Date: 2022-03-04T17:39:01+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: {

     13:   KSPSetWorkVecs(ksp,15);
     14:   return(0);
     15: }

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

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

     48:   /* Only supports right preconditioning */
     49:   if (ksp->pc_side != PC_RIGHT) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"KSP pipebcgs does not support %s",PCSides[ksp->pc_side]);
     50:   if (!ksp->guess_zero) {
     51:     if (!bcgs->guess) {
     52:       VecDuplicate(X,&bcgs->guess);
     53:     }
     54:     VecCopy(X,bcgs->guess);
     55:   } else {
     56:     VecSet(X,0.0);
     57:   }

     59:   /* Compute initial residual */
     60:   KSPGetPC(ksp,&pc);
     61:   PCSetUp(pc);
     62:   if (!ksp->guess_zero) {
     63:     KSP_MatMult(ksp,pc->mat,X,Q2);
     64:     VecCopy(B,R);
     65:     VecAXPY(R,-1.0,Q2);
     66:   } else {
     67:     VecCopy(B,R);
     68:   }

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

     83:   /* Initialize */
     84:   VecCopy(R,RP); /* rp <- r */

     86:   VecDotBegin(R,RP,&rho); /* rho <- (r,rp) */
     87:   PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)R));
     88:   KSP_PCApply(ksp,R,R2); /* r2 <- K r */
     89:   KSP_MatMult(ksp,pc->mat,R2,W); /* w <- A r2 */
     90:   VecDotEnd(R,RP,&rho);

     92:   VecDotBegin(W,RP,&d2); /* d2 <- (w,rp) */
     93:   PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)W));
     94:   KSP_PCApply(ksp,W,W2); /* w2 <- K w */
     95:   KSP_MatMult(ksp,pc->mat,W2,T); /* t <- A w2 */
     96:   VecDotEnd(W,RP,&d2);

     98:   alpha = rho/d2;
     99:   beta = 0.0;

    101:   /* Main loop */
    102:   i=0;
    103:   do {
    104:     if (i == 0) {
    105:       VecCopy(R2,P2); /* p2 <- r2 */
    106:       VecCopy(W,S);   /* s  <- w  */
    107:       VecCopy(W2,S2); /* s2 <- w2 */
    108:       VecCopy(T,Z);   /* z  <- t  */
    109:     } else {
    110:       VecAXPBYPCZ(P2,1.0,-beta*omega,beta,R2,S2); /* p2 <- beta * p2 + r2 - beta * omega * s2 */
    111:       VecAXPBYPCZ(S,1.0,-beta*omega,beta,W,Z);    /* s  <- beta * s  + w  - beta * omega * z  */
    112:       VecAXPBYPCZ(S2,1.0,-beta*omega,beta,W2,Z2); /* s2 <- beta * s2 + w2 - beta * omega * z2 */
    113:       VecAXPBYPCZ(Z,1.0,-beta*omega,beta,T,V);    /* z  <- beta * z  + t  - beta * omega * v  */
    114:     }
    115:     VecWAXPY(Q,-alpha,S,R);    /* q  <- r  - alpha s  */
    116:     VecWAXPY(Q2,-alpha,S2,R2); /* q2 <- r2 - alpha s2 */
    117:     VecWAXPY(Y,-alpha,Z,W);    /* y  <- w  - alpha z  */

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

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

    126:     VecDotEnd(Q,Y,&d1);
    127:     VecDotEnd(Y,Y,&d2);

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

    155:     if (ksp->normtype != KSP_NORM_NONE && ksp->chknorm < i+2) {
    156:       VecNormBegin(R,NORM_2,&dp); /* dp <- norm(r) */
    157:     }
    158:     VecDotBegin(R,RP,&rho); /* rho <- (r,rp) */
    159:     VecDotBegin(S,RP,&d1);  /* d1 <- (s,rp) */
    160:     VecDotBegin(W,RP,&d2);  /* d2 <- (w,rp) */
    161:     VecDotBegin(Z,RP,&d3);  /* d3 <- (z,rp) */

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

    167:     if (ksp->normtype != KSP_NORM_NONE && ksp->chknorm < i+2) {
    168:       VecNormEnd(R,NORM_2,&dp);
    169:     }
    170:     VecDotEnd(R,RP,&rho);
    171:     VecDotEnd(S,RP,&d1);
    172:     VecDotEnd(W,RP,&d2);
    173:     VecDotEnd(Z,RP,&d3);

    175:     if (d2 + beta * d1 - beta * omega * d3 == 0.0) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_PLIB,"Divide by zero");

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

    180:     PetscObjectSAWsTakeAccess((PetscObject)ksp);
    181:     ksp->its++;

    183:     /* Residual replacement step  */
    184:     if (i > 0 && i%100 == 0 && i < 1001) {
    185:       KSP_MatMult(ksp,pc->mat,X,R);
    186:       VecAYPX(R,-1.0,B);              /* r  <- b - Ax */
    187:       KSP_PCApply(ksp,R,R2);          /* r2 <- K r */
    188:       KSP_MatMult(ksp,pc->mat,R2,W);  /* w  <- A r2 */
    189:       KSP_PCApply(ksp,W,W2);          /* w2 <- K w */
    190:       KSP_MatMult(ksp,pc->mat,W2,T);  /* t  <- A w2 */
    191:       KSP_MatMult(ksp,pc->mat,P2,S);  /* s  <- A p2 */
    192:       KSP_PCApply(ksp,S,S2);          /* s2 <- K s */
    193:       KSP_MatMult(ksp,pc->mat,S2,Z);  /* z  <- A s2 */
    194:       KSP_PCApply(ksp,Z,Z2);          /* z2 <- K z */
    195:       KSP_MatMult(ksp,pc->mat,Z2,V);  /* v  <- A z2 */
    196:     }

    198:     ksp->rnorm = dp;
    199:     PetscObjectSAWsGrantAccess((PetscObject)ksp);
    200:     KSPLogResidualHistory(ksp,dp);
    201:     KSPMonitor(ksp,i+1,dp);
    202:     (*ksp->converged)(ksp,i+1,dp,&ksp->reason,ksp->cnvP);
    203:     if (ksp->reason) break;
    204:     if (rho == 0.0) {
    205:       ksp->reason = KSP_DIVERGED_BREAKDOWN;
    206:       break;
    207:     }
    208:     i++;
    209:   } while (i<ksp->max_it);

    211:   if (i >= ksp->max_it) ksp->reason = KSP_DIVERGED_ITS;
    212:   return(0);
    213: }

    215: /*MC
    216:     KSPPIPEBCGS - Implements the pipelined BiCGStab method.

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

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

    223:     Options Database Keys:
    224: .see KSPSolve()

    226:     Level: intermediate

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

    233:     Contributed by:
    234:     Siegfried Cools, Universiteit Antwerpen,
    235:     EXA2CT European Project on EXascale Algorithms and Advanced Computational Techniques, 2016.

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

    242: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPBICG, KSPFBCGS, KSPFBCGSL, KSPSetPCSide()
    243: M*/
    244: PETSC_EXTERN PetscErrorCode KSPCreate_PIPEBCGS(KSP ksp)
    245: {
    247:   KSP_BCGS       *bcgs;

    250:   PetscNewLog(ksp,&bcgs);

    252:   ksp->data                = bcgs;
    253:   ksp->ops->setup          = KSPSetUp_PIPEBCGS;
    254:   ksp->ops->solve          = KSPSolve_PIPEBCGS;
    255:   ksp->ops->destroy        = KSPDestroy_BCGS;
    256:   ksp->ops->reset          = KSPReset_BCGS;
    257:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
    258:   ksp->ops->setfromoptions = KSPSetFromOptions_BCGS;

    260:   KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,2);
    261:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_RIGHT,1);
    262:   return(0);
    263: }