Reference documentation for deal.II version 8.1.0
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SolverQMRS< VECTOR > Class Template Reference

#include <solver_qmrs.h>

Inheritance diagram for SolverQMRS< VECTOR >:
[legend]

Classes

struct  AdditionalData
 

Public Member Functions

 SolverQMRS (SolverControl &cn, VectorMemory< VECTOR > &mem, const AdditionalData &data=AdditionalData())
 
 SolverQMRS (SolverControl &cn, const AdditionalData &data=AdditionalData())
 
template<class MATRIX , class PRECONDITIONER >
void solve (const MATRIX &A, VECTOR &x, const VECTOR &b, const PRECONDITIONER &precondition)
 
virtual void print_vectors (const unsigned int step, const VECTOR &x, const VECTOR &r, const VECTOR &d) const
 
- 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

virtual double criterion ()
 

Protected Attributes

VECTOR * Vv
 
VECTOR * Vp
 
VECTOR * Vq
 
VECTOR * Vt
 
VECTOR * Vd
 
VECTOR * Vx
 
const VECTOR * Vb
 
double res2
 
AdditionalData additional_data
 
- Protected Attributes inherited from Solver< VECTOR >
GrowingVectorMemory< VECTOR > static_vector_memory
 
SolverControlcntrl
 
VectorMemory< VECTOR > & memory
 

Private Member Functions

template<class MATRIX , class PRECONDITIONER >
bool iterate (const MATRIX &A, const PRECONDITIONER &precondition)
 

Private Attributes

unsigned int step
 

Detailed Description

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

Quasi-minimal residual method for symmetric matrices.

The QMRS method is supposed to solve symmetric indefinite linear systems with symmetric, not necessarily definite preconditioners. This version of QMRS is adapted from Freund/Nachtigal: Software for simplified Lanczos and QMR algorithms, Appl. Num. Math. 19 (1995), pp. 319-341

This version is for right preconditioning only, since then only the preconditioner is used: left preconditioning seems to require the inverse.

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.

However, since the QMRS method does not need additional data, the respective structure is empty and does not offer any functionality. The constructor has a default argument, so you may call it without the additional parameter.

Author
Guido Kanschat, 1999

Definition at line 67 of file solver_qmrs.h.

Constructor & Destructor Documentation

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

Constructor.

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

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

Member Function Documentation

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

Solve the linear system $Ax=b$ for x.

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

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>>
virtual double SolverQMRS< VECTOR >::criterion ( )
protectedvirtual

Implementation of the computation of the norm of the residual.

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

The iteration loop itself.

Member Data Documentation

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

Temporary vectors, allocated through the VectorMemory object at the start of the actual solution process and deallocated at the end.

Definition at line 168 of file solver_qmrs.h.

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

Iteration vector.

Definition at line 176 of file solver_qmrs.h.

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

RHS vector.

Definition at line 180 of file solver_qmrs.h.

template<class VECTOR = Vector<double>>
double SolverQMRS< VECTOR >::res2
protected

Within the iteration loop, the square of the residual vector is stored in this variable. The function criterion uses this variable to compute the convergence value, which in this class is the norm of the residual vector and thus the square root of the res2 value.

Definition at line 192 of file solver_qmrs.h.

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

Additional parameters..

Definition at line 196 of file solver_qmrs.h.

template<class VECTOR = Vector<double>>
unsigned int SolverQMRS< VECTOR >::step
private

The current iteration step.

Definition at line 207 of file solver_qmrs.h.


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