Actual source code: fbcgs.c

      1: /*
      2:     This file implements flexible BiCGStab (FBiCGStab).
      3: */
      4: #include <../src/ksp/ksp/impls/bcgs/bcgsimpl.h>

      6: static PetscErrorCode KSPSetUp_FBCGS(KSP ksp)
      7: {
      8:   PetscFunctionBegin;
      9:   PetscCall(KSPSetWorkVecs(ksp, 8));
     10:   PetscFunctionReturn(PETSC_SUCCESS);
     11: }

     13: /* Only need a few hacks from KSPSolve_BCGS */

     15: static PetscErrorCode KSPSolve_FBCGS(KSP ksp)
     16: {
     17:   PetscInt    i;
     18:   PetscScalar rho, rhoold, alpha, beta, omega, omegaold, d1;
     19:   Vec         X, B, V, P, R, RP, T, S, P2, S2;
     20:   PetscReal   dp   = 0.0, d2;
     21:   KSP_BCGS   *bcgs = (KSP_BCGS *)ksp->data;
     22:   PC          pc;
     23:   Mat         mat;

     25:   PetscFunctionBegin;
     26:   X  = ksp->vec_sol;
     27:   B  = ksp->vec_rhs;
     28:   R  = ksp->work[0];
     29:   RP = ksp->work[1];
     30:   V  = ksp->work[2];
     31:   T  = ksp->work[3];
     32:   S  = ksp->work[4];
     33:   P  = ksp->work[5];
     34:   S2 = ksp->work[6];
     35:   P2 = ksp->work[7];

     37:   if (!ksp->guess_zero) {
     38:     if (!bcgs->guess) PetscCall(VecDuplicate(X, &bcgs->guess));
     39:     PetscCall(VecCopy(X, bcgs->guess));
     40:   } else {
     41:     PetscCall(VecSet(X, 0.0));
     42:   }

     44:   /* Compute initial residual */
     45:   PetscCall(KSPGetPC(ksp, &pc));
     46:   PetscCall(PCGetOperators(pc, &mat, NULL));
     47:   if (!ksp->guess_zero) {
     48:     PetscCall(KSP_MatMult(ksp, mat, X, S2));
     49:     PetscCall(VecCopy(B, R));
     50:     PetscCall(VecAXPY(R, -1.0, S2));
     51:   } else {
     52:     PetscCall(VecCopy(B, R));
     53:   }

     55:   /* Test for nothing to do */
     56:   if (ksp->normtype != KSP_NORM_NONE) PetscCall(VecNorm(R, NORM_2, &dp));
     57:   PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
     58:   ksp->its   = 0;
     59:   ksp->rnorm = dp;
     60:   PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
     61:   PetscCall(KSPLogResidualHistory(ksp, dp));
     62:   PetscCall(KSPMonitor(ksp, 0, dp));
     63:   PetscCall((*ksp->converged)(ksp, 0, dp, &ksp->reason, ksp->cnvP));
     64:   if (ksp->reason) PetscFunctionReturn(PETSC_SUCCESS);

     66:   /* Make the initial Rp == R */
     67:   PetscCall(VecCopy(R, RP));

     69:   rhoold   = 1.0;
     70:   alpha    = 1.0;
     71:   omegaold = 1.0;
     72:   PetscCall(VecSet(P, 0.0));
     73:   PetscCall(VecSet(V, 0.0));

     75:   i = 0;
     76:   do {
     77:     PetscCall(VecDot(R, RP, &rho)); /* rho <- (r,rp) */
     78:     beta = (rho / rhoold) * (alpha / omegaold);
     79:     PetscCall(VecAXPBYPCZ(P, 1.0, -omegaold * beta, beta, R, V)); /* p <- r - omega * beta* v + beta * p */

     81:     PetscCall(KSP_PCApply(ksp, P, P2));      /* p2 <- K p */
     82:     PetscCall(KSP_MatMult(ksp, mat, P2, V)); /* v <- A p2 */

     84:     PetscCall(VecDot(V, RP, &d1));
     85:     if (d1 == 0.0) {
     86:       PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "KSPSolve breakdown due to zero inner product");
     87:       ksp->reason = KSP_DIVERGED_BREAKDOWN;
     88:       PetscCall(PetscInfo(ksp, "Breakdown due to zero inner product\n"));
     89:       break;
     90:     }
     91:     alpha = rho / d1;                     /* alpha <- rho / (v,rp) */
     92:     PetscCall(VecWAXPY(S, -alpha, V, R)); /* s <- r - alpha v */

     94:     PetscCall(KSP_PCApply(ksp, S, S2));      /* s2 <- K s */
     95:     PetscCall(KSP_MatMult(ksp, mat, S2, T)); /* t <- A s2 */

     97:     PetscCall(VecDotNorm2(S, T, &d1, &d2));
     98:     if (d2 == 0.0) {
     99:       /* t is 0. if s is 0, then alpha v == r, and hence alpha p may be our solution. Give it a try? */
    100:       PetscCall(VecDot(S, S, &d1));
    101:       if (d1 != 0.0) {
    102:         PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "KSPSolve has failed due to singular preconditioned operator");
    103:         ksp->reason = KSP_DIVERGED_BREAKDOWN;
    104:         PetscCall(PetscInfo(ksp, "Failed due to singular preconditioned operator\n"));
    105:         break;
    106:       }
    107:       PetscCall(VecAXPY(X, alpha, P2)); /* x <- x + alpha p2 */
    108:       PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
    109:       ksp->its++;
    110:       ksp->rnorm  = 0.0;
    111:       ksp->reason = KSP_CONVERGED_RTOL;
    112:       PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
    113:       PetscCall(KSPLogResidualHistory(ksp, dp));
    114:       PetscCall(KSPMonitor(ksp, i + 1, 0.0));
    115:       break;
    116:     }
    117:     omega = d1 / d2;                                      /* omega <- (t's) / (t't) */
    118:     PetscCall(VecAXPBYPCZ(X, alpha, omega, 1.0, P2, S2)); /* x <- alpha * p2 + omega * s2 + x */

    120:     PetscCall(VecWAXPY(R, -omega, T, S)); /* r <- s - omega t */
    121:     if (ksp->normtype != KSP_NORM_NONE && ksp->chknorm < i + 2) PetscCall(VecNorm(R, NORM_2, &dp));

    123:     rhoold   = rho;
    124:     omegaold = omega;

    126:     PetscCall(PetscObjectSAWsTakeAccess((PetscObject)ksp));
    127:     ksp->its++;
    128:     ksp->rnorm = dp;
    129:     PetscCall(PetscObjectSAWsGrantAccess((PetscObject)ksp));
    130:     PetscCall(KSPLogResidualHistory(ksp, dp));
    131:     PetscCall(KSPMonitor(ksp, i + 1, dp));
    132:     PetscCall((*ksp->converged)(ksp, i + 1, dp, &ksp->reason, ksp->cnvP));
    133:     if (ksp->reason) break;
    134:     if (rho == 0.0) {
    135:       PetscCheck(!ksp->errorifnotconverged, PetscObjectComm((PetscObject)ksp), PETSC_ERR_NOT_CONVERGED, "KSPSolve breakdown due to zero rho inner product");
    136:       ksp->reason = KSP_DIVERGED_BREAKDOWN;
    137:       PetscCall(PetscInfo(ksp, "Breakdown due to zero rho inner product\n"));
    138:       break;
    139:     }
    140:     i++;
    141:   } while (i < ksp->max_it);

    143:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
    144:   PetscFunctionReturn(PETSC_SUCCESS);
    145: }

    147: /*MC
    148:    KSPFBCGS - Implements the flexible BiCGStab method. [](sec_flexibleksp)

    150:    Level: beginner

    152:    Notes:
    153:    Flexible BiCGStab, unlike most Krylov methods, allows the preconditioner to be nonlinear, that is the action of the preconditioner to a vector need not be linear
    154:    in the vector entries.

    156:    `KSPFBCGSR` provides another variant of this algorithm that requires fewer `MPI_Allreduce()` calls and my converge faster

    158:    See `KSPPIPEBCGS` for a pipelined version of the algorithm

    160:    Only supportst right preconditioning

    162: .seealso: [](ch_ksp),  [](sec_flexibleksp), `KSPFBCGSR`, `KSPPIPEBCGS`, `KSPBCGSL`, `KSPFBCGS`, `KSPCreate()`, `KSPFGMRES`, `KSPSetType()`, `KSPType`, `KSP`, `KSPBICG`, `KSPSetPCSide()`
    163: M*/
    164: PETSC_EXTERN PetscErrorCode KSPCreate_FBCGS(KSP ksp)
    165: {
    166:   KSP_BCGS *bcgs;

    168:   PetscFunctionBegin;
    169:   PetscCall(PetscNew(&bcgs));

    171:   ksp->data                = bcgs;
    172:   ksp->ops->setup          = KSPSetUp_FBCGS;
    173:   ksp->ops->solve          = KSPSolve_FBCGS;
    174:   ksp->ops->destroy        = KSPDestroy_BCGS;
    175:   ksp->ops->reset          = KSPReset_BCGS;
    176:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
    177:   ksp->ops->setfromoptions = KSPSetFromOptions_BCGS;
    178:   ksp->pc_side             = PC_RIGHT;

    180:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_RIGHT, 2));
    181:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_RIGHT, 1));
    182:   PetscFunctionReturn(PETSC_SUCCESS);
    183: }