PetscSolverFeti.h

// ============================================================================
// ==                                                                        ==
// == AMDiS - Adaptive multidimensional simulations                          ==
// ==                                                                        ==
// ==  http://www.amdis-fem.org                                              ==
// ==                                                                        ==
// ============================================================================
//
// Software License for AMDiS
//
// Copyright (c) 2010 Dresden University of Technology 
// All rights reserved.
// Authors: Simon Vey, Thomas Witkowski et al.
//
// This file is part of AMDiS
//
// See also license.opensource.txt in the distribution.



/** \file PetscSolverFeti.h */

#include "parallel/PetscSolver.h"
#include "parallel/ParallelTypes.h"

#ifndef AMDIS_PETSC_SOLVER_FETI_H
#define AMDIS_PETSC_SOLVER_FETI_H

namespace AMDiS {

  using namespace std;


  class PetscSolverFeti;

  /** \brief
   * This structure is used when defining the MatShell operation for solving 
   * primal schur complement. \ref petscMultMatSchurPrimal
   */
  struct SchurPrimalData {
    /// Pointers to the matrix containing the primal variables.
    Mat *mat_primal_primal;
   
    /// Coupling matrices between the primal and the B variables.
    Mat *mat_primal_b, *mat_b_primal;

    /// Temporal vector on the B variables.
    Vec tmp_vec_b;

    /// Temporal vecor in the primal variables.
    Vec tmp_vec_primal;

    PetscSolverFeti *fetiSolver;
  };


  /** \brief
   * This structure is used when defining the FETI-DP operator for solving 
   * the system matrix reduced to the Lagrange multipliers.
   * \ref petscMultMatFeti
   */
  struct FetiData {
    /// Coupling matrices between the primal and the B variables.
    Mat *mat_primal_b, *mat_b_primal;

    /// Matrix of Lagrange variables.
    Mat *mat_lagrange;

    /// Temporal vectors on the B variables.
    Vec tmp_vec_b;

    /// Temporal vector on the primal variables.
    Vec tmp_vec_primal;

    /// Temporal vector on the lagrange variables.
    Vec tmp_vec_lagrange;

    PetscSolverFeti *fetiSolver;

    /// Pointer to the solver of the schur complement on the primal variables.
    KSP *ksp_schur_primal;
  };


  struct FetiDirichletPreconData {
    /// Matrix of scaled Lagrange variables.
    Mat *mat_lagrange_scaled;

    Mat *mat_interior_interior, *mat_duals_duals, *mat_interior_duals, *mat_duals_interior;

    /// Pointer to the solver for \ref PetscSolverFeti::mat_bb.
    KSP *ksp_interior;

    /// Temporal vector on the B variables.
    Vec tmp_vec_b;

    /// Temporal vector on the dual variables.
    Vec tmp_vec_duals0, tmp_vec_duals1;
    
    /// Temporal vector on the interior variables.
    Vec tmp_vec_interior;    
  };


  struct FetiLumpedPreconData {
    /// Matrix of scaled Lagrange variables.
    Mat *mat_lagrange_scaled;

    Mat *mat_duals_duals;

    /// Temporal vector on the B variables.
    Vec tmp_vec_b;

    /// Temporal vector on the dual variables.
    Vec tmp_vec_duals0, tmp_vec_duals1;
  };


  typedef enum {
    FETI_NONE = 0,
    FETI_DIRICHLET = 1,
    FETI_LUMPED = 2
  } FetiPreconditioner;


/** \brief
   * FETI-DP implementation based on PETSc.
   */
  class PetscSolverFeti : public PetscSolver
  {
  public:
    PetscSolverFeti();

    /// Assemble the sequentially created matrices to the global matrices
    /// required by the FETI-DP method.
    void fillPetscMatrix(Matrix<DOFMatrix*> *mat);

    /// Assembles the global rhs vectors from the sequentially created ones.
    void fillPetscRhs(SystemVector *vec);

    /// Solve the system using FETI-DP method.
    void solvePetscMatrix(SystemVector &vec, AdaptInfo *adaptInfo);

    /// Destroys all matrix data structures.
    void destroyMatrixData();

    /// Returns flags to denote which information of the boundary DOFs are 
    /// required by the FETI-DP solver.
    Flag getBoundaryDofRequirement()
    {
      return 
	MeshDistributor::BOUNDARY_SUBOBJ_SORTED |
	MeshDistributor::BOUNDARY_FILL_INFO_SEND_DOFS |
	MeshDistributor::BOUNDARY_FILL_INFO_RECV_DOFS;
    }

    void solveLocalProblem(Vec &rhs, Vec &sol);

  protected:
    /// After mesh changes, or if the solver is called the first time, this
    /// function creates all matrix and vector objects with the approriated
    /// sizes.
    void updateDofData();

    /// Defines which boundary nodes are primal. Creates global index of
    /// the primal variables.
    void createPrimals();

    /// Defines the set of dual variables and creates the global index of
    // dual variables.
    void createDuals();

    /// Create Lagrange multiplier variables corresponding to the dual 
    /// variables.
    void createLagrange();

    /// Creates a global index of the B variables.
    void createIndexB();

    /// Creates the Lagrange multiplier constraints and assembles them 
    /// to \ref mat_lagrange.
    void createMatLagrange();

    /// Creates PETSc KSP solver object for solving the Schur complement
    /// system on the primal variables, \ref ksp_schur_primal
    void createSchurPrimalKsp();

    /// Destroys PETSc KSP solver object \ref ksp_schur_primal
    void destroySchurPrimalKsp();

    /// Creates PETSc KSP solver object for the FETI-DP operator, \ref ksp_feti
    void createFetiKsp();

    /// Destroys FETI-DP operator, \ref ksp_feti
    void destroyFetiKsp();

    /** \brief
     * Recovers AMDiS solution vector from PETSc's solution vectors of the
     * FETI-DP system. First, the B variables can locally be copied to the
     * corresponding entries in the DOF vectors. The primal variable must
     * be communicated such that all ranks sharing a primal get a copy of
     * the corresponding value.
     *
     * \param[in]   vec_sol_b        Global PETSc vector of the solution of
     *                               the B variables.
     * \param[in]   vec_sol_primal   Global PETSc vector of the solution of
     *                               the primal variables.
     * \param[out]  vec              SystemVector containing all solution 
     *                               DOF vectors.
     */
    void recoverSolution(Vec &vec_sol_b,
			 Vec &vec_sol_primal,
			 SystemVector &vec);

    /** \brief
     * Solves the FETI-DP system globally, thus without reducing it to the 
     * Lagrange multipliers. This should be used for debugging only to test
     * if the FETI-DP system is setup correctly.
     *
     * \param[out]  vec    Solution DOF vectors.
     */
    void solveFetiMatrix(SystemVector &vec);

    /** \brief
     * Solves the FETI-DP system with reducing it first to the Lagrange
     * multipliers. This is what one expects when using the FETI-DP methid :)
     *
     * \param[out]  vec    Solution DOF vectors.
     */
    void solveReducedFetiMatrix(SystemVector &vec);

    void resetStatistics();

    void printStatistics();

  protected:
    /// Number of components in the PDE to be solved.
    int nComponents;

    /// Mapping from primal DOF indices to a global index of primals.
    DofMapping globalPrimalIndex;

    /// Number of rank owned primals and global primals
    int nRankPrimals, nOverallPrimals, rStartPrimals;

    /// Set of DOF indices that are considered to be dual variables.
    DofIndexSet duals;
    
    /// Mapping from dual DOF indices to a global index of duals.
    DofMapping globalDualIndex;

    /// Stores to each dual boundary DOF the set of ranks in which the DOF
    /// is contained in.
    DofIndexToPartitions boundaryDofRanks;

    /// Stores to each dual DOF index the index of the first Lagrange
    /// constraint that is assigned to this DOF.
    DofMapping dofFirstLagrange;

    /// Number of rank owned Lagrange variables, number of global
    /// Lagrange variables.
    int nRankLagrange, nOverallLagrange, rStartLagrange;
    
    /// Index for each non primal variables to the global index of
    /// B variables.
    DofMapping globalIndexB, localIndexB;

    /// Number of non primal, thus B, variables on rank and globally.
    int nRankB, nOverallB, rStartB;    

    /// Global PETSc matrix of non primal variables.
    Mat mat_b_b;

    /// Global PETSc matrix of primal variables.
    Mat mat_primal_primal;

    /// Global PETSc matrices that connect the primal with the non 
    /// primal variables.
    Mat mat_b_primal, mat_primal_b;

    /// Global PETSc matrix of Lagrange variables.
    Mat mat_lagrange;

    /// Right hand side PETSc vectors for primal and non primal variables.
    Vec f_b, f_primal;

    /// PETSc solver object that inverts the matrix of non primal 
    /// variables, \ref mat_b_b
    KSP ksp_b;

    /// 0: Solve the Schur complement on primal variables with iterative solver.
    /// 1: Create the Schur complement matrix explicitly and solve it with a
    ///    direct solver.
    int schurPrimalSolver;

    /// PETSc solver object to solve the Schur complement on the 
    /// primal variables.
    KSP ksp_schur_primal;

    /// Matrix object that defines a matrix-free implementation for the action
    /// of the Schur complement on the primal variables.
    Mat mat_schur_primal;

    /// Data for MatMult operation in matrix \ref mat_schur_primal
    SchurPrimalData schurPrimalData;

    /// PETSc solver object to solve a system with FETI-DP.    
    KSP ksp_feti;

    /// Matrix object that defines a matrix-free implementation for the action
    /// of the FETI-DP operator.
    Mat mat_feti;

    /// Data for MatMult operation in matrix \ref mat_feti
    FetiData fetiData;

    /// Defines which preconditioner should be used to solve the reduced
    /// FETI-DP system.
    FetiPreconditioner fetiPreconditioner;

    /// Preconditioner object for the reduced FETI-DP system.
    PC precon_feti;

    Mat mat_lagrange_scaled;
   
    FetiDirichletPreconData fetiDirichletPreconData;

    FetiLumpedPreconData fetiLumpedPreconData;

    Mat mat_interior_interior, mat_duals_duals, mat_interior_duals, mat_duals_interior;

    KSP ksp_interior;

    int nLocalInterior;
    
    // Number of local nodes that are duals.
    int nLocalDuals;
  };
}

#endif