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

Inheritance diagram for SolverMinRes< VECTOR >:
Inheritance graph
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List of all members.

Classes

struct  AdditionalData
class  ExcPreconditionerNotDefinite

Public Member Functions

 SolverMinRes (SolverControl &cn, VectorMemory< VECTOR > &mem, const AdditionalData &data=AdditionalData())
 SolverMinRes (SolverControl &cn, const AdditionalData &data=AdditionalData())
virtual ~SolverMinRes ()
template<class MATRIX , class PRECONDITIONER >
void solve (const MATRIX &A, VECTOR &x, const VECTOR &b, const PRECONDITIONER &precondition)

Protected Member Functions

virtual double criterion ()
virtual void print_vectors (const unsigned int step, const VECTOR &x, const VECTOR &r, const VECTOR &d) const

Protected Attributes

VECTOR * Vu0
VECTOR * Vu1
VECTOR * Vu2
VECTOR * Vm0
VECTOR * Vm1
VECTOR * Vm2
VECTOR * Vv
double res2

Detailed Description

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

Minimal residual method for symmetric matrices.

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 MinRes 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.

The preconditioner has to be positive definite and symmetric

The algorithm is taken from the Master thesis of Astrid Batterman with some changes. The full text can be found at http://scholar.lib.vt.edu/theses/public/etd-12164379662151/etd-title.html

Author:
Thomas Richter, 2000, Luca Heltai, 2006

Constructor & Destructor Documentation

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

Constructor.

template<class VECTOR = Vector<double>>
SolverMinRes< VECTOR >::SolverMinRes ( 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 SolverMinRes< VECTOR >::~SolverMinRes (  )  [virtual]

Virtual destructor.


Member Function Documentation

template<class VECTOR = Vector<double>>
template<class MATRIX , class PRECONDITIONER >
void SolverMinRes< 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 double SolverMinRes< VECTOR >::criterion (  )  [protected, virtual]

Implementation of the computation of the norm of the residual.

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


Member Data Documentation

template<class VECTOR = Vector<double>>
VECTOR* SolverMinRes< VECTOR >::Vu0 [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 * SolverMinRes< VECTOR >::Vu1 [protected]
template<class VECTOR = Vector<double>>
VECTOR * SolverMinRes< VECTOR >::Vu2 [protected]
template<class VECTOR = Vector<double>>
VECTOR* SolverMinRes< VECTOR >::Vm0 [protected]
template<class VECTOR = Vector<double>>
VECTOR * SolverMinRes< VECTOR >::Vm1 [protected]
template<class VECTOR = Vector<double>>
VECTOR * SolverMinRes< VECTOR >::Vm2 [protected]
template<class VECTOR = Vector<double>>
VECTOR* SolverMinRes< VECTOR >::Vv [protected]
template<class VECTOR = Vector<double>>
double SolverMinRes< 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.


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

deal.II documentation generated on Mon Nov 23 22:58:05 2009 by doxygen 1.6.1