libtrilinos-teko-dev 12.4.2-2 / usr / include / trilinos / Teko_LSCStrategy.hpp

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#ifndef __Teko_LSCStrategy_hpp__
#define __Teko_LSCStrategy_hpp__

#include "Teuchos_RCP.hpp"

#include "Thyra_LinearOpBase.hpp"

#include "Teko_Utilities.hpp"
#include "Teko_InverseFactory.hpp"
#include "Teko_BlockPreconditionerFactory.hpp"

namespace Teko {
namespace NS {

class LSCPrecondState; // forward declaration

/** \brief Strategy for driving LSCPreconditionerFactory.
  *
  * Strategy for driving the LSCPreconditionerFactory. This
  * class provides all the pieces required by the LSC preconditioner.
  * The intent is that the user can overide them and build
  * there own implementation. Though a fairly substantial implementation
  * is provided in <code>InvLSCStrategy</code>.
  *
  * The basics of this method can be found in
  * 
  * [1] Elman, Howle, Shadid, Silvester, and Tuminaro, "Least Squares Preconditioners
  *     for Stabilized Discretizations of the Navier-Stokes Euqations," SISC-2007.
  *
  * [2] Elman, and Tuminaro, "Boundary Conditions in Approximate Commutator
  *     Preconditioners for the Navier-Stokes Equations," In press (8/2009)?
  *
  * The Least Squares Commuator preconditioner provides a (nearly) Algebraic approximation
  * of the Schur complement of the (Navier-)Stokes system
  *
  * \f$ A = \left[\begin{array}{cc} 
  *        F & B^T \\
  *        B & C
  *     \end{array}\right] \f$
  *
  * The approximation to the Schur complement is
  *
  * \f$ C - B F^{-1} B^T \approx (B \hat{Q}_u^{-1} B^T - \gamma C)^{-1}
  *       (B \hat{Q}_u^{-1} F H B^T+C_I) (B H B^T - \gamma C)^{-1}
  *     + C_O \f$.
  *
  * Where \f$\hat{Q}_u\f$ is typically a diagonal approximation of the mass matrix, 
  * and \f$H\f$ is an appropriate diagonal scaling matrix (see [2] for details). 
  * The scalars \f$\alpha\f$ and \f$\gamma\f$ are chosen to stabilize an unstable 
  * discretization (for the case of \f$C\neq 0\f$). If the system is stable then
  * they can be set to \f$0\f$ (see [1] for more details).
  *
  * In order to approximate \f$A\f$ two decompositions can be chosen, a full LU
  * decomposition and a purely upper triangular version. A full LU decomposition
  * requires that the velocity convection-diffusion operator (\f$F\f$) is inverted
  * twice, while an upper triangular approximation requires only a single inverse.
  *
  * The methods of this strategy provide the different pieces. For instance
  * <code>getInvF</code> provides \f$F^{-1}\f$. Similarly there are calls to get
  * the inverses of \f$B \hat{Q}_u^{-1} B^T - \gamma C\f$,
  * \f$B \hat{Q}_u^{-1} B^T - \gamma C\f$, and \f$\hat{Q}_u^{-1}\f$ as well as
  * the \f$H\f$ operator. All these methods are required by the
  * <code>LSCPreconditionerFactory</code>. Additionally there is a
  * <code>buildState</code> method that is called everytime a preconditiner is
  * (re)constructed. This is to allow for any preprocessing neccessary to be
  * handled.
  *
  * The final set of methods help construct a LSCStrategy object, they are
  * primarily used by the parameter list construction inteface. They are 
  * more advanced and can be ignored by initial implementations of this
  * class.
  */
class LSCStrategy {
public:
   virtual ~LSCStrategy() {}

   /** This informs the strategy object to build the state associated
     * with this operator.
     *
     * \param[in] A The linear operator to be preconditioned by LSC.
     * \param[in] state State object for storying reusable information about
     *                  the operator A.
     */
   virtual void buildState(BlockedLinearOp & A,BlockPreconditionerState & state) const = 0;

   /** Get the inverse of \f$B Q_u^{-1} B^T - \gamma C\f$. 
     *
     * \param[in] A The linear operator to be preconditioned by LSC.
     * \param[in] state State object for storying reusable information about
     *                  the operator A.
     *
     * \returns An (approximate) inverse of \f$B Q_u^{-1} B^T - \gamma C\f$.
     */
   virtual LinearOp getInvBQBt(const BlockedLinearOp & A,BlockPreconditionerState & state) const = 0;

   /** Get the inverse of \f$B H B^T - \gamma C\f$. 
     *
     * \param[in] A The linear operator to be preconditioned by LSC.
     * \param[in] state State object for storying reusable information about
     *                  the operator A.
     *
     * \returns An (approximate) inverse of \f$B H B^T - \gamma C\f$.
     */
   virtual LinearOp getInvBHBt(const BlockedLinearOp & A,BlockPreconditionerState & state) const = 0;

   /** Get the inverse of the \f$F\f$ block.
     *
     * \param[in] A The linear operator to be preconditioned by LSC.
     * \param[in] state State object for storying reusable information about
     *                  the operator A.
     *
     * \returns An (approximate) inverse of \f$F\f$.
     */
   virtual LinearOp getInvF(const BlockedLinearOp & A,BlockPreconditionerState & state) const = 0;

   #if 0
   /** Get the inverse for stabilizing the whole Schur complement approximation.
     *
     * \param[in] A The linear operator to be preconditioned by LSC.
     * \param[in] state State object for storying reusable information about
     *                  the operator A.
     *
     * \returns The operator to stabilize the whole Schur complement (\f$\alpha D^{-1} \f$).
     */
   virtual LinearOp getInvAlphaD(const BlockedLinearOp & A,BlockPreconditionerState & state) const = 0;
   #endif

   /** Get the inverse to stablized stabilizing the Schur complement approximation using
     * a placement on the ``outside''.  That is what is the value for \f$C_O\f$. This quantity
     * may be null.
     *
     * \param[in] A The linear operator to be preconditioned by LSC.
     * \param[in] state State object for storying reusable information about
     *                  the operator A.
     *
     * \returns The operator to stabilize the whole Schur complement (originally \f$\alpha D^{-1} \f$).
     */
   virtual LinearOp getOuterStabilization(const BlockedLinearOp & A,BlockPreconditionerState & state) const = 0;

   /** Get the inverse to stablized stabilizing the Schur complement approximation using
     * a placement on the ``inside''.  That is what is the value for \f$C_I\f$. This quantity
     * may be null.
     *
     * \param[in] A The linear operator to be preconditioned by LSC.
     * \param[in] state State object for storying reusable information about
     *                  the operator A.
     *
     * \returns The operator to stabilize the whole Schur complement.
     */
   virtual LinearOp getInnerStabilization(const BlockedLinearOp & A,BlockPreconditionerState & state) const = 0;

   /** Get the inverse mass matrix.
     *
     * \param[in] A The linear operator to be preconditioned by LSC.
     * \param[in] state State object for storying reusable information about
     *                  the operator A.
     *
     * \returns The inverse of the mass matrix \f$Q_u\f$.
     */
   virtual LinearOp getInvMass(const BlockedLinearOp & A,BlockPreconditionerState & state) const = 0;

   /** Get the \f$H\f$ scaling matrix.
     *
     * \param[in] A The linear operator to be preconditioned by LSC.
     * \param[in] state State object for storying reusable information about
     *                  the operator A.
     *
     * \returns The \f$H\f$ scaling matrix.
     */
   virtual LinearOp getHScaling(const BlockedLinearOp & A,BlockPreconditionerState & state) const = 0;

   /** Should the approximation of the inverse use a full LDU decomposition, or
     * is a upper triangular approximation sufficient.
     *
     * \returns True if the full LDU decomposition should be used, otherwise
     *          only an upper triangular version is used.
     */
   virtual bool useFullLDU() const = 0;

   /** Tell strategy that this operator is supposed to be symmetric.
     * Behavior of LSC is slightly different for non-symmetric case.
     *
     * \param[in] isSymmetric Is this operator symmetric?
     */
   virtual void setSymmetric(bool isSymmetric) = 0;

   //! Initialize from a parameter list
   virtual void initializeFromParameterList(const Teuchos::ParameterList & pl,const InverseLibrary & invLib) {}

   //! For assiting in construction of the preconditioner
   virtual Teuchos::RCP<Teuchos::ParameterList> getRequestedParameters() const { return Teuchos::null;}

   //! For assiting in construction of the preconditioner
   virtual bool updateRequestedParameters(const Teuchos::ParameterList & pl) { return true; }

   //! This method sets the request handler for this object
   void setRequestHandler(const Teuchos::RCP<RequestHandler> & rh)
   { requestHandler_ = rh; }

   //! This method gets the request handler uses by this object
   Teuchos::RCP<RequestHandler> getRequestHandler() const
   { return requestHandler_; }

private:
   Teuchos::RCP<RequestHandler> requestHandler_;

};

} // end namespace NS
} // end namespace Teko

#endif