xref: /petsc/src/ksp/pc/impls/bddc/bddcnullspace.c (revision 3ba1676111f5c958fe6c2729b46ca4d523958bb3)

#include <petsc/private/pcbddcimpl.h>
#include <petsc/private/pcbddcprivateimpl.h>
#include <../src/mat/impls/dense/seq/dense.h>

/* E + small_solve */
static PetscErrorCode PCBDDCNullSpaceCorrPreSolve(KSP ksp, Vec y, Vec x, void *ctx)
{
  NullSpaceCorrection_ctx corr_ctx = (NullSpaceCorrection_ctx)ctx;
  Mat                     K;

  PetscFunctionBegin;
  PetscCall(PetscLogEventBegin(corr_ctx->evapply, ksp, 0, 0, 0));
  PetscCall(MatMultTranspose(corr_ctx->basis_mat, y, corr_ctx->sw[0]));
  if (corr_ctx->symm) {
    PetscCall(MatMult(corr_ctx->inv_smat, corr_ctx->sw[0], corr_ctx->sw[1]));
  } else {
    PetscCall(MatMultTranspose(corr_ctx->inv_smat, corr_ctx->sw[0], corr_ctx->sw[1]));
  }
  PetscCall(VecScale(corr_ctx->sw[1], -1.0));
  PetscCall(MatMult(corr_ctx->basis_mat, corr_ctx->sw[1], corr_ctx->fw[0]));
  PetscCall(VecScale(corr_ctx->sw[1], -1.0));
  PetscCall(KSPGetOperators(ksp, &K, NULL));
  PetscCall(MatMultAdd(K, corr_ctx->fw[0], y, y));
  PetscCall(PetscLogEventEnd(corr_ctx->evapply, ksp, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/* E^t + small */
static PetscErrorCode PCBDDCNullSpaceCorrPostSolve(KSP ksp, Vec y, Vec x, void *ctx)
{
  NullSpaceCorrection_ctx corr_ctx = (NullSpaceCorrection_ctx)ctx;
  Mat                     K;

  PetscFunctionBegin;
  PetscCall(PetscLogEventBegin(corr_ctx->evapply, ksp, 0, 0, 0));
  PetscCall(KSPGetOperators(ksp, &K, NULL));
  if (corr_ctx->symm) {
    PetscCall(MatMult(K, x, corr_ctx->fw[0]));
  } else {
    PetscCall(MatMultTranspose(K, x, corr_ctx->fw[0]));
  }
  PetscCall(MatMultTranspose(corr_ctx->basis_mat, corr_ctx->fw[0], corr_ctx->sw[0]));
  PetscCall(VecScale(corr_ctx->sw[0], -1.0));
  PetscCall(MatMult(corr_ctx->inv_smat, corr_ctx->sw[0], corr_ctx->sw[2]));
  PetscCall(MatMultAdd(corr_ctx->basis_mat, corr_ctx->sw[2], x, corr_ctx->fw[0]));
  PetscCall(VecScale(corr_ctx->fw[0], corr_ctx->scale));
  /* Sum contributions from approximate solver and projected system */
  PetscCall(MatMultAdd(corr_ctx->basis_mat, corr_ctx->sw[1], corr_ctx->fw[0], x));
  PetscCall(PetscLogEventEnd(corr_ctx->evapply, ksp, 0, 0, 0));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode PCBDDCNullSpaceCorrDestroy(void *ctx)
{
  NullSpaceCorrection_ctx corr_ctx = (NullSpaceCorrection_ctx)ctx;

  PetscFunctionBegin;
  PetscCall(VecDestroyVecs(3, &corr_ctx->sw));
  PetscCall(VecDestroyVecs(1, &corr_ctx->fw));
  PetscCall(MatDestroy(&corr_ctx->basis_mat));
  PetscCall(MatDestroy(&corr_ctx->inv_smat));
  PetscCall(PetscFree(corr_ctx));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode PCBDDCNullSpaceAssembleCorrection(PC pc, PetscBool isdir, PetscBool needscaling)
{
  PC_BDDC                *pcbddc    = (PC_BDDC *)pc->data;
  MatNullSpace            NullSpace = NULL;
  KSP                     local_ksp;
  NullSpaceCorrection_ctx shell_ctx;
  Mat                     local_mat, local_pmat, dmat, Kbasis_mat;
  Vec                     v;
  PetscContainer          c;
  PetscInt                basis_size;
  IS                      zerorows;
  PetscBool               iscusp;

  PetscFunctionBegin;
  if (isdir) local_ksp = pcbddc->ksp_D; /* Dirichlet solver */
  else local_ksp = pcbddc->ksp_R;       /* Neumann solver */
  PetscCall(KSPGetOperators(local_ksp, &local_mat, &local_pmat));
  PetscCall(MatGetNearNullSpace(local_pmat, &NullSpace));
  if (!NullSpace) {
    if (pcbddc->dbg_flag) PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "Subdomain %04d doesn't have local (near) nullspace: no need for correction in %s solver \n", PetscGlobalRank, isdir ? "Dirichlet" : "Neumann"));
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  PetscCall(PetscObjectQuery((PetscObject)NullSpace, "_PBDDC_Null_dmat", (PetscObject *)&dmat));
  PetscCheck(dmat, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing dense matrix");
  PetscCall(PetscLogEventBegin(PC_BDDC_ApproxSetUp[pcbddc->current_level], pc, 0, 0, 0));

  PetscCall(PetscNew(&shell_ctx));
  shell_ctx->scale = 1.0;
  PetscCall(PetscObjectReference((PetscObject)dmat));
  shell_ctx->basis_mat = dmat;
  PetscCall(MatGetSize(dmat, NULL, &basis_size));
  shell_ctx->evapply = PC_BDDC_ApproxApply[pcbddc->current_level];

  PetscCall(MatIsSymmetric(local_mat, 0.0, &shell_ctx->symm));

  /* explicit construct (Phi^T K Phi)^-1 */
  PetscCall(PetscObjectTypeCompare((PetscObject)local_mat, MATSEQAIJCUSPARSE, &iscusp));
  if (iscusp) PetscCall(MatConvert(shell_ctx->basis_mat, MATSEQDENSECUDA, MAT_INPLACE_MATRIX, &shell_ctx->basis_mat));
  PetscCall(MatMatMult(local_mat, shell_ctx->basis_mat, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &Kbasis_mat));
  PetscCall(MatTransposeMatMult(Kbasis_mat, shell_ctx->basis_mat, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &shell_ctx->inv_smat));
  PetscCall(MatDestroy(&Kbasis_mat));
  PetscCall(MatBindToCPU(shell_ctx->inv_smat, PETSC_TRUE));
  PetscCall(MatFindZeroRows(shell_ctx->inv_smat, &zerorows));
  if (zerorows) { /* linearly dependent basis */
    const PetscInt *idxs;
    PetscInt        i, nz;

    PetscCall(ISGetLocalSize(zerorows, &nz));
    PetscCall(ISGetIndices(zerorows, &idxs));
    for (i = 0; i < nz; i++) PetscCall(MatSetValue(shell_ctx->inv_smat, idxs[i], idxs[i], 1.0, INSERT_VALUES));
    PetscCall(ISRestoreIndices(zerorows, &idxs));
    PetscCall(MatAssemblyBegin(shell_ctx->inv_smat, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(shell_ctx->inv_smat, MAT_FINAL_ASSEMBLY));
  }
  PetscCall(MatLUFactor(shell_ctx->inv_smat, NULL, NULL, NULL));
  PetscCall(MatSeqDenseInvertFactors_Private(shell_ctx->inv_smat));
  if (zerorows) { /* linearly dependent basis */
    const PetscInt *idxs;
    PetscInt        i, nz;

    PetscCall(ISGetLocalSize(zerorows, &nz));
    PetscCall(ISGetIndices(zerorows, &idxs));
    for (i = 0; i < nz; i++) PetscCall(MatSetValue(shell_ctx->inv_smat, idxs[i], idxs[i], 0.0, INSERT_VALUES));
    PetscCall(ISRestoreIndices(zerorows, &idxs));
    PetscCall(MatAssemblyBegin(shell_ctx->inv_smat, MAT_FINAL_ASSEMBLY));
    PetscCall(MatAssemblyEnd(shell_ctx->inv_smat, MAT_FINAL_ASSEMBLY));
  }
  PetscCall(ISDestroy(&zerorows));

  /* Create work vectors in shell context */
  PetscCall(MatCreateVecs(shell_ctx->inv_smat, &v, NULL));
  PetscCall(KSPCreateVecs(local_ksp, 1, &shell_ctx->fw, 0, NULL));
  PetscCall(VecDuplicateVecs(v, 3, &shell_ctx->sw));
  PetscCall(VecDestroy(&v));

  /* add special pre/post solve to KSP (see [1], eq. 48) */
  PetscCall(KSPSetPreSolve(local_ksp, PCBDDCNullSpaceCorrPreSolve, shell_ctx));
  PetscCall(KSPSetPostSolve(local_ksp, PCBDDCNullSpaceCorrPostSolve, shell_ctx));
  PetscCall(PetscContainerCreate(PetscObjectComm((PetscObject)local_ksp), &c));
  PetscCall(PetscContainerSetPointer(c, shell_ctx));
  PetscCall(PetscContainerSetUserDestroy(c, PCBDDCNullSpaceCorrDestroy));
  PetscCall(PetscObjectCompose((PetscObject)local_ksp, "_PCBDDC_Null_PrePost_ctx", (PetscObject)c));
  PetscCall(PetscContainerDestroy(&c));

  /* Create ksp object suitable for extreme eigenvalues' estimation */
  if (needscaling || pcbddc->dbg_flag) {
    KSP         check_ksp;
    PC          local_pc;
    Vec         work1, work2;
    const char *prefix;
    PetscReal   test_err, lambda_min, lambda_max;
    PetscInt    k, maxit;
    PetscBool   isspd, isset;

    PetscCall(VecDuplicate(shell_ctx->fw[0], &work1));
    PetscCall(VecDuplicate(shell_ctx->fw[0], &work2));
    PetscCall(KSPCreate(PETSC_COMM_SELF, &check_ksp));
    PetscCall(MatIsSPDKnown(local_mat, &isset, &isspd));
    if (isset && isspd) PetscCall(KSPSetType(check_ksp, KSPCG));
    PetscCall(PetscObjectIncrementTabLevel((PetscObject)check_ksp, (PetscObject)local_ksp, 0));
    PetscCall(KSPGetOptionsPrefix(local_ksp, &prefix));
    PetscCall(KSPSetOptionsPrefix(check_ksp, prefix));
    PetscCall(KSPAppendOptionsPrefix(check_ksp, "approximate_scale_"));
    PetscCall(KSPSetErrorIfNotConverged(check_ksp, PETSC_FALSE));
    PetscCall(KSPSetOperators(check_ksp, local_mat, local_pmat));
    PetscCall(KSPSetComputeSingularValues(check_ksp, PETSC_TRUE));
    PetscCall(KSPSetPreSolve(check_ksp, PCBDDCNullSpaceCorrPreSolve, shell_ctx));
    PetscCall(KSPSetPostSolve(check_ksp, PCBDDCNullSpaceCorrPostSolve, shell_ctx));
    PetscCall(KSPSetTolerances(check_ksp, PETSC_SMALL, PETSC_SMALL, PETSC_DEFAULT, PETSC_DEFAULT));
    PetscCall(KSPSetFromOptions(check_ksp));
    /* setup with default maxit, then set maxit to min(10,any_set_from_command_line) (bug in computing eigenvalues when changing the number of iterations */
    PetscCall(KSPSetUp(check_ksp));
    PetscCall(KSPGetPC(local_ksp, &local_pc));
    PetscCall(KSPSetPC(check_ksp, local_pc));
    PetscCall(KSPGetTolerances(check_ksp, NULL, NULL, NULL, &maxit));
    PetscCall(KSPSetTolerances(check_ksp, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT, PetscMin(10, maxit)));
    PetscCall(VecSetRandom(work2, NULL));
    PetscCall(MatMult(local_mat, work2, work1));
    PetscCall(KSPSolve(check_ksp, work1, work1));
    PetscCall(KSPCheckSolve(check_ksp, pc, work1));
    PetscCall(VecAXPY(work1, -1., work2));
    PetscCall(VecNorm(work1, NORM_INFINITY, &test_err));
    PetscCall(KSPComputeExtremeSingularValues(check_ksp, &lambda_max, &lambda_min));
    PetscCall(KSPGetIterationNumber(check_ksp, &k));
    if (pcbddc->dbg_flag) {
      if (isdir) {
        PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "Subdomain %04d infinity error for Dirichlet adapted solver (no scale) %1.14e (it %" PetscInt_FMT ", eigs %1.6e %1.6e)\n", PetscGlobalRank, (double)test_err, k, (double)lambda_min, (double)lambda_max));
      } else {
        PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "Subdomain %04d infinity error for Neumann adapted solver (no scale) %1.14e (it %" PetscInt_FMT ", eigs %1.6e %1.6e)\n", PetscGlobalRank, (double)test_err, k, (double)lambda_min, (double)lambda_max));
      }
    }
    if (needscaling) shell_ctx->scale = 1.0 / lambda_max;

    if (needscaling && pcbddc->dbg_flag) { /* test for scaling factor */
      PC new_pc;

      PetscCall(VecSetRandom(work2, NULL));
      PetscCall(MatMult(local_mat, work2, work1));
      PetscCall(PCCreate(PetscObjectComm((PetscObject)check_ksp), &new_pc));
      PetscCall(PCSetType(new_pc, PCKSP));
      PetscCall(PCSetOperators(new_pc, local_mat, local_pmat));
      PetscCall(PCKSPSetKSP(new_pc, local_ksp));
      PetscCall(KSPSetPC(check_ksp, new_pc));
      PetscCall(PCDestroy(&new_pc));
      PetscCall(KSPSetTolerances(check_ksp, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT, maxit));
      PetscCall(KSPSetPreSolve(check_ksp, NULL, NULL));
      PetscCall(KSPSetPostSolve(check_ksp, NULL, NULL));
      PetscCall(KSPSolve(check_ksp, work1, work1));
      PetscCall(KSPCheckSolve(check_ksp, pc, work1));
      PetscCall(VecAXPY(work1, -1., work2));
      PetscCall(VecNorm(work1, NORM_INFINITY, &test_err));
      PetscCall(KSPComputeExtremeSingularValues(check_ksp, &lambda_max, &lambda_min));
      PetscCall(KSPGetIterationNumber(check_ksp, &k));
      if (pcbddc->dbg_flag) {
        if (isdir) {
          PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "Subdomain %04d infinity error for Dirichlet adapted solver (scale %g) %1.14e (it %" PetscInt_FMT ", eigs %1.6e %1.6e)\n", PetscGlobalRank, (double)PetscRealPart(shell_ctx->scale), (double)test_err, k, (double)lambda_min, (double)lambda_max));
        } else {
          PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "Subdomain %04d infinity error for Neumann adapted solver (scale %g) %1.14e (it %" PetscInt_FMT ", eigs %1.6e %1.6e)\n", PetscGlobalRank, (double)PetscRealPart(shell_ctx->scale), (double)test_err, k, (double)lambda_min, (double)lambda_max));
        }
      }
    }
    PetscCall(KSPDestroy(&check_ksp));
    PetscCall(VecDestroy(&work1));
    PetscCall(VecDestroy(&work2));
  }
  PetscCall(PetscLogEventEnd(PC_BDDC_ApproxSetUp[pcbddc->current_level], pc, 0, 0, 0));

  if (pcbddc->dbg_flag) {
    Vec       work1, work2, work3;
    PetscReal test_err;

    /* check nullspace basis is solved exactly */
    PetscCall(VecDuplicate(shell_ctx->fw[0], &work1));
    PetscCall(VecDuplicate(shell_ctx->fw[0], &work2));
    PetscCall(VecDuplicate(shell_ctx->fw[0], &work3));
    PetscCall(VecSetRandom(shell_ctx->sw[0], NULL));
    PetscCall(MatMult(shell_ctx->basis_mat, shell_ctx->sw[0], work1));
    PetscCall(VecCopy(work1, work2));
    PetscCall(MatMult(local_mat, work1, work3));
    PetscCall(KSPSolve(local_ksp, work3, work1));
    PetscCall(VecAXPY(work1, -1., work2));
    PetscCall(VecNorm(work1, NORM_INFINITY, &test_err));
    if (isdir) {
      PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "Subdomain %04d infinity error for Dirichlet nullspace correction solver: %1.14e\n", PetscGlobalRank, (double)test_err));
    } else {
      PetscCall(PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer, "Subdomain %04d infinity error for Neumann nullspace correction solver: %1.14e\n", PetscGlobalRank, (double)test_err));
    }
    PetscCall(VecDestroy(&work1));
    PetscCall(VecDestroy(&work2));
    PetscCall(VecDestroy(&work3));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}