linked to from http://www.dealii.org/) for "<< "more information on what this error means.")
 
 DeclException2 (ExcNoSubscriber, char *, char *,<< "No subscriber with identifier \""<< arg2<< "\" did subscribe to this object of class "<< arg1)
 
template<class Archive >
void serialize (Archive &ar, const unsigned int version)
 

Protected Member Functions

template<class MATRIX >
double criterion (const MATRIX &A, const VECTOR &x, const VECTOR &b)
 
virtual void print_vectors (const unsigned int step, const VECTOR &x, const VECTOR &r, const VECTOR &d) const
 

Protected Attributes

VECTOR * Vx
 
VECTOR * Vr
 
VECTOR * Vrbar
 
VECTOR * Vp
 
VECTOR * Vy
 
VECTOR * Vz
 
VECTOR * Vt
 
VECTOR * Vv
 
const VECTOR * Vb
 
double alpha
 
double beta
 
double omega
 
double rho
 
double rhobar
 
unsigned int step
 
double res
 
AdditionalData additional_data
 
- Protected Attributes inherited from Solver< VECTOR >
GrowingVectorMemory< VECTOR > static_vector_memory
 
SolverControlcntrl
 
VectorMemory< VECTOR > & memory
 

Private Member Functions

template<class MATRIX >
SolverControl::State start (const MATRIX &A)
 
template<class MATRIX , class PRECONDITIONER >
bool iterate (const MATRIX &A, const PRECONDITIONER &precondition)
 

Detailed Description

template<class VECTOR = Vector<double>>
class SolverBicgstab< VECTOR >

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.

Definition at line 67 of file solver_bicgstab.h.

Constructor & Destructor Documentation

template<class VECTOR = Vector<double>>
SolverBicgstab< VECTOR >::SolverBicgstab ( SolverControl cn,
VectorMemory< VECTOR > &  mem,
const AdditionalData data = AdditionalData() 
)

Constructor.

template<class VECTOR = Vector<double>>
SolverBicgstab< VECTOR >::SolverBicgstab ( SolverControl cn,
const AdditionalData data = AdditionalData() 
)

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

template<class VECTOR = Vector<double>>
virtual SolverBicgstab< VECTOR >::~SolverBicgstab ( )
virtual

Virtual destructor.

Member Function Documentation

template<class VECTOR = Vector<double>>
template<class MATRIX , class PRECONDITIONER >
void SolverBicgstab< VECTOR >::solve ( const MATRIX A,
VECTOR &  x,
const VECTOR &  b,
const PRECONDITIONER &  precondition 
)

Solve primal problem only.

template<class VECTOR = Vector<double>>
template<class MATRIX >
double SolverBicgstab< VECTOR >::criterion ( const MATRIX A,
const VECTOR &  x,
const VECTOR &  b 
)
protected

Computation of the stopping criterion.

template<class VECTOR = Vector<double>>
virtual void SolverBicgstab< VECTOR >::print_vectors ( const unsigned int  step,
const VECTOR &  x,
const VECTOR &  r,
const VECTOR &  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.

template<class VECTOR = Vector<double>>
template<class MATRIX >
SolverControl::State SolverBicgstab< VECTOR >::start ( const MATRIX A)
private

Everything before the iteration loop.

template<class VECTOR = Vector<double>>
template<class MATRIX , class PRECONDITIONER >
bool SolverBicgstab< VECTOR >::iterate ( const MATRIX A,
const PRECONDITIONER &  precondition 
)
private

The iteration loop itself.

Member Data Documentation

template<class VECTOR = Vector<double>>
VECTOR* SolverBicgstab< VECTOR >::Vx
protected

Auxiliary vector.

Definition at line 152 of file solver_bicgstab.h.

template<class VECTOR = Vector<double>>
VECTOR* SolverBicgstab< VECTOR >::Vr
protected

Auxiliary vector.

Definition at line 156 of file solver_bicgstab.h.

template<class VECTOR = Vector<double>>
VECTOR* SolverBicgstab< VECTOR >::Vrbar
protected

Auxiliary vector.

Definition at line 160 of file solver_bicgstab.h.

template<class VECTOR = Vector<double>>
VECTOR* SolverBicgstab< VECTOR >::Vp
protected

Auxiliary vector.

Definition at line 164 of file solver_bicgstab.h.

template<class VECTOR = Vector<double>>
VECTOR* SolverBicgstab< VECTOR >::Vy
protected

Auxiliary vector.

Definition at line 168 of file solver_bicgstab.h.

template<class VECTOR = Vector<double>>
VECTOR* SolverBicgstab< VECTOR >::Vz
protected

Auxiliary vector.

Definition at line 172 of file solver_bicgstab.h.

template<class VECTOR = Vector<double>>
VECTOR* SolverBicgstab< VECTOR >::Vt
protected

Auxiliary vector.

Definition at line 176 of file solver_bicgstab.h.

template<class VECTOR = Vector<double>>
VECTOR* SolverBicgstab< VECTOR >::Vv
protected

Auxiliary vector.

Definition at line 180 of file solver_bicgstab.h.

template<class VECTOR = Vector<double>>
const VECTOR* SolverBicgstab< VECTOR >::Vb
protected

Right hand side vector.

Definition at line 184 of file solver_bicgstab.h.

template<class VECTOR = Vector<double>>
double SolverBicgstab< VECTOR >::alpha
protected

Auxiliary value.

Definition at line 189 of file solver_bicgstab.h.

template<class VECTOR = Vector<double>>
double SolverBicgstab< VECTOR >::beta
protected

Auxiliary value.

Definition at line 193 of file solver_bicgstab.h.

template<class VECTOR = Vector<double>>
double SolverBicgstab< VECTOR >::omega
protected

Auxiliary value.

Definition at line 197 of file solver_bicgstab.h.

template<class VECTOR = Vector<double>>
double SolverBicgstab< VECTOR >::rho
protected

Auxiliary value.

Definition at line 201 of file solver_bicgstab.h.

template<class VECTOR = Vector<double>>
double SolverBicgstab< VECTOR >::rhobar
protected

Auxiliary value.

Definition at line 205 of file solver_bicgstab.h.

template<class VECTOR = Vector<double>>
unsigned int SolverBicgstab< VECTOR >::step
protected

Current iteration step.

Definition at line 210 of file solver_bicgstab.h.

template<class VECTOR = Vector<double>>
double SolverBicgstab< VECTOR >::res
protected

Residual.

Definition at line 215 of file solver_bicgstab.h.

template<class VECTOR = Vector<double>>
AdditionalData SolverBicgstab< VECTOR >::additional_data
protected

Additional parameters.

Definition at line 220 of file solver_bicgstab.h.


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