Date: 2022-08-02T03:14:42+00:00

Actual source code: lcd.c

      2: #include <../src/ksp/ksp/impls/lcd/lcdimpl.h>

      4: PetscErrorCode KSPSetUp_LCD(KSP ksp)
      5: {
      6:   KSP_LCD        *lcd = (KSP_LCD*)ksp->data;
      7:   PetscInt       restart = lcd->restart;

      9:   /* get work vectors needed by LCD */
     10:   KSPSetWorkVecs(ksp,2);

     12:   VecDuplicateVecs(ksp->work[0],restart+1,&lcd->P);
     13:   VecDuplicateVecs(ksp->work[0], restart + 1, &lcd->Q);
     14:   PetscLogObjectMemory((PetscObject)ksp,2*(restart+2)*sizeof(Vec));
     15:   return 0;
     16: }

     18: /*     KSPSolve_LCD - This routine actually applies the left conjugate
     19:     direction method

     21:    Input Parameter:
     22: .     ksp - the Krylov space object that was set to use LCD, by, for
     23:             example, KSPCreate(MPI_Comm,KSP *ksp); KSPSetType(ksp,KSPLCD);

     25:    Output Parameter:
     26: .     its - number of iterations used

     28: */
     29: PetscErrorCode  KSPSolve_LCD(KSP ksp)
     30: {
     31:   PetscInt       it,j,max_k;
     32:   PetscScalar    alfa, beta, num, den, mone;
     33:   PetscReal      rnorm = 0.0;
     34:   Vec            X,B,R,Z;
     35:   KSP_LCD        *lcd;
     36:   Mat            Amat,Pmat;
     37:   PetscBool      diagonalscale;

     39:   PCGetDiagonalScale(ksp->pc,&diagonalscale);

     42:   lcd   = (KSP_LCD*)ksp->data;
     43:   X     = ksp->vec_sol;
     44:   B     = ksp->vec_rhs;
     45:   R     = ksp->work[0];
     46:   Z     = ksp->work[1];
     47:   max_k = lcd->restart;
     48:   mone  = -1;

     50:   PCGetOperators(ksp->pc,&Amat,&Pmat);

     52:   ksp->its = 0;
     53:   if (!ksp->guess_zero) {
     54:     KSP_MatMult(ksp,Amat,X,Z);             /*   z <- b - Ax       */
     55:     VecAYPX(Z,mone,B);
     56:   } else {
     57:     VecCopy(B,Z);                         /*     z <- b (x is 0) */
     58:   }

     60:   KSP_PCApply(ksp,Z,R);                   /*     r <- M^-1z         */
     61:   if (ksp->normtype != KSP_NORM_NONE) {
     62:     VecNorm(R,NORM_2,&rnorm);
     63:     KSPCheckNorm(ksp,rnorm);
     64:   }
     65:   KSPLogResidualHistory(ksp,rnorm);
     66:   KSPMonitor(ksp,0,rnorm);
     67:   ksp->rnorm = rnorm;

     69:   /* test for convergence */
     70:   (*ksp->converged)(ksp,0,rnorm,&ksp->reason,ksp->cnvP);
     71:   if (ksp->reason) return 0;

     73:   VecCopy(R,lcd->P[0]);

     75:   while (!ksp->reason && ksp->its < ksp->max_it) {
     76:     it   = 0;
     77:     KSP_MatMult(ksp,Amat,lcd->P[it],Z);
     78:     KSP_PCApply(ksp,Z,lcd->Q[it]);

     80:     while (!ksp->reason && it < max_k && ksp->its < ksp->max_it) {
     81:       ksp->its++;
     82:       VecDot(lcd->P[it],R,&num);
     83:       VecDot(lcd->P[it],lcd->Q[it], &den);
     84:       KSPCheckDot(ksp,den);
     85:       alfa = num/den;
     86:       VecAXPY(X,alfa,lcd->P[it]);
     87:       VecAXPY(R,-alfa,lcd->Q[it]);
     88:       if (ksp->normtype != KSP_NORM_NONE) {
     89:         VecNorm(R,NORM_2,&rnorm);
     90:         KSPCheckNorm(ksp,rnorm);
     91:       }

     93:       ksp->rnorm = rnorm;
     94:       KSPLogResidualHistory(ksp,rnorm);
     95:       KSPMonitor(ksp,ksp->its,rnorm);
     96:       (*ksp->converged)(ksp,ksp->its,rnorm,&ksp->reason,ksp->cnvP);

     98:       if (ksp->reason) break;

    100:       VecCopy(R,lcd->P[it+1]);
    101:       KSP_MatMult(ksp,Amat,lcd->P[it+1],Z);
    102:       KSP_PCApply(ksp,Z,lcd->Q[it+1]);

    104:       for (j = 0; j <= it; j++) {
    105:         VecDot(lcd->P[j],lcd->Q[it+1],&num);
    106:         KSPCheckDot(ksp,num);
    107:         VecDot(lcd->P[j],lcd->Q[j],&den);
    108:         beta = -num/den;
    109:         VecAXPY(lcd->P[it+1],beta,lcd->P[j]);
    110:         VecAXPY(lcd->Q[it+1],beta,lcd->Q[j]);
    111:       }
    112:       it++;
    113:     }
    114:     VecCopy(lcd->P[it],lcd->P[0]);
    115:   }
    116:   if (ksp->its >= ksp->max_it && !ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
    117:   VecCopy(X,ksp->vec_sol);
    118:   return 0;
    119: }
    120: /*
    121:        KSPDestroy_LCD - Frees all memory space used by the Krylov method

    123: */
    124: PetscErrorCode KSPReset_LCD(KSP ksp)
    125: {
    126:   KSP_LCD        *lcd = (KSP_LCD*)ksp->data;

    128:   if (lcd->P) VecDestroyVecs(lcd->restart+1,&lcd->P);
    129:   if (lcd->Q) VecDestroyVecs(lcd->restart+1,&lcd->Q);
    130:   return 0;
    131: }

    133: PetscErrorCode KSPDestroy_LCD(KSP ksp)
    134: {
    135:   KSPReset_LCD(ksp);
    136:   PetscFree(ksp->data);
    137:   return 0;
    138: }

    140: /*
    141:      KSPView_LCD - Prints information about the current Krylov method being used

    143:       Currently this only prints information to a file (or stdout) about the
    144:       symmetry of the problem. If your Krylov method has special options or
    145:       flags that information should be printed here.

    147: */
    148: PetscErrorCode KSPView_LCD(KSP ksp,PetscViewer viewer)
    149: {

    151:   KSP_LCD        *lcd = (KSP_LCD*)ksp->data;
    152:   PetscBool      iascii;

    154:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    155:   if (iascii) {
    156:     PetscViewerASCIIPrintf(viewer,"  restart=%d\n",lcd->restart);
    157:     PetscViewerASCIIPrintf(viewer,"  happy breakdown tolerance %g\n",lcd->haptol);
    158:   }
    159:   return 0;
    160: }

    162: /*
    163:     KSPSetFromOptions_LCD - Checks the options database for options related to the
    164:                             LCD method.
    165: */
    166: PetscErrorCode KSPSetFromOptions_LCD(PetscOptionItems *PetscOptionsObject,KSP ksp)
    167: {
    168:   PetscBool      flg;
    169:   KSP_LCD        *lcd = (KSP_LCD*)ksp->data;

    171:   PetscOptionsHead(PetscOptionsObject,"KSP LCD options");
    172:   PetscOptionsInt("-ksp_lcd_restart","Number of vectors conjugate","KSPLCDSetRestart",lcd->restart,&lcd->restart,&flg);
    174:   PetscOptionsReal("-ksp_lcd_haptol","Tolerance for exact convergence (happy ending)","KSPLCDSetHapTol",lcd->haptol,&lcd->haptol,&flg);
    176:   return 0;
    177: }

    179: /*MC
    180:      KSPLCD -  Implements the LCD (left conjugate direction) method in PETSc.

    182:    Options Database Keys:
    183: +   -ksp_lcd_restart - number of vectors conjudate
    184: -   -ksp_lcd_haptol - tolerance for exact convergence (happing ending)

    186:    Level: beginner

    188:     Notes:
    189:     Support only for left preconditioning

    191:     References:
    192: +   * - J.Y. Yuan, G.H.Golub, R.J. Plemmons, and W.A.G. Cecilio. Semiconjugate
    193:      direction methods for real positive definite system. BIT Numerical
    194:      Mathematics, 44(1),2004.
    195: .   * - Y. Dai and J.Y. Yuan. Study on semiconjugate direction methods for
    196:      nonsymmetric systems. International Journal for Numerical Methods in
    197:      Engineering, 60, 2004.
    198: .   * - L. Catabriga, A.L.G.A. Coutinho, and L.P.Franca. Evaluating the LCD
    199:      algorithm for solving linear systems of equations arising from implicit
    200:      SUPG formulation of compressible flows. International Journal for
    201:      Numerical Methods in Engineering, 60, 2004
    202: -   * - L. Catabriga, A. M. P. Valli, B. Z. Melotti, L. M. Pessoa,
    203:      A. L. G. A. Coutinho, Performance of LCD iterative method in the finite
    204:      element and finite difference solution of convection diffusion
    205:      equations,  Communications in Numerical Methods in Engineering, (Early
    206:      View).

    208:   Contributed by: Lucia Catabriga <luciac@ices.utexas.edu>

    210: .seealso:  KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP,
    211:            KSPCGSetType(), KSPLCDSetRestart(), KSPLCDSetHapTol()

    213: M*/

    215: PETSC_EXTERN PetscErrorCode KSPCreate_LCD(KSP ksp)
    216: {
    217:   KSP_LCD        *lcd;

    219:   PetscNewLog(ksp,&lcd);
    220:   ksp->data    = (void*)lcd;
    221:   KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);
    222:   KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
    223:   lcd->restart = 30;
    224:   lcd->haptol  = 1.0e-30;

    226:   /*
    227:        Sets the functions that are associated with this data structure
    228:        (in C++ this is the same as defining virtual functions)
    229:   */
    230:   ksp->ops->setup          = KSPSetUp_LCD;
    231:   ksp->ops->solve          = KSPSolve_LCD;
    232:   ksp->ops->reset          = KSPReset_LCD;
    233:   ksp->ops->destroy        = KSPDestroy_LCD;
    234:   ksp->ops->view           = KSPView_LCD;
    235:   ksp->ops->setfromoptions = KSPSetFromOptions_LCD;
    236:   ksp->ops->buildsolution  = KSPBuildSolutionDefault;
    237:   ksp->ops->buildresidual  = KSPBuildResidualDefault;
    238:   return 0;
    239: }