libtrilinos-teko-dev 12.4.2-2 / usr / include / trilinos / Teko_LU2x2PreconditionerFactory.hpp

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#ifndef __Teko_LU2x2PreconditionerFactory_hpp__
#define __Teko_LU2x2PreconditionerFactory_hpp__

#include "Teuchos_RCP.hpp"

#include "Teko_BlockPreconditionerFactory.hpp"
#include "Teko_LU2x2Strategy.hpp"

namespace Teko {

/** \brief Construct a preconditioner using a LDU dcomposition of a block
 *  2x2 matrix.
 *
 * This produces a preconditioner using the block-LDU decomposition of
 * the matrix. The general assumption made is that the matrix is 2x2 
 * and the block factorization can be constructed (i.e. assumptions about
 * the invertability of some blocks). The pattern used, and the one you
 * should follow if you want to use this software is
 *
 * \f$
 * A = \left[ 
 * \begin{array}{cc}
 * A_{00} & A_{01} \\
 * A_{10} & A_{11}
 * \end{array}
 * \right]
 * = \left[ 
 * \begin{array}{cc}
 * I & 0  \\
 * A_{10} A_{00}^{-1} & I
 * \end{array}
 * \right]
 * \left[ 
 * \begin{array}{cc}
 * A_{00} & 0  \\
 * 0 & -S
 * \end{array}
 * \right]
 * \left[ 
 * \begin{array}{cc}
 * I &  A_{00}^{-1} A_{01} \\
 * 0 & I
 * \end{array}
 * \right]
 * \f$
 *
 * where the Schur complement is \f$ S=-A_{11}+A_{10} A_{00}^{-1} A_{01} \f$ .
 *
 * To use an LDU approximation 2 evaluations of \f$ A_{00}^{-1} \f$ and a single
 * evalution of \f$ S^{-1} \f$ are needed. For increased flexibility both
 * evaluations of \f$A_{00}^{-1}\f$ can be specified independently. 
 * For righthand side vector \f$[f, g]^T\f$ and solution vector \f$[u,v]^T\f$
 * the two inverses (\f$A\f$-hat and \f$A\f$-tilde) are needed to evaluate 
 *
 * \f$\hat{A}_{00} u^* = f\f$,
 *
 * \f$\tilde{A}_{00} v = A_{01} v\f$
 *
 * where \f$u^*\f$ is an intermediate step.
 *
 * In order to facilate using this class in a nonlinear solve (or for a 
 * time-dependent problem) the additional abstraction of a ``Strategy''
 * has been added. This strategy, abstractly represented as the LU2x2Strategy,
 * provides the \f$A_{00}^{-1}\f$ and \f$S^{-1}\f$ operators. Typical usage for this class
 * is to build a LU2x2Strategy and pass it into the primary constructor. 
 * Additional constructors are provided both for convenience and to ease
 * adoption. Underneath the hood all these constructors do is invoke the
 * corresponding strategy object.
 *
 * For example, assume that you have the particularly nice case that
 * your approximations of \f$A_{00}^{-1}\f$ and \f$S^{-1}\f$ are independent of the source
 * operator. Then, one way to instantiate a LU2x2PreconditionerFactory
 * is

   <code>
      RCP<LinearOpBase<double> > invA00 = buildInvA00(...);\n
      RCP<LinearOpBase<double> > invS   = buildInvS(...);\n
      RCP<LU2x2PreconditionerFactory> precFact = rcp(new LU2x2PreconditionerFactory(invA00,invS));
   </code>

 * Now using the strategy constructor, an entirely equivalent factory
 * object can be constructed by

   <code>
      RCP<LinearOpBase<double> > invA00 = buildInvA00(...);\n
      RCP<LinearOpBase<double> > invS   = buildInvS(...);\n
      RCP<LU2x2Strateghy> precStrat = rcp(new StaticLU2x2Strategy(invA00,invS));\n
      RCP<LU2x2PreconditionerFactory> precFact = rcp(new LU2x2PreconditionerFactory(precStrat));
   </code>
 
 * Notice that the StaticLU2x2Strategy takes the same objects 
 * as the original constructor, it acts as an intermediary to tell the 
 * LU2x2PreconditionerFactory what those operators are.
 **/
class LU2x2PreconditionerFactory : public BlockPreconditionerFactory {
public:
   //! @name Constructors.
   //@{
 
   /** @brief Build a simple static LU2x2 preconditioner */
   LU2x2PreconditionerFactory(LinearOp & invA00,LinearOp & invS);

   /** @brief Build a simple static LU2x2 preconditioner */
   LU2x2PreconditionerFactory(LinearOp & hatInvA00,LinearOp & tildeInvA00,LinearOp & invS);

   /** @brief Constructor that permits the most generality in building \f$A_{00}^{-1}\f$ and
     *        \f$S^{-1}\f$.
     *
     * Constructor that permits the most generality in building \f$A_{00}^{-1}\f$ and \f$S^{-1}\f$.
     *
     * @param[in] strategy  Strategy object that takes a 2x2 block matrix and
     *                      and constructs the \f$A_{00}^{-1}\f$ and \f$S^{-1}\f$ objects.
     */
   LU2x2PreconditionerFactory(const Teuchos::RCP<LU2x2Strategy> & strategy);


   /** \brief Default constructor for use with AutoClone
     *
     * Default constructor for use with AutoClone
     */
   LU2x2PreconditionerFactory();

   //@}

   /** \brief Create the LU 2x2 preconditioner operator.
     *
     * This method breaks apart the BlockLinearOp and builds a block
     * LU preconditioner. This will require two applications of the inverse
     * of the (0,0) block and one application of the inverse Schur complement.
     */
   LinearOp buildPreconditionerOperator(BlockedLinearOp & blo,BlockPreconditionerState & state) const;

   /** \brief This function builds the internals of the preconditioner factory
     *        from a parameter list.
     *        
     * This function builds the internals of the preconditioner factory
     * from a parameter list. Furthermore, it allows a preconditioner factory
     * developer to easily add a factory to the build system. This function
     * is required for building a preconditioner from a parameter list.
     *
     * \param[in] settings Parmaeter list to use as the internal settings
     *
     * \note The default implementation does nothing.
     */
   virtual void initializeFromParameterList(const Teuchos::ParameterList & settings);

   /** \brief Request the additional parameters this preconditioner factory
     *        needs. 
     *
     * Request the additonal parameters needed by this preconditioner factory.
     * The parameter list will have a set of fields that can be filled with 
     * the requested values. These fields include all requirements, even those
     * of the sub-solvers if there are any.  Once correctly filled the object
     * can be updated by calling the updateRequestedParameters with the filled
     * parameter list.
     *
     * \returns A parameter list with the requested parameters.
     *
     * \note The default implementation returns Teuchos::null.
     */
   virtual Teuchos::RCP<Teuchos::ParameterList> getRequestedParameters() const;
   
   /** \brief Update this object with the fields from a parameter list.
     *
     * Update the requested fields using a parameter list. This method is
     * expected to pair with the getRequestedParameters method (i.e. the fields
     * requested are going to be update using this method).
     *
     * \param[in] pl Parameter list containing the requested parameters.
     *
     * \returns If the method succeeded (found all its required parameters) this
     *          method returns true, otherwise it returns false.
     *
     * \note The default implementation returns true (it does nothing!).
     */
   virtual bool updateRequestedParameters(const Teuchos::ParameterList & pl);

   /** \brief Determine the type of inverse operator to build. 
     *
     * Determine the type of inverse operator to build. If true
     * use the full LDU decomposition. If false only the upper
     * triangular solve should be used. Motivation for doing this
     * can be found in Murphy, Golub and Wathen, SISC 2000.
     *
     * \returns A boolean indicating the type of inverse operator
     *          to use.
     *
     * \note Default behavior for this class is to return true.
     */
   virtual bool useFullLDU() const { return useFullLDU_; }

   /** \brief Set the type of inverse operation to use.
     *
     * Set the type of inverse operator to use. If true
     * use the full LDU decomposition. If false only the upper
     * triangular solve should be used. Motivation for doing this
     * can be found in Murphy, Golub and Wathen, SISC 2000.
     *
     * \param[in] value Boolean indicating type of inverse operator
     *                  to build.
     */
   virtual void setFullLDU(bool value)
   { useFullLDU_ = value; }
 
protected: 
   //! some members
   Teuchos::RCP<LU2x2Strategy> invOpsStrategy_;

   /** If true, use full LDU decomposition, otherwise
     * use the Golub & Wathen style upper block. This is
     * true by default.
     */
   bool useFullLDU_;

public:
   /** \brief Builder function for creating strategies.
     *
     * Builder function for creating strategies.
     * 
     * \param[in] name     String name of strategy to build
     * \param[in] settings Parameter list describing the parameters for the
     *                     strategy to build
     * \param[in] invLib   Inverse library for the strategy to use.
     *
     * \returns If the name is associated with a strategy
     *          a pointer is returned, otherwise Teuchos::null is returned.
     */
   static RCP<LU2x2Strategy> 
   buildStrategy(const std::string & name, 
                 const Teuchos::ParameterList & settings,
                 const RCP<const InverseLibrary> & invLib,
                 const RCP<RequestHandler> & rh);

   /** \brief Add a strategy to the builder. This is done using the
     *        clone pattern. 
     *
     * Add a strategy to the builder. This is done using the
     * clone pattern. If your class does not support the Cloneable interface then
     * you can use the AutoClone class to construct your object.
     *
     * \note If this method is called twice with the same string, the latter clone pointer
     *       will be used.
     *
     * \param[in] name String to associate with this object
     * \param[in] clone Pointer to Cloneable object
     */
   static void addStrategy(const std::string & name,const RCP<Cloneable> & clone);

private:
   //! for creating the strategy objects
   static CloneFactory<LU2x2Strategy> strategyBuilder_;

   //! This is where the default objects are put into the strategyBuilder_
   static void initializeStrategyBuilder();
};

} // end namespace Teko

#endif