PetscSolverFetiOperators.cc 17.5 KB
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//
// 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.

#include "parallel/PetscSolverFetiOperators.h"
#include "parallel/PetscSolverFetiStructs.h"
#include "parallel/PetscSolverFetiTimings.h"

namespace AMDiS {

  int petscMultMatSchurPrimal(Mat mat, Vec x, Vec y)
  {
    // S_PiPi = K_PiPi - K_PiB inv(K_BB) K_BPi

    void *ctx;
    MatShellGetContext(mat, &ctx);
    SchurPrimalData* data = static_cast<SchurPrimalData*>(ctx);

    MatMult(data->subSolver->getMatInteriorCoarse(), x, data->tmp_vec_b);
    data->subSolver->solveGlobal(data->tmp_vec_b, data->tmp_vec_b);
    MatMult(data->subSolver->getMatCoarseInterior(), data->tmp_vec_b, 
	    data->tmp_vec_primal);
    MatMult(data->subSolver->getMatCoarse(), x, y);
    VecAXPBY(y, -1.0, 1.0, data->tmp_vec_primal);

    return 0;
  }


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  int petscMultMatSchurPrimalAugmented(Mat mat, Vec x, Vec y)
  {
    void *ctx;
    MatShellGetContext(mat, &ctx);
    SchurPrimalAugmentedData* data = 
      static_cast<SchurPrimalAugmentedData*>(ctx);

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    Vec x_primal, x_mu, y_primal, y_mu;
    
    if (data->nestedVec) {
      VecNestGetSubVec(x, 0, &x_primal);
      VecNestGetSubVec(x, 1, &x_mu);
      VecNestGetSubVec(y, 0, &y_primal);
      VecNestGetSubVec(y, 1, &y_mu);
    } else {
      VecDuplicate(data->tmp_vec_primal, &x_primal);
      VecDuplicate(data->tmp_vec_primal, &y_primal);

      PetscInt allLocalSize, allSize;
      VecGetLocalSize(x, &allLocalSize);
      VecGetSize(x, &allSize);

      PetscInt primalLocalSize, primalSize;
      VecGetLocalSize(x_primal, &primalLocalSize);
      VecGetSize(x_primal, &primalSize);

      TEST_EXIT_DBG(allSize > primalSize)("Should not happen!\n");
      TEST_EXIT_DBG(allLocalSize >= primalLocalSize)("Should not happen!\n");

      PetscInt muLocalSize = allLocalSize - primalLocalSize;
      PetscInt muSize = allSize - primalSize;

      VecCreateMPI(PETSC_COMM_WORLD, muLocalSize, muSize, &x_mu);
      VecCreateMPI(PETSC_COMM_WORLD, muLocalSize, muSize, &y_mu);

      PetscScalar *allValue;
      PetscScalar *primalValue;
      PetscScalar *muValue;
      VecGetArray(x, &allValue);
      VecGetArray(x_primal, &primalValue);
      VecGetArray(x_mu, &muValue);

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      for (int i = 0; i < primalLocalSize; i++)
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	primalValue[i] = allValue[i];
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      for (int i = 0; i < muLocalSize; i++)
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	muValue[i] = allValue[primalLocalSize + i];

      VecRestoreArray(x, &allValue);
      VecRestoreArray(x_primal, &primalValue);
      VecRestoreArray(x_mu, &muValue);
    }
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    // inv(K_BB) K_BPi x_Pi
    MatMult(data->subSolver->getMatInteriorCoarse(), x_primal, data->tmp_vec_b0);
    data->subSolver->solveGlobal(data->tmp_vec_b0, data->tmp_vec_b0);

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    // inv(K_BB) trans(J) trans(Q) x_mu
    MatMultTranspose(*(data->mat_augmented_lagrange), x_mu, data->tmp_vec_lagrange);
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    MatMultTranspose(*(data->mat_lagrange), data->tmp_vec_lagrange, data->tmp_vec_b1);
    data->subSolver->solveGlobal(data->tmp_vec_b1, data->tmp_vec_b1);

    // y_Pi = (K_PiPi - K_PiB inv(K_BB) K_BPi) x_pi
    MatMult(data->subSolver->getMatCoarseInterior(), data->tmp_vec_b0,
	    data->tmp_vec_primal);
    MatMult(data->subSolver->getMatCoarse(), x_primal, y_primal);
    VecAXPY(y_primal, -1.0, data->tmp_vec_primal);

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    // y_Pi += (-K_PiB inv(K_BB) J^T Q^T) x_mu
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    MatMult(data->subSolver->getMatCoarseInterior(), data->tmp_vec_b1,
	    data->tmp_vec_primal);
    VecAXPY(y_primal, -1.0, data->tmp_vec_primal);

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    // y_mu = (-Q J inv(K_BB) K_BPi) x_Pi + (-Q J inv(K_BB) J^T Q) x_mu
    //      = -Q J (inv(K_BB) K_BPi x_Pi + inv(K_BB) J^T Q x_mu)
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    VecAXPY(data->tmp_vec_b0, 1.0, data->tmp_vec_b1);
    MatMult(*(data->mat_lagrange), data->tmp_vec_b0, data->tmp_vec_lagrange);
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    MatMult(*(data->mat_augmented_lagrange), data->tmp_vec_lagrange, y_mu);
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    VecScale(y_mu, -1.0);

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    if (!data->nestedVec) {
      PetscInt allLocalSize;
      VecGetLocalSize(x, &allLocalSize);
      PetscInt primalLocalSize;
      VecGetLocalSize(x_primal, &primalLocalSize);
      PetscInt muLocalSize = allLocalSize - primalLocalSize;

      PetscScalar *allValue;
      PetscScalar *primalValue;
      PetscScalar *muValue;
      VecGetArray(y, &allValue);
      VecGetArray(y_primal, &primalValue);
      VecGetArray(y_mu, &muValue);

      for (int i = 0; i < primalLocalSize; i++)
	allValue[i] = primalValue[i];

      for (int i = 0; i < muLocalSize; i++)
	allValue[primalLocalSize + i] = muValue[i];

      VecRestoreArray(y, &allValue);
      VecRestoreArray(y_primal, &primalValue);
      VecRestoreArray(y_mu, &muValue);

      VecDestroy(&x_primal);
      VecDestroy(&y_primal);
      VecDestroy(&x_mu);
      VecDestroy(&y_mu);
    }

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    return 0;
  }


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  // y = mat * x
  int petscMultMatFeti(Mat mat, Vec x, Vec y)
  {
    FUNCNAME("petscMultMatFeti()");

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    //    F = J inv(K_BB) trans(J) + J inv(K_BB) K_BPi inv(S_PiPi) K_PiB inv(K_BB) trans(J)
    // => F = J [I + inv(K_BB) K_BPi inv(S_PiPi) K_PiB] inv(K_BB) trans(J)
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    double wtime = MPI::Wtime();

    void *ctx;
    MatShellGetContext(mat, &ctx);
    FetiData* data = static_cast<FetiData*>(ctx);

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    MatMultTranspose(*(data->mat_lagrange), x, data->tmp_vec_b0);
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    double wtime01 = MPI::Wtime();
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    data->subSolver->solveGlobal(data->tmp_vec_b0, data->tmp_vec_b0);
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    FetiTimings::fetiSolve01 += (MPI::Wtime() - wtime01);

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    MatMult(*(data->mat_lagrange), data->tmp_vec_b0, data->tmp_vec_lagrange);
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    MatMult(data->subSolver->getMatCoarseInterior(), 
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	    data->tmp_vec_b0, data->tmp_vec_primal0);
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    wtime01 = MPI::Wtime();
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    KSPSolve(*(data->ksp_schur_primal), data->tmp_vec_primal0, data->tmp_vec_primal0);
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    FetiTimings::fetiSolve02 += (MPI::Wtime() - wtime01);

    MatMult(data->subSolver->getMatInteriorCoarse(), 
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	    data->tmp_vec_primal0, data->tmp_vec_b0);
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    wtime01 = MPI::Wtime();
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    data->subSolver->solveGlobal(data->tmp_vec_b0, data->tmp_vec_b0);
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    FetiTimings::fetiSolve01 += (MPI::Wtime() - wtime01);

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    MatMult(*(data->mat_lagrange), data->tmp_vec_b0, y);
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    VecAXPBY(y, 1.0, 1.0, data->tmp_vec_lagrange);

    FetiTimings::fetiSolve += (MPI::Wtime() - wtime);

    return 0;
  }


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  // y = mat * x
  int petscMultMatFetiAugmented(Mat mat, Vec x, Vec y)
  {
    FUNCNAME("petscMultMatFetiAugmented()");

    void *ctx;
    MatShellGetContext(mat, &ctx);
    FetiData* data = static_cast<FetiData*>(ctx);

    Vec vec_mu0, vec_mu1;
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    MatGetVecs(*(data->mat_augmented_lagrange), PETSC_NULL, &vec_mu0);
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    VecDuplicate(vec_mu0, &vec_mu1);

    MatMultTranspose(*(data->mat_lagrange), x, data->tmp_vec_b0);
    data->subSolver->solveGlobal(data->tmp_vec_b0, data->tmp_vec_b0);

    MatMult(data->subSolver->getMatCoarseInterior(), data->tmp_vec_b0, data->tmp_vec_primal0);
    MatMult(*(data->mat_lagrange), data->tmp_vec_b0, data->tmp_vec_lagrange);
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    MatMult(*(data->mat_augmented_lagrange), data->tmp_vec_lagrange, vec_mu0);
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    Vec vec_array0[2] = {data->tmp_vec_primal0, vec_mu0};
    Vec vec_array1[2] = {data->tmp_vec_primal1, vec_mu1};
    Vec vec_nest0, vec_nest1;
    VecCreateNest(PETSC_COMM_WORLD, 2, PETSC_NULL, vec_array0, &vec_nest0);
    VecCreateNest(PETSC_COMM_WORLD, 2, PETSC_NULL, vec_array1, &vec_nest1);

    KSPSolve(*(data->ksp_schur_primal), vec_nest0, vec_nest1);

    // Step 1
    MatMult(*(data->mat_lagrange), data->tmp_vec_b0, y);

    // Step 2
    MatMult(data->subSolver->getMatInteriorCoarse(), data->tmp_vec_primal1, data->tmp_vec_b0);
    data->subSolver->solveGlobal(data->tmp_vec_b0, data->tmp_vec_b0);
    MatMult(*(data->mat_lagrange), data->tmp_vec_b0, data->tmp_vec_lagrange);
    VecAXPY(y, 1.0, data->tmp_vec_lagrange);

    // Step 3
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    MatMultTranspose(*(data->mat_augmented_lagrange), vec_mu1, data->tmp_vec_lagrange);
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    MatMultTranspose(*(data->mat_lagrange), data->tmp_vec_lagrange, data->tmp_vec_b0);
    data->subSolver->solveGlobal(data->tmp_vec_b0, data->tmp_vec_b0);
    MatMult(*(data->mat_lagrange), data->tmp_vec_b0, data->tmp_vec_lagrange);
    VecAXPY(y, 1.0, data->tmp_vec_lagrange);

    VecDestroy(&vec_mu0);
    VecDestroy(&vec_mu1);
    VecDestroy(&vec_nest0);
    VecDestroy(&vec_nest1);
    return 0;
  }


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  int petscMultMatFetiInterface(Mat mat, Vec x, Vec y)
  {
    FUNCNAME("petscMultMatFetiInterface()");

    double wtime = MPI::Wtime();

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      {
	MatNullSpace nullSpace;
	MatGetNullSpace(mat, &nullSpace);

	PetscBool hasConst;
	PetscInt nVec;
	const Vec *vecs;
	//	MatNullSpaceGetVecs(nullSpace, &hasConst, &nVec, &vecs);
	MatNullSpaceRemove(nullSpace, x, PETSC_NULL);
      }


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    Vec x_interface, x_lagrange, y_interface, y_lagrange;    
    VecNestGetSubVec(x, 0, &x_interface);
    VecNestGetSubVec(x, 1, &x_lagrange);
    VecNestGetSubVec(y, 0, &y_interface);
    VecNestGetSubVec(y, 1, &y_lagrange);

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      {
	int n;
	VecGetSize(x_interface, &n);
	double sum;
	VecSum(x_interface, &sum);
	sum = -sum / static_cast<int>(n);
	MSG("xbegin = %e\n", sum);
      }

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    void *ctx;
    MatShellGetContext(mat, &ctx);
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    FetiData* data = static_cast<FetiData*>(ctx);
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    // === Calculation of v_{B} ===
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    // tmp_vec_b0 = J^{T} \lambda
    MatMultTranspose(*(data->mat_lagrange), x_lagrange, data->tmp_vec_b0);
    // tmp_vec_b1 = A_{B\Gamma} u_{\Gamma}
    MatMult(data->subSolver->getMatInteriorCoarse(1), x_interface, data->tmp_vec_b1);
    // tmp_vec_b0 = A_{B\Gamma} u_{\Gamma} + J^{T} \lambda
    VecAXPY(data->tmp_vec_b0, 1.0, data->tmp_vec_b1);


    // == Calculation of v_{\Pi}
    
    // tmp_vec_primal0 = A_{\Pi\Gamma} u_{\Gamma}
    MatMult(data->subSolver->getMatCoarse(0, 1), x_interface, data->tmp_vec_primal0);
    

    // === Calculate action of FETI-DP operator ===
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    double wtime01 = MPI::Wtime();
    // tmp_vec_b0 = A_{BB}^{-1} v_{B}
    data->subSolver->solveGlobal(data->tmp_vec_b0, data->tmp_vec_b0);
    FetiTimings::fetiSolve01 += (MPI::Wtime() - wtime01);
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    // tmp_vec_primal1 = A_{\Pi B} A_{BB}^{-1} v_{B}
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    MatMult(data->subSolver->getMatCoarseInterior(), 
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	    data->tmp_vec_b0, data->tmp_vec_primal1);

    // tmp_vec_primal0 = v_{\Pi} - A_{\Pi B} A_{BB}^{-1} v_{B}
    VecAXPY(data->tmp_vec_primal0, -1.0, data->tmp_vec_primal1);
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    wtime01 = MPI::Wtime();
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    // tmp_vec_primal0 = S_{\Pi\Pi}^{-1} (v_{\Pi} - A_{\Pi B} A_{BB}^{-1} v_{B})
    KSPSolve(*(data->ksp_schur_primal), data->tmp_vec_primal0, data->tmp_vec_primal0);
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    FetiTimings::fetiSolve02 += (MPI::Wtime() - wtime01);

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    // tmp_vec_b1 = A_{B\Pi} S_{\Pi\Pi}^{-1} (v_{\Pi} - A_{\Pi B} A_{BB}^{-1} v_{B})
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    MatMult(data->subSolver->getMatInteriorCoarse(), 
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	    data->tmp_vec_primal0, data->tmp_vec_b1);
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    wtime01 = MPI::Wtime();
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    // tmp_vec_b1 = A_{BB}^{-1} A_{B\Pi} S_{\Pi\Pi}^{-1} (v_{\Pi} - A_{\Pi B} A_{BB}^{-1} v_{B})
    data->subSolver->solveGlobal(data->tmp_vec_b1, data->tmp_vec_b1);
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    FetiTimings::fetiSolve01 += (MPI::Wtime() - wtime01);

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    // tmp_vec_b0 = A_{BB}^{-1} v_{B} - A_{BB}^{-1} A_{B\Pi} S_{\Pi\Pi}^{-1} (v_{\Pi} - A_{\Pi B} A_{BB}^{-1} v_{B})
    VecAXPY(data->tmp_vec_b0, -1.0, data->tmp_vec_b1);


    // === Calculate projection to interface and constraint variable ===

    // y_interface = A_{\Gamma B} tmp_vec_b0
    MatMult(data->subSolver->getMatCoarseInterior(1), data->tmp_vec_b0, y_interface);

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      {
	int n;
	VecGetSize(y_interface, &n);
	double sum;
	VecSum(y_interface, &sum);
	sum = -sum / static_cast<int>(n);
	MSG("yend = %e\n", sum);
      }


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    // tmp_vec_primal0 = S_{\Pi\Pi}^{-1} (v_{\Pi} - A_{\Pi B} A_{BB}^{-1} v_{B})
    // tmp_vec_interface = A_{\Gamma \Pi} tmp_vec_primal0
    MatMult(data->subSolver->getMatCoarse(1, 0), data->tmp_vec_primal0, data->tmp_vec_interface);
    // y_interface = A_{\Gamma B} tmp_vec_b0 + A_{\Gamma \Pi} tmp_vec_primal0
    VecAXPY(y_interface, 1.0, data->tmp_vec_interface);
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    // y_lagrange = J tmp_vec_b0
    MatMult(*(data->mat_lagrange), data->tmp_vec_b0, y_lagrange);
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    FetiTimings::fetiSolve += (MPI::Wtime() - wtime);

    return 0;
  }


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  PetscErrorCode petscApplyFetiDirichletPrecon(PC pc, Vec x, Vec y)
  {
    double wtime = MPI::Wtime();

    // Get data for the preconditioner
    void *ctx;
    PCShellGetContext(pc, &ctx);
    FetiDirichletPreconData* data = static_cast<FetiDirichletPreconData*>(ctx);

    // Multiply with scaled Lagrange constraint matrix.
    MatMultTranspose(*(data->mat_lagrange_scaled), x, data->tmp_vec_b);


    // === Restriction of the B nodes to the boundary nodes. ===

    int nLocalB;
    int nLocalDuals;
    VecGetLocalSize(data->tmp_vec_b, &nLocalB);
    VecGetLocalSize(data->tmp_vec_duals0, &nLocalDuals);

    PetscScalar *local_b, *local_duals;
    VecGetArray(data->tmp_vec_b, &local_b);
    VecGetArray(data->tmp_vec_duals0, &local_duals);

    for (map<int, int>::iterator it = data->localToDualMap.begin();
	 it != data->localToDualMap.end(); ++it)
      local_duals[it->second] = local_b[it->first];

    VecRestoreArray(data->tmp_vec_b, &local_b);
    VecRestoreArray(data->tmp_vec_duals0, &local_duals);


    // === K_DD - K_DI inv(K_II) K_ID ===

    MatMult(*(data->mat_duals_duals), data->tmp_vec_duals0, data->tmp_vec_duals1);

    MatMult(*(data->mat_interior_duals), data->tmp_vec_duals0, data->tmp_vec_interior);
    KSPSolve(*(data->ksp_interior), data->tmp_vec_interior, data->tmp_vec_interior);
    MatMult(*(data->mat_duals_interior), data->tmp_vec_interior, data->tmp_vec_duals0);

    VecAXPBY(data->tmp_vec_duals0, 1.0, -1.0, data->tmp_vec_duals1);


    // === Prolongation from local dual nodes to B nodes.

    VecGetArray(data->tmp_vec_b, &local_b);
    VecGetArray(data->tmp_vec_duals0, &local_duals);

    for (map<int, int>::iterator it = data->localToDualMap.begin();
	 it != data->localToDualMap.end(); ++it)
      local_b[it->first] = local_duals[it->second];

    VecRestoreArray(data->tmp_vec_b, &local_b);
    VecRestoreArray(data->tmp_vec_duals0, &local_duals);


    // Multiply with scaled Lagrange constraint matrix.
    MatMult(*(data->mat_lagrange_scaled), data->tmp_vec_b, y);

    FetiTimings::fetiPreconditioner += (MPI::Wtime() - wtime);

    return 0;
  }


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  PetscErrorCode petscApplyFetiLumpedPrecon(PC pc, Vec xvec, Vec yvec)
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  {
    // Get data for the preconditioner
    void *ctx;
    PCShellGetContext(pc, &ctx);
    FetiLumpedPreconData* data = static_cast<FetiLumpedPreconData*>(ctx);

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    // Multiply with scaled Lagrange constraint matrix.
    MatMultTranspose(*(data->mat_lagrange_scaled), xvec, data->tmp_vec_b0);


    // === Restriction of the B nodes to the boundary nodes. ===

    int nLocalB;
    int nLocalDuals;
    VecGetLocalSize(data->tmp_vec_b0, &nLocalB);
    VecGetLocalSize(data->tmp_vec_duals0, &nLocalDuals);

    PetscScalar *local_b, *local_duals;
    VecGetArray(data->tmp_vec_b0, &local_b);
    VecGetArray(data->tmp_vec_duals0, &local_duals);

    for (map<int, int>::iterator it = data->localToDualMap.begin();
	 it != data->localToDualMap.end(); ++it)
      local_duals[it->second] = local_b[it->first];

    VecRestoreArray(data->tmp_vec_b0, &local_b);
    VecRestoreArray(data->tmp_vec_duals0, &local_duals);


    // === K_DD ===

    MatMult(*(data->mat_duals_duals), data->tmp_vec_duals0, data->tmp_vec_duals1);


    // === Prolongation from local dual nodes to B nodes.

    VecGetArray(data->tmp_vec_b0, &local_b);
    VecGetArray(data->tmp_vec_duals1, &local_duals);

    for (map<int, int>::iterator it = data->localToDualMap.begin();
	 it != data->localToDualMap.end(); ++it)
      local_b[it->first] = local_duals[it->second];

    VecRestoreArray(data->tmp_vec_b0, &local_b);
    VecRestoreArray(data->tmp_vec_duals0, &local_duals);


    // Multiply with scaled Lagrange constraint matrix.
    MatMult(*(data->mat_lagrange_scaled), data->tmp_vec_b0, yvec);

    return 0;
  }


  PetscErrorCode petscApplyFetiInterfaceLumpedPrecon(PC pc, Vec xvec, Vec yvec)
  {
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    FUNCNAME("precon");
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    // Get data for the preconditioner
    void *ctx;
    PCShellGetContext(pc, &ctx);
    FetiInterfaceLumpedPreconData* data = 
      static_cast<FetiInterfaceLumpedPreconData*>(ctx);
    
    Vec x_interface, x_lagrange, y_interface, y_lagrange;    
    VecNestGetSubVec(xvec, 0, &x_interface);
    VecNestGetSubVec(xvec, 1, &x_lagrange);
    VecNestGetSubVec(yvec, 0, &y_interface);
    VecNestGetSubVec(yvec, 1, &y_lagrange);

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    VecCopy(x_interface, y_interface);
    // KSPSolve(data->ksp_mass, x_interface, y_interface);
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    MatMultTranspose(*(data->mat_lagrange_scaled), x_lagrange, data->tmp_vec_b0);   
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    // === Restriction of the B nodes to the boundary nodes. ===
    int nLocalB;
    int nLocalDuals;
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    VecGetLocalSize(data->tmp_vec_b0, &nLocalB);
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    VecGetLocalSize(data->tmp_vec_duals0, &nLocalDuals);
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    PetscScalar *local_b, *local_duals;
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    VecGetArray(data->tmp_vec_b0, &local_b);
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    VecGetArray(data->tmp_vec_duals0, &local_duals);
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    for (map<int, int>::iterator it = data->localToDualMap.begin();
	 it != data->localToDualMap.end(); ++it)
      local_duals[it->second] = local_b[it->first];
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    VecRestoreArray(data->tmp_vec_b0, &local_b);
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    VecRestoreArray(data->tmp_vec_duals0, &local_duals);
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    // === K_DD ===
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    MatMult(*(data->mat_duals_duals), data->tmp_vec_duals0, data->tmp_vec_duals1);
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    // === Prolongation from local dual nodes to B nodes.
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    VecGetArray(data->tmp_vec_b0, &local_b);
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    VecGetArray(data->tmp_vec_duals1, &local_duals);
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    for (map<int, int>::iterator it = data->localToDualMap.begin();
	 it != data->localToDualMap.end(); ++it)
      local_b[it->first] = local_duals[it->second];
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    VecRestoreArray(data->tmp_vec_b0, &local_b);
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    VecRestoreArray(data->tmp_vec_duals0, &local_duals);
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    // Multiply with scaled Lagrange constraint matrix.
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    MatMult(*(data->mat_lagrange_scaled), data->tmp_vec_b0, y_lagrange);
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    return 0;
  }

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}