Date: 2022-08-02T03:14:39+00:00

Actual source code: pipebcgs.c

      2: /*
      3:     This file implements pipelined BiCGStab (pipe-BiCGStab).
      4:     Only allow right preconditioning.
      5: */
      6: #include <../src/ksp/ksp/impls/bcgs/bcgsimpl.h>

      8: static PetscErrorCode KSPSetUp_PIPEBCGS(KSP ksp)
      9: {
     10:   KSPSetWorkVecs(ksp,15);
     11:   return 0;
     12: }

     14: /* Only need a few hacks from KSPSolve_BCGS */
     15: #include <petsc/private/pcimpl.h>
     16: static PetscErrorCode  KSPSolve_PIPEBCGS(KSP ksp)
     17: {
     18:   PetscInt       i;
     19:   PetscScalar    rho,rhoold,alpha,beta,omega=0.0,d1,d2,d3;
     20:   Vec            X,B,S,R,RP,Y,Q,P2,Q2,R2,S2,W,Z,W2,Z2,T,V;
     21:   PetscReal      dp    = 0.0;
     22:   KSP_BCGS       *bcgs = (KSP_BCGS*)ksp->data;
     23:   PC             pc;

     25:   X  = ksp->vec_sol;
     26:   B  = ksp->vec_rhs;
     27:   R  = ksp->work[0];
     28:   RP = ksp->work[1];
     29:   S  = ksp->work[2];
     30:   Y  = ksp->work[3];
     31:   Q  = ksp->work[4];
     32:   Q2 = ksp->work[5];
     33:   P2 = ksp->work[6];
     34:   R2 = ksp->work[7];
     35:   S2 = ksp->work[8];
     36:   W  = ksp->work[9];
     37:   Z  = ksp->work[10];
     38:   W2 = ksp->work[11];
     39:   Z2 = ksp->work[12];
     40:   T  = ksp->work[13];
     41:   V  = ksp->work[14];

     43:   /* Only supports right preconditioning */
     45:   if (!ksp->guess_zero) {
     46:     if (!bcgs->guess) {
     47:       VecDuplicate(X,&bcgs->guess);
     48:     }
     49:     VecCopy(X,bcgs->guess);
     50:   } else {
     51:     VecSet(X,0.0);
     52:   }

     54:   /* Compute initial residual */
     55:   KSPGetPC(ksp,&pc);
     56:   PCSetUp(pc);
     57:   if (!ksp->guess_zero) {
     58:     KSP_MatMult(ksp,pc->mat,X,Q2);
     59:     VecCopy(B,R);
     60:     VecAXPY(R,-1.0,Q2);
     61:   } else {
     62:     VecCopy(B,R);
     63:   }

     65:   /* Test for nothing to do */
     66:   if (ksp->normtype != KSP_NORM_NONE) {
     67:     VecNorm(R,NORM_2,&dp);
     68:   } else dp = 0.0;
     69:   PetscObjectSAWsTakeAccess((PetscObject)ksp);
     70:   ksp->its   = 0;
     71:   ksp->rnorm = dp;
     72:   PetscObjectSAWsGrantAccess((PetscObject)ksp);
     73:   KSPLogResidualHistory(ksp,dp);
     74:   KSPMonitor(ksp,0,dp);
     75:   (*ksp->converged)(ksp,0,dp,&ksp->reason,ksp->cnvP);
     76:   if (ksp->reason) return 0;

     78:   /* Initialize */
     79:   VecCopy(R,RP); /* rp <- r */

     81:   VecDotBegin(R,RP,&rho); /* rho <- (r,rp) */
     82:   PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)R));
     83:   KSP_PCApply(ksp,R,R2); /* r2 <- K r */
     84:   KSP_MatMult(ksp,pc->mat,R2,W); /* w <- A r2 */
     85:   VecDotEnd(R,RP,&rho);

     87:   VecDotBegin(W,RP,&d2); /* d2 <- (w,rp) */
     88:   PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)W));
     89:   KSP_PCApply(ksp,W,W2); /* w2 <- K w */
     90:   KSP_MatMult(ksp,pc->mat,W2,T); /* t <- A w2 */
     91:   VecDotEnd(W,RP,&d2);

     93:   alpha = rho/d2;
     94:   beta = 0.0;

     96:   /* Main loop */
     97:   i=0;
     98:   do {
     99:     if (i == 0) {
    100:       VecCopy(R2,P2); /* p2 <- r2 */
    101:       VecCopy(W,S);   /* s  <- w  */
    102:       VecCopy(W2,S2); /* s2 <- w2 */
    103:       VecCopy(T,Z);   /* z  <- t  */
    104:     } else {
    105:       VecAXPBYPCZ(P2,1.0,-beta*omega,beta,R2,S2); /* p2 <- beta * p2 + r2 - beta * omega * s2 */
    106:       VecAXPBYPCZ(S,1.0,-beta*omega,beta,W,Z);    /* s  <- beta * s  + w  - beta * omega * z  */
    107:       VecAXPBYPCZ(S2,1.0,-beta*omega,beta,W2,Z2); /* s2 <- beta * s2 + w2 - beta * omega * z2 */
    108:       VecAXPBYPCZ(Z,1.0,-beta*omega,beta,T,V);    /* z  <- beta * z  + t  - beta * omega * v  */
    109:     }
    110:     VecWAXPY(Q,-alpha,S,R);    /* q  <- r  - alpha s  */
    111:     VecWAXPY(Q2,-alpha,S2,R2); /* q2 <- r2 - alpha s2 */
    112:     VecWAXPY(Y,-alpha,Z,W);    /* y  <- w  - alpha z  */

    114:     VecDotBegin(Q,Y,&d1); /* d1 <- (q,y) */
    115:     VecDotBegin(Y,Y,&d2); /* d2 <- (y,y) */

    117:     PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)Q));
    118:     KSP_PCApply(ksp,Z,Z2); /* z2 <- K z */
    119:     KSP_MatMult(ksp,pc->mat,Z2,V); /* v <- A z2 */

    121:     VecDotEnd(Q,Y,&d1);
    122:     VecDotEnd(Y,Y,&d2);

    124:     if (d2 == 0.0) {
    125:       /* y is 0. if q is 0, then alpha s == r, and hence alpha p may be our solution. Give it a try? */
    126:       VecDot(Q,Q,&d1);
    127:       if (d1 != 0.0) {
    128:         ksp->reason = KSP_DIVERGED_BREAKDOWN;
    129:         break;
    130:       }
    131:       VecAXPY(X,alpha,P2);   /* x <- x + alpha p2 */
    132:       PetscObjectSAWsTakeAccess((PetscObject)ksp);
    133:       ksp->its++;
    134:       ksp->rnorm  = 0.0;
    135:       ksp->reason = KSP_CONVERGED_RTOL;
    136:       PetscObjectSAWsGrantAccess((PetscObject)ksp);
    137:       KSPLogResidualHistory(ksp,dp);
    138:       KSPMonitor(ksp,i+1,0.0);
    139:       break;
    140:     }
    141:     omega = d1/d2; /* omega <- (y'q) / (y'y) */
    142:     VecAXPBYPCZ(X,alpha,omega,1.0,P2,Q2); /* x <- alpha * p2 + omega * q2 + x */
    143:     VecWAXPY(R,-omega,Y,Q);    /* r <- q - omega y */
    144:     VecWAXPY(R2,-alpha,Z2,W2); /* r2 <- w2 - alpha z2 */
    145:     VecAYPX(R2,-omega,Q2);     /* r2 <- q2 - omega r2 */
    146:     VecWAXPY(W,-alpha,V,T);    /* w <- t - alpha v */
    147:     VecAYPX(W,-omega,Y);       /* w <- y - omega w */
    148:     rhoold = rho;

    150:     if (ksp->normtype != KSP_NORM_NONE && ksp->chknorm < i+2) {
    151:       VecNormBegin(R,NORM_2,&dp); /* dp <- norm(r) */
    152:     }
    153:     VecDotBegin(R,RP,&rho); /* rho <- (r,rp) */
    154:     VecDotBegin(S,RP,&d1);  /* d1 <- (s,rp) */
    155:     VecDotBegin(W,RP,&d2);  /* d2 <- (w,rp) */
    156:     VecDotBegin(Z,RP,&d3);  /* d3 <- (z,rp) */

    158:     PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)R));
    159:     KSP_PCApply(ksp,W,W2); /* w2 <- K w */
    160:     KSP_MatMult(ksp,pc->mat,W2,T); /* t <- A w2 */

    162:     if (ksp->normtype != KSP_NORM_NONE && ksp->chknorm < i+2) {
    163:       VecNormEnd(R,NORM_2,&dp);
    164:     }
    165:     VecDotEnd(R,RP,&rho);
    166:     VecDotEnd(S,RP,&d1);
    167:     VecDotEnd(W,RP,&d2);
    168:     VecDotEnd(Z,RP,&d3);

    172:     beta = (rho/rhoold) * (alpha/omega);
    173:     alpha = rho/(d2 + beta * d1 - beta * omega * d3); /* alpha <- rho / (d2 + beta * d1 - beta * omega * d3) */

    175:     PetscObjectSAWsTakeAccess((PetscObject)ksp);
    176:     ksp->its++;

    178:     /* Residual replacement step  */
    179:     if (i > 0 && i%100 == 0 && i < 1001) {
    180:       KSP_MatMult(ksp,pc->mat,X,R);
    181:       VecAYPX(R,-1.0,B);              /* r  <- b - Ax */
    182:       KSP_PCApply(ksp,R,R2);          /* r2 <- K r */
    183:       KSP_MatMult(ksp,pc->mat,R2,W);  /* w  <- A r2 */
    184:       KSP_PCApply(ksp,W,W2);          /* w2 <- K w */
    185:       KSP_MatMult(ksp,pc->mat,W2,T);  /* t  <- A w2 */
    186:       KSP_MatMult(ksp,pc->mat,P2,S);  /* s  <- A p2 */
    187:       KSP_PCApply(ksp,S,S2);          /* s2 <- K s */
    188:       KSP_MatMult(ksp,pc->mat,S2,Z);  /* z  <- A s2 */
    189:       KSP_PCApply(ksp,Z,Z2);          /* z2 <- K z */
    190:       KSP_MatMult(ksp,pc->mat,Z2,V);  /* v  <- A z2 */
    191:     }

    193:     ksp->rnorm = dp;
    194:     PetscObjectSAWsGrantAccess((PetscObject)ksp);
    195:     KSPLogResidualHistory(ksp,dp);
    196:     KSPMonitor(ksp,i+1,dp);
    197:     (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
    198:     if (ksp->reason) break;
    199:     if (rho == 0.0) {
    200:       ksp->reason = KSP_DIVERGED_BREAKDOWN;
    201:       break;
    202:     }
    203:     i++;
    204:   } while (i<ksp->max_it);

    206:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
    207:   return 0;
    208: }

    210: /*MC
    211:     KSPPIPEBCGS - Implements the pipelined BiCGStab method.

    213:     This method has only two non-blocking reductions per iteration, compared to 3 blocking for standard FBCGS.  The
    214:     non-blocking reductions are overlapped by matrix-vector products and preconditioner applications.

    216:     Periodic residual replacement may be used to increase robustness and maximal attainable accuracy.

    218:     Options Database Keys:
    219:     see KSPSolve()

    221:     Level: intermediate

    223:     Notes:
    224:     Like KSPFBCGS, the KSPPIPEBCGS implementation only allows for right preconditioning.
    225:     MPI configuration may be necessary for reductions to make asynchronous progress, which is important for
    226:     performance of pipelined methods. See the FAQ on the PETSc website for details.

    228:     Contributed by:
    229:     Siegfried Cools, Universiteit Antwerpen,
    230:     EXA2CT European Project on EXascale Algorithms and Advanced Computational Techniques, 2016.

    232:     Reference:
    233:     S. Cools and W. Vanroose,
    234:     "The communication-hiding pipelined BiCGStab method for the parallel solution of large unsymmetric linear systems",
    235:     Parallel Computing, 65:1-20, 2017.

    237: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPBICG, KSPFBCGS, KSPFBCGSL, KSPSetPCSide()
    238: M*/
    239: PETSC_EXTERN PetscErrorCode KSPCreate_PIPEBCGS(KSP ksp)
    240: {
    241:   KSP_BCGS       *bcgs;

    243:   PetscNewLog(ksp,&bcgs);

    245:   ksp->data                = bcgs;
    246:   ksp->ops->setup          = KSPSetUp_PIPEBCGS;
    247:   ksp->ops->solve          = KSPSolve_PIPEBCGS;
    248:   ksp->ops->destroy        = KSPDestroy_BCGS;
    249:   ksp->ops->reset          = KSPReset_BCGS;
    250:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
    251:   ksp->ops->setfromoptions = KSPSetFromOptions_BCGS;

    253:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,2);
    254:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_RIGHT,1);
    255:   return 0;
    256: }