SolverQMRS< VECTOR > Class Template Reference
[Linear solver classes]

Inheritance diagram for SolverQMRS< VECTOR >:

Inheritance graph
[legend]

List of all members.

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

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

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

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 
) [inline]

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 (  )  [protected, virtual]

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 
) [inline, 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.

template<class VECTOR = Vector<double>>
VECTOR* SolverQMRS< VECTOR >::Vp [protected]

template<class VECTOR = Vector<double>>
VECTOR* SolverQMRS< VECTOR >::Vq [protected]

template<class VECTOR = Vector<double>>
VECTOR* SolverQMRS< VECTOR >::Vt [protected]

template<class VECTOR = Vector<double>>
VECTOR* SolverQMRS< VECTOR >::Vd [protected]

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

Iteration vector.

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

RHS vector.

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.

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

Additional parameters..

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

The current iteration step.


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

deal.II documentation generated on Sat Aug 15 16:52:18 2009 by doxygen 1.5.9