Meros::LSCPreconditionerFactory Class Reference

Factory for building least squares commutator style block preconditioner. More...

#include <Meros_LSCPreconditionerFactory.h>

List of all members.

Public Member Functions

Constructors/initializers/accessors
 LSCPreconditionerFactory ()
 Default constructor.
 LSCPreconditionerFactory (RCP< const LinearOpWithSolveFactoryBase< double > > const &FSolveStrategy, RCP< const LinearOpWithSolveFactoryBase< double > > const &BBtSolveStrategy)
 Constructor for Pressure Convection-Diffusion preconditioner factory. Takes an AztecOO parameter list for the F (convection-diffusion) solve and the B*Bt solve.
Overridden from PreconditionerFactoryBase
bool isCompatible (const LinearOpSourceBase< double > &fwdOpSrc) const
 Check that a LinearOperator object is compatible with *this factory object.
RCP< PreconditionerBase< double > > createPrec () const
 Create an (uninitialized) LinearOperator object to be initalized as the preconditioner later in this->initializePrecOp().
void initializePrec (const RCP< const LinearOpSourceBase< double > > &fwdOpSrc, PreconditionerBase< double > *precOp, const ESupportSolveUse supportSolveUse=SUPPORT_SOLVE_UNSPECIFIED) const
 Initialize the LSCPreconditioner object.
void uninitializePrec (PreconditionerBase< double > *prec, RCP< const LinearOpSourceBase< double > > *fwdOpSrc, ESupportSolveUse *supportSolveUse=NULL) const
 Uninitialize the LSCPreconditioner object.
Overridden from ParameterListAcceptor
void setParameterList (RCP< ParameterList > const &paramList)
 
RCP< ParameterList > getNonconstParameterList ()
 
RCP< ParameterList > unsetParameterList ()
 
RCP< const ParameterList > getParameterList () const
 
RCP< const Teuchos::ParameterList > getValidParameters () const
 


Detailed Description

Factory for building least squares commutator style block preconditioner.

Note that the LSC preconditioner assumes that we are using a stable discretization an a uniform mesh.

The LDU factors of a saddle point system are given as follows:

$ \left[ \begin{array}{cc} A & B^T \\ B & C \end{array} \right] = \left[ \begin{array}{cc} I & \\ BF^{-1} & I \end{array} \right] \left[ \begin{array}{cc} F & \\ & -S \end{array} \right] \left[ \begin{array}{cc} I & F^{-1} B^T \\ & I \end{array} \right], $

where $S$ is the Schur complement $S = B F^{-1} B^T - C$. A pressure convection-diffusion style preconditioner is then given by

$ P^{-1} = \left[ \begin{array}{cc} F & B^T \\ & -\tilde S \end{array} \right]^{-1} = \left[ \begin{array}{cc} F^{-1} & \\ & I \end{array} \right] \left[ \begin{array}{cc} I & -B^T \\ & I \end{array} \right] \left[ \begin{array}{cc} I & \\ & -\tilde S^{-1} \end{array} \right] $

where for $\tilde S$ is an approximation to the Schur complement S.

To apply the above preconditioner, we need a linear solver on the (0,0) block and an approximation to the inverse of the Schur complement.

To build a concrete preconditioner object, we will also need a 2x2 block Thyra matrix or the 4 separate blocks as either Thyra or Epetra matrices. If Thyra, assumes each block is a Thyra EpetraMatrix.


Member Function Documentation

RCP< PreconditionerBase< double > > LSCPreconditionerFactory::createPrec (  )  const

Create an (uninitialized) LinearOperator object to be initalized as the preconditioner later in this->initializePrecOp().

Note that on output return->domain().get()==NULL may be true which means that the operator is not fully initialized. In fact, the output operator object is not guaranteed to be fully initialized until after it is passed through this->initializePrecOp().


The documentation for this class was generated from the following files:
Generated on Wed May 12 21:40:17 2010 for Meros by  doxygen 1.4.7