Date: 2026-03-31T05:46:13+00:00

Actual source code: rich.c

      1: /*
      2:             This implements Richardson Iteration.
      3: */
      4: #include <../src/ksp/ksp/impls/rich/richardsonimpl.h>

      6: static PetscErrorCode KSPSetUp_Richardson(KSP ksp)
      7: {
      8:   KSP_Richardson *richardsonP = (KSP_Richardson *)ksp->data;

     10:   PetscFunctionBegin;
     11:   if (richardsonP->selfscale) {
     12:     PetscCall(KSPSetWorkVecs(ksp, 4));
     13:   } else {
     14:     PetscCall(KSPSetWorkVecs(ksp, 2));
     15:   }
     16:   PetscFunctionReturn(PETSC_SUCCESS);
     17: }

     19: static PetscErrorCode KSPSolve_Richardson(KSP ksp)
     20: {
     21:   PetscInt        i, maxit;
     22:   PetscReal       rnorm = 0.0, abr;
     23:   PetscScalar     scale, rdot;
     24:   Vec             x, b, r, z, w = NULL, y = NULL;
     25:   PetscInt        xs, ws;
     26:   Mat             Amat, Pmat;
     27:   KSP_Richardson *richardsonP = (KSP_Richardson *)ksp->data;
     28:   PetscBool       exists, diagonalscale;
     29:   MatNullSpace    nullsp;

     31:   PetscFunctionBegin;
     32:   PetscCall(PCGetDiagonalScale(ksp->pc, &diagonalscale));
     33:   PetscCheck(!diagonalscale, PetscObjectComm((PetscObject)ksp), PETSC_ERR_SUP, "Krylov method %s does not support diagonal scaling", ((PetscObject)ksp)->type_name);

     35:   ksp->its = 0;

     37:   PetscCall(PCGetOperators(ksp->pc, &Amat, &Pmat));
     38:   x = ksp->vec_sol;
     39:   b = ksp->vec_rhs;
     40:   PetscCall(VecGetSize(x, &xs));
     41:   PetscCall(VecGetSize(ksp->work[0], &ws));
     42:   if (xs != ws) {
     43:     if (richardsonP->selfscale) {
     44:       PetscCall(KSPSetWorkVecs(ksp, 4));
     45:     } else {
     46:       PetscCall(KSPSetWorkVecs(ksp, 2));
     47:     }
     48:   }
     49:   r = ksp->work[0];
     50:   z = ksp->work[1];
     51:   if (richardsonP->selfscale) {
     52:     w = ksp->work[2];
     53:     y = ksp->work[3];
     54:   }
     55:   maxit = ksp->max_it;

     57:   /* if user has provided fast Richardson code use that */
     58:   PetscCall(PCApplyRichardsonExists(ksp->pc, &exists));
     59:   PetscCall(MatGetNullSpace(Pmat, &nullsp));
     60:   if (exists && maxit > 0 && richardsonP->scale == 1.0 && (ksp->converged == KSPConvergedDefault || ksp->converged == KSPConvergedSkip) && !ksp->numbermonitors && !ksp->transpose_solve && !nullsp) {
     61:     PCRichardsonConvergedReason reason;
     62:     PetscCall(PCApplyRichardson(ksp->pc, b, x, r, ksp->rtol, ksp->abstol, ksp->divtol, maxit, ksp->guess_zero, &ksp->its, &reason));
     63:     ksp->reason = (KSPConvergedReason)reason;
     64:     PetscFunctionReturn(PETSC_SUCCESS);
     65:   }

     67:   if (!ksp->guess_zero) { /*   r <- b - A x     */
     68:     PetscCall(KSP_MatMult(ksp, Amat, x, r));
     69:     PetscCall(VecAYPX(r, -1.0, b));
     70:   } else {
     71:     PetscCall(VecCopy(b, r));
     72:   }

     74:   ksp->its = 0;
     75:   if (richardsonP->selfscale) {
     76:     PetscCall(KSP_PCApply(ksp, r, z)); /*   z <- B r          */
     77:     for (i = 0; i < maxit; i++) {
     78:       if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
     79:         PetscCall(VecNorm(r, NORM_2, &rnorm)); /*   rnorm <- r'*r     */
     80:       } else if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
     81:         PetscCall(VecNorm(z, NORM_2, &rnorm)); /*   rnorm <- z'*z     */
     82:       } else rnorm = 0.0;

     84:       KSPCheckNorm(ksp, rnorm);
     85:       ksp->rnorm = rnorm;
     86:       PetscCall(KSPMonitor(ksp, i, rnorm));
     87:       PetscCall(KSPLogResidualHistory(ksp, rnorm));
     88:       PetscCall((*ksp->converged)(ksp, i, rnorm, &ksp->reason, ksp->cnvP));
     89:       if (ksp->reason) break;
     90:       PetscCall(KSP_PCApplyBAorAB(ksp, z, y, w)); /* y = BAz = BABr */
     91:       PetscCall(VecDotNorm2(z, y, &rdot, &abr));  /*   rdot = (Br)^T(BABR); abr = (BABr)^T (BABr) */
     92:       scale = rdot / abr;
     93:       PetscCall(PetscInfo(ksp, "Self-scale factor %g\n", (double)PetscRealPart(scale)));
     94:       PetscCall(VecAXPY(x, scale, z));  /*   x  <- x + scale z */
     95:       PetscCall(VecAXPY(r, -scale, w)); /*  r <- r - scale*Az */
     96:       PetscCall(VecAXPY(z, -scale, y)); /*  z <- z - scale*y */
     97:       ksp->its++;
     98:     }
     99:   } else {
    100:     for (i = 0; i < maxit; i++) {
    101:       if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
    102:         PetscCall(VecNorm(r, NORM_2, &rnorm)); /*   rnorm <- r'*r     */
    103:       } else if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
    104:         PetscCall(KSP_PCApply(ksp, r, z));     /*   z <- B r          */
    105:         PetscCall(VecNorm(z, NORM_2, &rnorm)); /*   rnorm <- z'*z     */
    106:       } else rnorm = 0.0;
    107:       ksp->rnorm = rnorm;
    108:       PetscCall(KSPMonitor(ksp, i, rnorm));
    109:       PetscCall(KSPLogResidualHistory(ksp, rnorm));
    110:       PetscCall((*ksp->converged)(ksp, i, rnorm, &ksp->reason, ksp->cnvP));
    111:       if (ksp->reason) break;
    112:       if (ksp->normtype != KSP_NORM_PRECONDITIONED) PetscCall(KSP_PCApply(ksp, r, z)); /*   z <- B r          */

    114:       PetscCall(VecAXPY(x, richardsonP->scale, z)); /*   x  <- x + scale z */
    115:       ksp->its++;

    117:       if (i + 1 < maxit || ksp->normtype != KSP_NORM_NONE) {
    118:         PetscCall(KSP_MatMult(ksp, Amat, x, r)); /*   r  <- b - Ax      */
    119:         PetscCall(VecAYPX(r, -1.0, b));
    120:       }
    121:     }
    122:   }
    123:   if (!ksp->reason) {
    124:     if (ksp->normtype == KSP_NORM_UNPRECONDITIONED) {
    125:       PetscCall(VecNorm(r, NORM_2, &rnorm)); /*   rnorm <- r'*r     */
    126:     } else if (ksp->normtype == KSP_NORM_PRECONDITIONED) {
    127:       PetscCall(KSP_PCApply(ksp, r, z));     /*   z <- B r          */
    128:       PetscCall(VecNorm(z, NORM_2, &rnorm)); /*   rnorm <- z'*z     */
    129:     } else rnorm = 0.0;

    131:     KSPCheckNorm(ksp, rnorm);
    132:     ksp->rnorm = rnorm;
    133:     PetscCall(KSPLogResidualHistory(ksp, rnorm));
    134:     PetscCall(KSPMonitor(ksp, i, rnorm));
    135:     if (ksp->its >= ksp->max_it) {
    136:       if (ksp->normtype != KSP_NORM_NONE) {
    137:         PetscCall((*ksp->converged)(ksp, i, rnorm, &ksp->reason, ksp->cnvP));
    138:         if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
    139:       } else {
    140:         ksp->reason = KSP_CONVERGED_ITS;
    141:       }
    142:     }
    143:   }
    144:   PetscFunctionReturn(PETSC_SUCCESS);
    145: }

    147: static PetscErrorCode KSPView_Richardson(KSP ksp, PetscViewer viewer)
    148: {
    149:   KSP_Richardson *richardsonP = (KSP_Richardson *)ksp->data;
    150:   PetscBool       isascii;

    152:   PetscFunctionBegin;
    153:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
    154:   if (isascii) {
    155:     if (richardsonP->selfscale) {
    156:       PetscCall(PetscViewerASCIIPrintf(viewer, "  using self-scale best computed damping factor\n"));
    157:     } else {
    158:       PetscCall(PetscViewerASCIIPrintf(viewer, "  damping factor=%g\n", (double)richardsonP->scale));
    159:     }
    160:   }
    161:   PetscFunctionReturn(PETSC_SUCCESS);
    162: }

    164: static PetscErrorCode KSPSetFromOptions_Richardson(KSP ksp, PetscOptionItems PetscOptionsObject)
    165: {
    166:   KSP_Richardson *rich = (KSP_Richardson *)ksp->data;
    167:   PetscReal       tmp;
    168:   PetscBool       flg, flg2;

    170:   PetscFunctionBegin;
    171:   PetscOptionsHeadBegin(PetscOptionsObject, "KSP Richardson Options");
    172:   PetscCall(PetscOptionsReal("-ksp_richardson_scale", "damping factor", "KSPRichardsonSetScale", rich->scale, &tmp, &flg));
    173:   if (flg) PetscCall(KSPRichardsonSetScale(ksp, tmp));
    174:   PetscCall(PetscOptionsBool("-ksp_richardson_self_scale", "dynamically determine optimal damping factor", "KSPRichardsonSetSelfScale", rich->selfscale, &flg2, &flg));
    175:   if (flg) PetscCall(KSPRichardsonSetSelfScale(ksp, flg2));
    176:   PetscOptionsHeadEnd();
    177:   PetscFunctionReturn(PETSC_SUCCESS);
    178: }

    180: static PetscErrorCode KSPDestroy_Richardson(KSP ksp)
    181: {
    182:   PetscFunctionBegin;
    183:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPRichardsonSetScale_C", NULL));
    184:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPRichardsonSetSelfScale_C", NULL));
    185:   PetscCall(KSPDestroyDefault(ksp));
    186:   PetscFunctionReturn(PETSC_SUCCESS);
    187: }

    189: static PetscErrorCode KSPRichardsonSetScale_Richardson(KSP ksp, PetscReal scale)
    190: {
    191:   KSP_Richardson *richardsonP;

    193:   PetscFunctionBegin;
    194:   richardsonP        = (KSP_Richardson *)ksp->data;
    195:   richardsonP->scale = scale;
    196:   PetscFunctionReturn(PETSC_SUCCESS);
    197: }

    199: static PetscErrorCode KSPRichardsonSetSelfScale_Richardson(KSP ksp, PetscBool selfscale)
    200: {
    201:   KSP_Richardson *richardsonP;

    203:   PetscFunctionBegin;
    204:   richardsonP            = (KSP_Richardson *)ksp->data;
    205:   richardsonP->selfscale = selfscale;
    206:   PetscFunctionReturn(PETSC_SUCCESS);
    207: }

    209: static PetscErrorCode KSPBuildResidual_Richardson(KSP ksp, Vec t, Vec v, Vec *V)
    210: {
    211:   PetscFunctionBegin;
    212:   if (ksp->normtype == KSP_NORM_NONE) {
    213:     PetscCall(KSPBuildResidualDefault(ksp, t, v, V));
    214:   } else {
    215:     PetscCall(VecCopy(ksp->work[0], v));
    216:     *V = v;
    217:   }
    218:   PetscFunctionReturn(PETSC_SUCCESS);
    219: }

    221: /*MC
    222:     KSPRICHARDSON - The preconditioned Richardson iterative method {cite}`richarson1911`

    224:    Options Database Key:
    225: .   -ksp_richardson_scale - damping factor on the correction (defaults to 1.0)

    227:    Level: beginner

    229:    Notes:
    230:    $ x^{n+1} = x^{n} + scale*B(b - A x^{n})$

    232:    Here B is the application of the preconditioner

    234:    This method often (usually) will not converge unless scale is very small.

    236:    For some preconditioners, currently `PCSOR`, the convergence test is skipped to improve speed,
    237:    thus it always iterates the maximum number of iterations you've selected. When -ksp_monitor
    238:    (or any other monitor) is turned on, the norm is computed at each iteration and so the convergence test is run unless
    239:    you specifically call `KSPSetNormType`(ksp,`KSP_NORM_NONE`);

    241:    For some preconditioners, currently `PCMG` and `PCHYPRE` with BoomerAMG if -ksp_monitor (and also
    242:    any other monitor) is not turned on then the convergence test is done by the preconditioner itself and
    243:    so the solver may run more or fewer iterations then if -ksp_monitor is selected.

    245:    Supports only left preconditioning

    247:    If using direct solvers such as `PCLU` and `PCCHOLESKY` one generally uses `KSPPREONLY` instead of this which uses exactly one iteration

    249:    `-ksp_type richardson -pc_type jacobi` gives one classical Jacobi preconditioning

    251: .seealso: [](ch_ksp), `KSPCreate()`, `KSPSetType()`, `KSPType`, `KSP`,
    252:           `KSPRichardsonSetScale()`, `KSPPREONLY`, `KSPRichardsonSetSelfScale()`
    253: M*/

    255: PETSC_EXTERN PetscErrorCode KSPCreate_Richardson(KSP ksp)
    256: {
    257:   KSP_Richardson *richardsonP;

    259:   PetscFunctionBegin;
    260:   PetscCall(PetscNew(&richardsonP));
    261:   ksp->data = (void *)richardsonP;

    263:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_PRECONDITIONED, PC_LEFT, 3));
    264:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_UNPRECONDITIONED, PC_LEFT, 2));
    265:   PetscCall(KSPSetSupportedNorm(ksp, KSP_NORM_NONE, PC_LEFT, 1));

    267:   ksp->ops->setup          = KSPSetUp_Richardson;
    268:   ksp->ops->solve          = KSPSolve_Richardson;
    269:   ksp->ops->destroy        = KSPDestroy_Richardson;
    270:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    271:   ksp->ops->buildresidual  = KSPBuildResidual_Richardson;
    272:   ksp->ops->view           = KSPView_Richardson;
    273:   ksp->ops->setfromoptions = KSPSetFromOptions_Richardson;

    275:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPRichardsonSetScale_C", KSPRichardsonSetScale_Richardson));
    276:   PetscCall(PetscObjectComposeFunction((PetscObject)ksp, "KSPRichardsonSetSelfScale_C", KSPRichardsonSetSelfScale_Richardson));

    278:   richardsonP->scale = 1.0;
    279:   PetscFunctionReturn(PETSC_SUCCESS);
    280: }