/usr/include/trilinos/Teko_ModALPreconditionerFactory.hpp is in libtrilinos-teko-dev 12.12.1-5.
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* Author: Zhen Wang
* Email: wangz@ornl.gov
* zhen.wang@alum.emory.edu
*/
#ifndef __Teko_ModALPreconditionerFactory_hpp__
#define __Teko_ModALPreconditionerFactory_hpp__
#include "Teko_BlockPreconditionerFactory.hpp"
#include "Teko_InvModALStrategy.hpp"
namespace Teko
{
namespace NS
{
/** \brief Class for saving state variables for
* ModALPreconditionerFactory.
*/
class ModALPrecondState : public BlockPreconditionerState
{
public:
ModALPrecondState();
LinearOp pressureMassMatrix_;
LinearOp invPressureMassMatrix_;
ModifiableLinearOp B1tMpB1_, B2tMpB2_, B3tMpB3_;
ModifiableLinearOp A11p_, A22p_, A33p_;
ModifiableLinearOp invA11p_, invA22p_, invA33p_, invS_;
ModifiableLinearOp S_;
double gamma_;
bool isStabilized_;
};
/** \brief Modified augmented Lagrangian-based preconditioner
* for incompressible Navier-Stokes equations.
*
* This class implements sparse matrix vector multiplication
* for augmented Lagrangian-based preconditioners.
* Details can be found in the following papers:
*
* [1] Benzi, M. A. Olshanskii and Z. Wang,
* Modified Augmented Lagrangian Preconditioners for the Incompressible Navier-Stokes Equations,
* International Journal for Numerical Methods in Fluids, 66 (2011), pp. 486-508.
*
* [2] M. Benzi and Z. Wang,
* Analysis of Augmented Lagrangian-Based Preconditioners
* for the Steady Incompressible Navier-Stokes Equations,
* SIAM J. Scientific Computing, 33 (2011), pp. 2761-2784.
*
* Suppose we are solving the following linear system:
*
* \f$
* \left[ \begin{array}{cc}
* A & B^T \\
* B & -C
* \end{array} \right]
* \left[ \begin{array}{c}
* u \\
* p
* \end{array} \right]
* =
* \left[ \begin{array}{c}
* f \\
* g
* \end{array} \right].
* \f$
*
* The equivalent augmented Lagrangian (AL) formulation is:
*
* \f$
* \left[ \begin{array}{cc}
* A + \gamma B^T W^{-1} B & B^T - \gamma B^T W^{-1} C \\
* B & -C
* \end{array} \right]
* \left[ \begin{array}{c}
* u \\
* p
* \end{array} \right]
* =
* \left[ \begin{array}{c}
* f + \gamma B^T W^{-1} g \\
* g
* \end{array} \right].
* \f$
*
* Here \f$ W \f$ can be take as the diagonal of the pressure
* mass matrix and \f$ \gamma \f$ is a positive number.
*
* If
* \f$ A = (A_{11}, A_{12}; A_{21}, A_{22})
* \quad \mathrm{and} \quad
* B = (B_1, B_2)
* \f$,
*
* then the modified AL preconditioner is defined as
*
* \f$
* \left[ \begin{array}{ccc}
* A_{11} + \gamma B_1^T W^{-1} B_1^T & A_{12} + \gamma B_1^T W^{-1} B_2^T & B_1^T - \gamma B_1^T W^{-1} C \\
* 0 & A_{22} + \gamma B_2^T W^{-1} B_2^T & B_1^T - \gamma B_2^T W^{-1} C \\
* 0 & 0 & S
* \end{array} \right].
* \f$
*
* More details (analysis, numerical results) can be found in [2].
*/
class ModALPreconditionerFactory : public BlockPreconditionerFactory
{
public:
ModALPreconditionerFactory();
ModALPreconditionerFactory(const Teuchos::RCP<InverseFactory> & factory);
ModALPreconditionerFactory(const Teuchos::RCP<InverseFactory> & invFactoryA,
const Teuchos::RCP<InverseFactory> & invFactoryS);
ModALPreconditionerFactory(const Teuchos::RCP<InverseFactory> & factory,
LinearOp & pressureMassMatrix);
ModALPreconditionerFactory(const Teuchos::RCP<InverseFactory> & invFactoryA,
const Teuchos::RCP<InverseFactory> & invFactoryS,
LinearOp & pressureMassMatrix);
ModALPreconditionerFactory(const Teuchos::RCP<InvModALStrategy> & strategy);
/** Set pressure mass matrix.
*
* \param[in] pressureMassMatrix
* Pressure mass matrix.
*/
void
setPressureMassMatrix(const LinearOp & pressureMassMatrix)
{
invOpsStrategy_->setPressureMassMatrix(pressureMassMatrix);
}
/** Set the augmentation parameter gamma.
*
* \param[in] gamma
* Augmentation paramter.
*/
void
setGamma(double gamma)
{
invOpsStrategy_->setGamma(gamma);
}
/**
* Build modified AL preconditioner.
*
* \param[in] alOp
* The AL operator.
* \param[in] state
* State object for storying reusable information about the AL operator.
*/
virtual LinearOp
buildPreconditionerOperator(BlockedLinearOp & alOp,
BlockPreconditionerState & state) const;
/**
* Build the ModALPrecondState object.
*/
virtual Teuchos::RCP<PreconditionerState>
buildPreconditionerState() const
{
return Teuchos::rcp(new ModALPrecondState());
}
protected:
using BlockPreconditionerFactory::buildPreconditionerOperator;
Teuchos::RCP<InvModALStrategy> invOpsStrategy_;
bool isSymmetric_;
};
} // end namespace NS
} // end namespace Teko
#endif /* __Teko_ModALPreconditionerFactory_hpp__ */
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