Пример #1
0
static void
do_test(MAP *rmap, MAP *cmap)
{
    MAT *A;
    VEC *x, *y;
    INT i, j, m0, n0;
    INT *cols = phgAlloc(cmap->nglobal * sizeof(*cols));
    FLOAT *data = phgAlloc(cmap->nglobal * sizeof(*data));

    A = phgMapCreateMat(rmap, cmap);
    m0 = A->rmap->partition[A->rmap->rank];
    n0 = A->cmap->partition[A->cmap->rank];

    /* Matrix entries: A(I,J) = 1 + (I-1) + (J-1) */
    for (i = m0; i < m0 + A->rmap->nlocal; i++) {
#if 0
	/* Test MatAddEntry */
	for (j = 0; j < A->cmap->nglobal; j++)
	    phgMatAddGlobalEntry(A, i, j, 1.0 + i + j);
#else
	/* Test MatAddEntries */
	for (j = 0; j < A->cmap->nglobal; j++) {
	    cols[j] = j;
	    data[j] = 1.0 + i + j;
	}
	phgMatAddGlobalEntries(A, 1, &i, A->cmap->nglobal, cols, data);
#endif
    }
    phgFree(cols);
    phgFree(data);
    phgMatAssemble(A);

    phgInfo(-1, "y = A * x\n");
    x = phgMapCreateVec(A->cmap, 1);
    for (i = 0; i < x->map->nlocal; i++)
	x->data[i] = 1.0 + i + n0;
    phgVecAssemble(x);
    y = phgMatVec(MAT_OP_N, 1.0, A, x, 0.0, NULL);
    for (i = 0; i < y->map->nlocal; i++)
	phgInfo(-1, "    y->data[%d] = %lg\n", i + m0, (double)y->data[i]);
    phgVecDestroy(&x);
    phgVecDestroy(&y);

    phgInfo(-1, "y = A' * x\n");
    x = phgMapCreateVec(A->rmap, 1);
    for (i = 0; i < x->map->nlocal; i++)
	x->data[i] = 1.0 + i + m0;
    phgVecAssemble(x);
    y = phgMatVec(MAT_OP_T, 1.0, A, x, 0.0, NULL);
    for (i = 0; i < y->map->nlocal; i++)
	phgInfo(-1, "    y->data[%d] = %lg\n", i + n0, (double)y->data[i]);
    phgVecDestroy(&x);
    phgVecDestroy(&y);

    phgMatDestroy(&A);
}
Пример #2
0
int
main(int argc, char *argv[])
{
    GRID *g;
    DOF *u_h;
    MAT *A, *A0, *B;
    MAP *map;
    INT i;
    size_t nnz, mem, mem_peak;
    VEC *x, *y0, *y1, *y2;
    double t0, t1, dnz, dnz1, mflops, mop;
    char *fn = "../test/cube.dat";
    FLOAT mem_max = 300;
    INT refine = 0;

    phgOptionsRegisterFilename("-mesh_file", "Mesh file", (char **)&fn);
    phgOptionsRegisterInt("-loop_count", "Loop count", &loop_count);
    phgOptionsRegisterInt("-refine", "Refinement level", &refine);
    phgOptionsRegisterFloat("-mem_max", "Maximum memory", &mem_max);

    phgInit(&argc, &argv);
    g = phgNewGrid(-1);
    if (!phgImport(g, fn, FALSE))
	phgError(1, "can't read file \"%s\".\n", fn);
    phgRefineAllElements(g, refine);
    u_h = phgDofNew(g, DOF_DEFAULT, 1, "u_h", DofNoAction);

    while (TRUE) {
	phgPrintf("\n");
	if (phgBalanceGrid(g, 1.2, 1, NULL, 0.))
	    phgPrintf("Repartition mesh, %d submeshes, load imbalance: %lg\n",
			g->nprocs, (double)g->lif);
	map = phgMapCreate(u_h, NULL);
	A = phgMapCreateMat(map, map);
	A->handle_bdry_eqns = TRUE;
	build_matrix(A, u_h);
	phgMatAssemble(A);

	/* Note: A is unsymmetric (A' != A) if boundary entries not removed */
	phgMatRemoveBoundaryEntries(A);

#if 0
	/* test block matrix operation */
	A0 = phgMatCreateBlockMatrix(g->comm, 1, 1, &A, NULL);
#else
	A0 = A;
#endif

	phgPrintf("%d DOF, %d elems, %d submeshes, matrix size: %d, LIF: %lg\n",
			DofGetDataCountGlobal(u_h), g->nleaf_global,
			g->nprocs, A->rmap->nglobal, (double)g->lif);

	/* test PHG mat-vec multiply */
	x = phgMapCreateVec(A->cmap, 1);
	y1 = phgMapCreateVec(A->rmap, 1);
	phgVecRandomize(x, 123);
	phgMatVec(MAT_OP_N, 1.0, A0, x, 0.0, &y1);

	phgPerfGetMflops(g, NULL, NULL);	/* reset flops counter */
	t0 = phgGetTime(NULL);
	for (i = 0; i < loop_count; i++) {
	    phgMatVec(MAT_OP_N, 1.0, A0, x, 0.0, &y1);
	}
	t1 = phgGetTime(NULL);
	mflops = phgPerfGetMflops(g, NULL, NULL);
	y0 = phgVecCopy(y1, NULL);
	nnz = A->nnz_d + A->nnz_o;
#if USE_MPI
	dnz1 = nnz;
	MPI_Reduce(&dnz1, &dnz, 1, MPI_DOUBLE, MPI_SUM, 0, g->comm);
#else
	dnz = nnz;
#endif
	mop = loop_count * (dnz + dnz - A->rmap->nlocal) * 1e-6;

	phgPrintf("\n");
	t1 -= t0;
	phgPrintf("   PHG:  time %0.4lf, nnz %0.16lg, %0.2lfMF (%0.2lfMF)\n",
			t1, dnz, mop / (t1 == 0 ? 1. : t1), mflops);

	/* test trans(A)*x */
	phgPerfGetMflops(g, NULL, NULL);	/* reset flops counter */
	t0 = phgGetTime(NULL);
	for (i = 0; i < loop_count; i++) {
	    phgMatVec(MAT_OP_T, 1.0, A0, x, 0.0, &y1);
	}
	t1 = phgGetTime(NULL);
	mflops = phgPerfGetMflops(g, NULL, NULL);
	t1 -= t0;
	phgPrintf("  A'*x:  time %0.4lf, nnz %0.16lg, %0.2lfMF (%0.2lfMF), "
		  "err: %le\n", t1, dnz, mop / (t1 == 0 ? 1. : t1), mflops,
		 (double)phgVecNorm2(phgVecAXPBY(-1.0, y0, 1.0, &y1), 0, NULL));

	/* time A * trans(A) */
	phgPerfGetMflops(g, NULL, NULL);	/* reset flops counter */
	t0 = phgGetTime(NULL);
	B = phgMatMat(MAT_OP_N, MAT_OP_N, 1.0, A, A, 0.0, NULL);
	t1 = phgGetTime(NULL);
	mflops = phgPerfGetMflops(g, NULL, NULL);
	nnz = B->nnz_d + B->nnz_o;
#if USE_MPI
	dnz1 = nnz;
	MPI_Reduce(&dnz1, &dnz, 1, MPI_DOUBLE, MPI_SUM, 0, g->comm);
#else
	dnz = nnz;
#endif
	/* compare B*x <--> A*A*x */
	y2 = phgMatVec(MAT_OP_N, 1.0, B, x, 0.0, NULL);
	phgMatVec(MAT_OP_N, 1.0, A0, y0, 0.0, &y1);
	phgMatDestroy(&B);
	t1 -= t0;
	phgPrintf("   A*A:  time %0.4lf, nnz %0.16lg, %0.2lfMF, err: %le\n",
		  t1, dnz, mflops,
		 (double)phgVecNorm2(phgVecAXPBY(-1.0, y1, 1.0, &y2), 0, NULL));

#if USE_PETSC
	{
	    Mat ma, mb;
	    MatInfo info;
	    Vec va, vb, vc;
	    PetscScalar *vec;

	    ma = phgPetscCreateMatAIJ(A);
	    MatGetVecs(ma, PETSC_NULL, &va);
	    VecDuplicate(va, &vb);
	    VecGetArray(va, &vec);
	    memcpy(vec, x->data, x->map->nlocal * sizeof(*vec));
	    VecRestoreArray(va, &vec);
	    MatMult(ma, va, vb);
	    phgPerfGetMflops(g, NULL, NULL);	/* reset flops counter */
	    t0 = phgGetTime(NULL);
	    for (i = 0; i < loop_count; i++) {
		MatMult(ma, va, vb);
	    }
	    t1 = phgGetTime(NULL);
	    mflops = phgPerfGetMflops(g, NULL, NULL);
	    VecGetArray(vb, &vec);
	    memcpy(y1->data, vec, x->map->nlocal * sizeof(*vec));
	    VecRestoreArray(vb, &vec);

	    MatGetInfo(ma, MAT_GLOBAL_SUM, &info);
	    /*phgPrintf("    --------------------------------------------"
		      "-------------------------\n");*/
	    phgPrintf("\n");
	    t1 -= t0;
	    dnz = info.nz_used;
	    phgPrintf(" PETSc:  time %0.4lf, nnz %0.16lg, %0.2lfMF (%0.2lfMF), "
		      "err: %le\n", t1, dnz, mop / (t1==0 ? 1.:t1), mflops,
		 (double)phgVecNorm2(phgVecAXPBY(-1.0, y0, 1.0, &y1), 0, NULL));

	    phgPerfGetMflops(g, NULL, NULL);	/* reset flops counter */
	    t0 = phgGetTime(NULL);
	    for (i = 0; i < loop_count; i++) {
		MatMultTranspose(ma, va, vb);
	    }
	    t1 = phgGetTime(NULL);
	    mflops = phgPerfGetMflops(g, NULL, NULL);
	    VecGetArray(vb, &vec);
	    memcpy(y1->data, vec, x->map->nlocal * sizeof(*vec));
	    VecRestoreArray(vb, &vec);
	    t1 -= t0;
	    phgPrintf("  A'*x:  time %0.4lf, nnz %0.16lg, %0.2lfMF (%0.2lfMF), "
		      "err: %le\n", t1, dnz, mop / (t1==0 ? 1.:t1), mflops,
		(double)phgVecNorm2(phgVecAXPBY(-1.0, y0, 1.0, &y1), 0, NULL));

	    phgPerfGetMflops(g, NULL, NULL);	/* reset flops counter */
	    t0 = phgGetTime(NULL);
	    MatMatMult(ma, ma, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &mb);
	    t1 = phgGetTime(NULL);
	    mflops = phgPerfGetMflops(g, NULL, NULL);
	    t1 -= t0;
	    MatGetInfo(mb, MAT_GLOBAL_SUM, &info);
	    dnz = info.nz_used;
	    VecDuplicate(va, &vc);
	    /* compare B*x <--> A*A*x */
	    MatMult(ma, vb, vc);
	    MatMult(mb, va, vb);
	    VecGetArray(vb, &vec);
	    memcpy(y1->data, vec, x->map->nlocal * sizeof(*vec));
	    VecRestoreArray(vb, &vec);
	    VecGetArray(vc, &vec);
	    memcpy(y2->data, vec, x->map->nlocal * sizeof(*vec));
	    VecRestoreArray(vc, &vec);
	    phgPrintf("   A*A:  time %0.4lf, nnz %0.16lg, %0.2lfMF, err: %le\n",
		  t1, dnz, mflops,
		 (double)phgVecNorm2(phgVecAXPBY(-1.0, y1, 1.0, &y2), 0, NULL));

	    phgPetscMatDestroy(&mb);
	    phgPetscMatDestroy(&ma);
	    phgPetscVecDestroy(&va);
	    phgPetscVecDestroy(&vb);
	    phgPetscVecDestroy(&vc);
	}
#endif	/* USE_PETSC */

#if USE_HYPRE
	{
	    HYPRE_IJMatrix ma;
	    HYPRE_IJVector va, vb, vc;
	    HYPRE_ParCSRMatrix  par_ma;
	    hypre_ParCSRMatrix  *par_mb;
	    HYPRE_ParVector	par_va, par_vb, par_vc;
	    HYPRE_Int offset, *ni, start, end;
	    assert(sizeof(INT)==sizeof(int) && sizeof(FLOAT)==sizeof(double));
	    setup_hypre_mat(A, &ma);
	    ni = phgAlloc(2 * A->rmap->nlocal * sizeof(*ni));
	    offset = A->cmap->partition[A->cmap->rank];
	    for (i = 0; i < A->rmap->nlocal; i++)
		ni[i] = i + offset;
	    HYPRE_IJVectorCreate(g->comm, offset, offset + A->rmap->nlocal - 1,
				 &va);
	    HYPRE_IJVectorCreate(g->comm, offset, offset + A->rmap->nlocal - 1,
				 &vb);
	    HYPRE_IJVectorCreate(g->comm, offset, offset + A->rmap->nlocal - 1,
				 &vc);
	    HYPRE_IJVectorSetObjectType(va, HYPRE_PARCSR);
	    HYPRE_IJVectorSetObjectType(vb, HYPRE_PARCSR);
	    HYPRE_IJVectorSetObjectType(vc, HYPRE_PARCSR);
	    HYPRE_IJVectorSetMaxOffProcElmts(va, 0);
	    HYPRE_IJVectorSetMaxOffProcElmts(vb, 0);
	    HYPRE_IJVectorSetMaxOffProcElmts(vc, 0);
	    HYPRE_IJVectorInitialize(va);
	    HYPRE_IJVectorInitialize(vb);
	    HYPRE_IJVectorInitialize(vc);
	    HYPRE_IJMatrixGetObject(ma, (void **)(void *)&par_ma);
	    HYPRE_IJVectorGetObject(va, (void **)(void *)&par_va);
	    HYPRE_IJVectorGetObject(vb, (void **)(void *)&par_vb);
	    HYPRE_IJVectorGetObject(vc, (void **)(void *)&par_vc);
	    HYPRE_IJVectorSetValues(va, A->cmap->nlocal, ni, (double *)x->data);
	    HYPRE_IJVectorAssemble(va);
	    HYPRE_IJVectorAssemble(vb);
	    HYPRE_IJVectorAssemble(vc);

	    HYPRE_IJMatrixGetRowCounts(ma, A->cmap->nlocal,
					ni, ni + A->rmap->nlocal);
	    for (i = 0, nnz = 0; i < A->rmap->nlocal; i++)
		nnz += ni[A->rmap->nlocal + i];
#if USE_MPI
	    dnz1 = nnz;
	    MPI_Reduce(&dnz1, &dnz, 1, MPI_DOUBLE, MPI_SUM, 0, g->comm);
#else
	    dnz = nnz;
#endif

	    HYPRE_ParCSRMatrixMatvec(1.0, par_ma, par_va, 0.0, par_vb);
	    phgPerfGetMflops(g, NULL, NULL);	/* reset flops counter */
	    t0 = phgGetTime(NULL);
	    for (i = 0; i < loop_count; i++) {
		HYPRE_ParCSRMatrixMatvec(1.0, par_ma, par_va, 0.0, par_vb);
	    }
	    t1 = phgGetTime(NULL);
	    mflops = phgPerfGetMflops(g, NULL, NULL);
	    HYPRE_IJVectorGetValues(vb, A->rmap->nlocal, ni, (double*)y1->data);
	    /*phgPrintf("    --------------------------------------------"
		      "-------------------------\n");*/
	    phgPrintf("\n");
	    t1 -= t0;
	    phgPrintf(" HYPRE:  time %0.4lf, nnz %0.16lg, %0.2lfMF (%0.2lfMF), "
		      "err: %le\n", t1, dnz, mop / (t1==0 ? 1.:t1), mflops,
		(double)phgVecNorm2(phgVecAXPBY(-1.0, y0, 1.0, &y1), 0, NULL));

	    phgPerfGetMflops(g, NULL, NULL);	/* reset flops counter */
	    t0 = phgGetTime(NULL);
	    for (i = 0; i < loop_count; i++) {
		HYPRE_ParCSRMatrixMatvecT(1.0, par_ma, par_va, 0.0, par_vb);
	    }
	    t1 = phgGetTime(NULL);
	    mflops = phgPerfGetMflops(g, NULL, NULL);
	    HYPRE_IJVectorGetValues(vb, A->rmap->nlocal, ni, (double*)y1->data);
	    t1 -= t0;
	    phgPrintf("  A'*x:  time %0.4lf, nnz %0.16lg, %0.2lfMF (%0.2lfMF), "
		      "err: %le\n", t1, dnz, mop / (t1==0 ? 1.:t1), mflops,
		(double)phgVecNorm2(phgVecAXPBY(-1.0, y0, 1.0, &y1), 0, NULL));

	    phgPerfGetMflops(g, NULL, NULL);	/* reset flops counter */
	    t0 = phgGetTime(NULL);
	    /* Note: 'HYPRE_ParCSRMatrix' is currently typedef'ed to
	     *	     'hypre_ParCSRMatrix *' */
	    par_mb = hypre_ParMatmul((hypre_ParCSRMatrix *)par_ma,
					(hypre_ParCSRMatrix *)par_ma);
	    t1 = phgGetTime(NULL);
	    mflops = phgPerfGetMflops(g, NULL, NULL);
	    start = hypre_ParCSRMatrixFirstRowIndex(par_mb);
	    end = hypre_ParCSRMatrixLastRowIndex(par_mb) + 1;
	    for (i = start, nnz = 0; i < end; i++) {
		HYPRE_Int ncols;
		hypre_ParCSRMatrixGetRow(par_mb, i, &ncols, NULL, NULL);
		hypre_ParCSRMatrixRestoreRow(par_mb, i, &ncols, NULL, NULL);
		nnz += ncols;
	    }
#if USE_MPI
	    dnz1 = nnz;
	    MPI_Reduce(&dnz1, &dnz, 1, MPI_DOUBLE, MPI_SUM, 0, g->comm);
#else
	    dnz = nnz;
#endif
	    /* compare B*x <--> A*A*x */
	    HYPRE_ParCSRMatrixMatvec(1.0, par_ma, par_vb, 0.0, par_vc);
	    HYPRE_ParCSRMatrixMatvec(1.0, (void *)par_mb, par_va, 0.0, par_vb);
	    HYPRE_IJVectorGetValues(vb, A->rmap->nlocal, ni, (double*)y1->data);
	    HYPRE_IJVectorGetValues(vc, A->rmap->nlocal, ni, (double*)y2->data);
	    hypre_ParCSRMatrixDestroy((par_mb));
	    t1 -= t0;
	    phgPrintf("   A*A:  time %0.4lf, nnz %0.16lg, %0.2lfMF, err: %le\n",
		  t1, dnz, mflops,
		 (double)phgVecNorm2(phgVecAXPBY(-1.0, y1, 1.0, &y2), 0, NULL));

	    phgFree(ni);
	    HYPRE_IJMatrixDestroy(ma);
	    HYPRE_IJVectorDestroy(va);
	    HYPRE_IJVectorDestroy(vb);
	    HYPRE_IJVectorDestroy(vc);
	}
#endif	/* USE_HYPRE */

	if (A0 != A)
	    phgMatDestroy(&A0);
#if 0
if (A->rmap->nglobal > 1000) {
    VEC *v = phgMapCreateVec(A->rmap, 3);
    for (i = 0; i < v->map->nlocal; i++) {
	v->data[i + 0 * v->map->nlocal] = 1 * (i + v->map->partition[g->rank]);
	v->data[i + 1 * v->map->nlocal] = 2 * (i + v->map->partition[g->rank]);
	v->data[i + 2 * v->map->nlocal] = 3 * (i + v->map->partition[g->rank]);
    }
    phgMatDumpMATLAB(A, "A", "A.m");
    phgVecDumpMATLAB(v, "v", "v.m");
    phgFinalize();
    exit(0);
}
#endif
	phgMatDestroy(&A);
	phgVecDestroy(&x);
	phgVecDestroy(&y0);
	phgVecDestroy(&y1);
	phgVecDestroy(&y2);
	phgMapDestroy(&map);
	mem = phgMemoryUsage(g, &mem_peak);
	dnz = mem / (1024.0 * 1024.0);
	dnz1 = mem_peak / (1024.0 * 1024.0);
	/*phgPrintf("    --------------------------------------------"
		  "-------------------------\n");*/
	phgPrintf("\n");
	phgPrintf("  Memory: current %0.4lgMB, peak %0.4lgMB\n", dnz, dnz1);
#if 0
{
    static int loop_count = 0;
    if (++loop_count == 4)
	break;
}
#endif
	if (mem_peak > 1024 * (size_t)1024 * mem_max)
	    break;
	phgRefineAllElements(g, 1);
    }
    phgDofFree(&u_h);
    phgFreeGrid(&g);
    phgFinalize();

    return 0;
}
Пример #3
0
void phgNSInitPc(NSSolver *ns)
{
    GRID *g = ns->g;
    MAP *Pmap = ns->Pmap, *Pbcmap;
    BOOLEAN use_Fu = _nsp->use_Fu;
    int verb;

    /* pcd boundary type test */
    _pcd->dof_inflow = phgDofNew(g, _nsp->ptype, 1, "dof inflow", DofNoAction);
    _pcd->dof_outflow = phgDofNew(g, _nsp->ptype, 1, "dof outflow", DofNoAction);
    _pcd->dof_nobdry = phgDofNew(g, _nsp->ptype, 1, "dof nobdry", DofNoAction);

    phgDofSetDirichletBoundaryMask(_pcd->dof_inflow, INFLOW);
    phgDofSetDirichletBoundaryMask(_pcd->dof_outflow, OUTFLOW);
    phgDofSetDirichletBoundaryMask(_pcd->dof_nobdry, 0);

    _pcd->map_inflow = phgMapCreate(_pcd->dof_inflow, NULL);
    _pcd->map_outflow = phgMapCreate(_pcd->dof_outflow, NULL);
    _pcd->map_nobdry = phgMapCreate(_pcd->dof_nobdry, NULL);

    _pcd->Pbcmap = phgMapCreate(_pcd->pbc, NULL);
    Pbcmap = _pcd->Pbcmap;

    Unused(Pmap);
#warning PCD B.C.: step 1. build mat using map... 
    /*
     * PCD boundary setup: should be consistent with code above
     */
    if (_nsp->pin_node) {
	_pcd->matFp = phgMapCreateMat(Pbcmap, Pbcmap);
	_pcd->matAp = phgMapCreateMat(Pbcmap, Pbcmap);
	_pcd->matQp = phgMapCreateMat(Pbcmap, Pbcmap);
    } else {
	//_pcd->matAp = phgMapCreateMat(_pcd->map_inflow, _pcd->map_inflow);
	//_pcd->matFp = phgMapCreateMat(_pcd->map_inflow, _pcd->map_inflow);
	_pcd->matFp = phgMapCreateMat(_pcd->map_outflow, _pcd->map_outflow);
	_pcd->matAp = phgMapCreateMat(_pcd->map_outflow, _pcd->map_outflow);
	//_pcd->matQp = phgMapCreateMat(_pcd->map_outflow, _pcd->map_outflow);
	//_pcd->matQp = phgMapCreateMat(_pcd->map_inflow, _pcd->map_inflow);
	//_pcd->matFp = phgMapCreateMat(_pcd->map_nobdry, _pcd->map_nobdry);
	//_pcd->matAp = phgMapCreateMat(_pcd->map_nobdry, _pcd->map_nobdry);
	//_pcd->matFp = phgMapCreateMat(_pcd->map_nobdry, _pcd->map_nobdry);
	_pcd->matQp = phgMapCreateMat(_pcd->map_nobdry, _pcd->map_nobdry);
    }

    /* stokes problem: get SYMETRIC mat when assemble.
     * Handle_bdry_eqns means mat is composed with row of boundary row
     * and non-bdry row, and eliminating mat columes of dirichlet dof. 
     */
    if (_nsp->use_symetric) {
	_pcd->matFp->handle_bdry_eqns = TRUE;
	_pcd->matAp->handle_bdry_eqns = TRUE;
	_pcd->matQp->handle_bdry_eqns = TRUE;
    } 
    /* genearl NS: no need to eliminate mat columes of dirichlet dof */
    else {
	_pcd->matFp->handle_bdry_eqns = FALSE;
	_pcd->matAp->handle_bdry_eqns = FALSE;
	_pcd->matQp->handle_bdry_eqns = FALSE;
    }	
    
    _pcd->rhsScale = phgMapCreateVec(_pcd->matQp->rmap, 1);
    phgVecDisassemble(_pcd->rhsScale);

    ns->pc = phgMat2Solver(SOLVER_PreOnly, ns->solver_u->mat);
    if (_nsp->use_PCD)
	phgSolverSetPC(ns->solver_u, ns->pc, pc_proc);

    /* solver F */
    phgOptionsPush();
    phgOptionsSetOptions("-solver hypre "
			 "-hypre_solver pcg "
			 "-hypre_pc boomeramg "
			 "-solver_maxit 10 "
			 "-solver_rtol 1e-4");
    phgOptionsSetOptions(_nsp->F_opts);
    /* use matF in the preconditioning matrix */
    _pcd->solver_F = phgMat2Solver(SOLVER_DEFAULT, ns->matF);
    _pcd->solver_F->verb = SUB_SOLVER_VERB; /* Set user options. */
    _pcd->pc_F = NULL;
#if USE_MG 
    if (ns_params->use_mg_F) {
	MAT *matF = ns->matF;

	assert(ns_params->use_PCD && !ns_params->use_Fu);
	_pcd->pc_F = phgMat2Solver(SOLVER_PreOnly, matF);
	phgOptionsSetOptions("-solver petsc ");
	matF->mv_data = phgAlloc(sizeof(*matF->mv_data));
	matF->mv_data[0] = (void *) ns->mg;
	phgSolverSetPC(_pcd->solver_F, _pcd->pc_F, mg_pc_proc);
    }
#endif /* USE_MG */
    _pcd->solver_F->warn_maxit = FALSE;
    phgOptionsPop();

    /* solver Ap */
    phgOptionsPush();
    phgOptionsSetOptions("-solver hypre "
			 "-hypre_solver gmres "
			 "-hypre_pc boomeramg "
			 "-solver_maxit 10 "
			 "-solver_rtol 1e-3");
    phgOptionsSetOptions(_nsp->Ap_opts);
    _pcd->solver_Ap = phgMat2Solver(SOLVER_DEFAULT, _pcd->matAp);
    _pcd->solver_Ap->warn_maxit = FALSE;
    _pcd->solver_Ap->verb = SUB_SOLVER_VERB;
    phgOptionsPop();
    _pcd->pc_Ap = NULL;
#if USE_MG 
    if (ns_params->use_mg_Ap) {
	MAT *matAp = _pcd->matAp;

	assert(ns_params->use_PCD);
	_pcd->pc_Ap = phgMat2Solver(SOLVER_PreOnly, matAp);
	phgOptionsSetOptions("-solver petsc ");
	matAp->mv_data = phgAlloc(sizeof(*matAp->mv_data));
	matAp->mv_data[0] = (void *) ns->mg;
	phgSolverSetPC(_pcd->solver_Ap, _pcd->pc_Ap, mg_pc_proc);
    }
#endif /* USE_MG */


    /* solver Qp */
    phgOptionsPush();
    phgOptionsSetOptions("-solver hypre "
			 "-hypre_solver pcg "
			 "-hypre_pc boomeramg "
			 "-solver_maxit 10 "
			 "-solver_rtol 1e-3");
    phgOptionsSetOptions(_nsp->Qp_opts);
    _pcd->solver_Qp = phgMat2Solver(SOLVER_DEFAULT, _pcd->matQp);
    _pcd->solver_Qp->warn_maxit = FALSE;
    _pcd->solver_Qp->verb = SUB_SOLVER_VERB;
    phgOptionsPop();
    _pcd->pc_Qp = NULL;
#if USE_MG 
    if (ns_params->use_mg_Qp) {
	MAT *matQp = _pcd->matQp;

	assert(ns_params->use_PCD);
	_pcd->pc_Qp = phgMat2Solver(SOLVER_PreOnly, matQp);
	phgOptionsSetOptions("-solver petsc ");
	matQp->mv_data = phgAlloc(sizeof(*matQp->mv_data));
	matQp->mv_data[0] = (void *) ns->mg;
	phgSolverSetPC(_pcd->solver_Qp, _pcd->pc_Qp, mg_pc_proc);
    }
#endif /* USE_MG */

    /* Fu for solve F^{-1} */
    if (use_Fu) { /* _nsp->implicit_centrip &&  */
	DOF *u1;
	MAP *u1map;
	MAT *matFu;
	u1 = _pcd->u1 = 
	    phgDofNew(g, _nsp->utype, 1, "velocity component u", DofNoAction);
	phgDofSetDirichletBoundaryMask(u1, SETFLOW);
	
	u1map = _pcd->u1map
	    = phgMapCreate(_pcd->u1, NULL);
	matFu = _pcd->matFu 
	    = phgMapCreateMat(u1map, u1map);
	if (_nsp->use_symetric)
	    matFu->handle_bdry_eqns = TRUE;

	/* solver Fu */
	phgOptionsPush();
	phgOptionsSetOptions("-solver hypre "
			     "-hypre_solver pcg "
			     "-hypre_pc boomeramg "
			     "-solver_maxit 10 "
			     "-solver_rtol 1e-4");
	phgOptionsSetOptions(_nsp->Fu_opts);
	_pcd->solver_Fu = phgMat2Solver(SOLVER_DEFAULT, _pcd->matFu);
	_pcd->solver_Fu->warn_maxit = FALSE;
	_pcd->solver_Fu->verb = SUB_SOLVER_VERB;
	phgOptionsPop();

    }

    return;
}