Date: 2022-11-02T11:47:37+00:00

Actual source code: test4.c
slepc-3.18.1 2022-11-02
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.
      7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: */

     11: static char help[] = "Test the RII solver with a user-provided KSP.\n\n"
     12:   "This is a simplified version of ex20.\n"
     13:   "The command line options are:\n"
     14:   "  -n <n>, where <n> = number of grid subdivisions.\n";

     16: /*
     17:    Solve 1-D PDE
     18:             -u'' = lambda*u
     19:    on [0,1] subject to
     20:             u(0)=0, u'(1)=u(1)*lambda*kappa/(kappa-lambda)
     21: */

     23: #include <slepcnep.h>

     25: /*
     26:    User-defined routines
     27: */
     28: PetscErrorCode FormFunction(NEP,PetscScalar,Mat,Mat,void*);
     29: PetscErrorCode FormJacobian(NEP,PetscScalar,Mat,void*);

     31: /*
     32:    User-defined application context
     33: */
     34: typedef struct {
     35:   PetscScalar kappa;   /* ratio between stiffness of spring and attached mass */
     36:   PetscReal   h;       /* mesh spacing */
     37: } ApplicationCtx;

     39: int main(int argc,char **argv)
     40: {
     41:   NEP            nep;
     42:   KSP            ksp;
     43:   PC             pc;
     44:   Mat            F,J;
     45:   ApplicationCtx ctx;
     46:   PetscInt       n=128,lag,its;
     47:   PetscBool      terse,flg,cct,herm;
     48:   PetscReal      thres;

     51:   SlepcInitialize(&argc,&argv,(char*)0,help);
     52:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     53:   PetscPrintf(PETSC_COMM_WORLD,"\n1-D Nonlinear Eigenproblem, n=%" PetscInt_FMT "\n\n",n);
     54:   ctx.h = 1.0/(PetscReal)n;
     55:   ctx.kappa = 1.0;

     57:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     58:         Create a standalone KSP with appropriate settings
     59:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     61:   KSPCreate(PETSC_COMM_WORLD,&ksp);
     62:   KSPSetType(ksp,KSPBCGS);
     63:   KSPGetPC(ksp,&pc);
     64:   PCSetType(pc,PCBJACOBI);
     65:   KSPSetFromOptions(ksp);

     67:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     68:                Prepare nonlinear eigensolver context
     69:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     71:   NEPCreate(PETSC_COMM_WORLD,&nep);

     73:   /* Create Function and Jacobian matrices; set evaluation routines */
     74:   MatCreate(PETSC_COMM_WORLD,&F);
     75:   MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n);
     76:   MatSetFromOptions(F);
     77:   MatSeqAIJSetPreallocation(F,3,NULL);
     78:   MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
     79:   MatSetUp(F);
     80:   NEPSetFunction(nep,F,F,FormFunction,&ctx);

     82:   MatCreate(PETSC_COMM_WORLD,&J);
     83:   MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n);
     84:   MatSetFromOptions(J);
     85:   MatSeqAIJSetPreallocation(J,3,NULL);
     86:   MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
     87:   MatSetUp(J);
     88:   NEPSetJacobian(nep,J,FormJacobian,&ctx);

     90:   NEPSetType(nep,NEPRII);
     91:   NEPRIISetKSP(nep,ksp);
     92:   NEPRIISetMaximumIterations(nep,6);
     93:   NEPRIISetConstCorrectionTol(nep,PETSC_TRUE);
     94:   NEPRIISetHermitian(nep,PETSC_TRUE);
     95:   NEPSetFromOptions(nep);

     97:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     98:                       Solve the eigensystem
     99:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    101:   NEPSolve(nep);
    102:   PetscObjectTypeCompare((PetscObject)nep,NEPRII,&flg);
    103:   if (flg) {
    104:     NEPRIIGetMaximumIterations(nep,&its);
    105:     NEPRIIGetLagPreconditioner(nep,&lag);
    106:     NEPRIIGetDeflationThreshold(nep,&thres);
    107:     NEPRIIGetConstCorrectionTol(nep,&cct);
    108:     NEPRIIGetHermitian(nep,&herm);
    109:     PetscPrintf(PETSC_COMM_WORLD," Maximum inner iterations of RII is %" PetscInt_FMT "\n",its);
    110:     PetscPrintf(PETSC_COMM_WORLD," Preconditioner rebuilt every %" PetscInt_FMT " iterations\n",lag);
    111:     if (thres>0.0) PetscPrintf(PETSC_COMM_WORLD," Using deflation threshold=%g\n",(double)thres);
    112:     if (cct) PetscPrintf(PETSC_COMM_WORLD," Using a constant correction tolerance\n");
    113:     if (herm) PetscPrintf(PETSC_COMM_WORLD," Hermitian version of scalar equation\n");
    114:     PetscPrintf(PETSC_COMM_WORLD,"\n");
    115:   }

    117:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    118:                     Display solution and clean up
    119:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    121:   /* show detailed info unless -terse option is given by user */
    122:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    123:   if (terse) NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
    124:   else {
    125:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    126:     NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
    127:     NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
    128:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    129:   }

    131:   NEPDestroy(&nep);
    132:   KSPDestroy(&ksp);
    133:   MatDestroy(&F);
    134:   MatDestroy(&J);
    135:   SlepcFinalize();
    136:   return 0;
    137: }

    139: /* ------------------------------------------------------------------- */
    140: /*
    141:    FormFunction - Computes Function matrix  T(lambda)

    143:    Input Parameters:
    144: .  nep    - the NEP context
    145: .  lambda - the scalar argument
    146: .  ctx    - optional user-defined context, as set by NEPSetFunction()

    148:    Output Parameters:
    149: .  fun - Function matrix
    150: .  B   - optionally different preconditioning matrix
    151: */
    152: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
    153: {
    154:   ApplicationCtx *user = (ApplicationCtx*)ctx;
    155:   PetscScalar    A[3],c,d;
    156:   PetscReal      h;
    157:   PetscInt       i,n,j[3],Istart,Iend;
    158:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;

    161:   /*
    162:      Compute Function entries and insert into matrix
    163:   */
    164:   MatGetSize(fun,&n,NULL);
    165:   MatGetOwnershipRange(fun,&Istart,&Iend);
    166:   if (Istart==0) FirstBlock=PETSC_TRUE;
    167:   if (Iend==n) LastBlock=PETSC_TRUE;
    168:   h = user->h;
    169:   c = user->kappa/(lambda-user->kappa);
    170:   d = n;

    172:   /*
    173:      Interior grid points
    174:   */
    175:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
    176:     j[0] = i-1; j[1] = i; j[2] = i+1;
    177:     A[0] = A[2] = -d-lambda*h/6.0; A[1] = 2.0*(d-lambda*h/3.0);
    178:     MatSetValues(fun,1,&i,3,j,A,INSERT_VALUES);
    179:   }

    181:   /*
    182:      Boundary points
    183:   */
    184:   if (FirstBlock) {
    185:     i = 0;
    186:     j[0] = 0; j[1] = 1;
    187:     A[0] = 2.0*(d-lambda*h/3.0); A[1] = -d-lambda*h/6.0;
    188:     MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
    189:   }

    191:   if (LastBlock) {
    192:     i = n-1;
    193:     j[0] = n-2; j[1] = n-1;
    194:     A[0] = -d-lambda*h/6.0; A[1] = d-lambda*h/3.0+lambda*c;
    195:     MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
    196:   }

    198:   /*
    199:      Assemble matrix
    200:   */
    201:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    202:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    203:   if (fun != B) {
    204:     MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY);
    205:     MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY);
    206:   }
    207:   return 0;
    208: }

    210: /* ------------------------------------------------------------------- */
    211: /*
    212:    FormJacobian - Computes Jacobian matrix  T'(lambda)

    214:    Input Parameters:
    215: .  nep    - the NEP context
    216: .  lambda - the scalar argument
    217: .  ctx    - optional user-defined context, as set by NEPSetJacobian()

    219:    Output Parameters:
    220: .  jac - Jacobian matrix
    221: .  B   - optionally different preconditioning matrix
    222: */
    223: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
    224: {
    225:   ApplicationCtx *user = (ApplicationCtx*)ctx;
    226:   PetscScalar    A[3],c;
    227:   PetscReal      h;
    228:   PetscInt       i,n,j[3],Istart,Iend;
    229:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;

    232:   /*
    233:      Compute Jacobian entries and insert into matrix
    234:   */
    235:   MatGetSize(jac,&n,NULL);
    236:   MatGetOwnershipRange(jac,&Istart,&Iend);
    237:   if (Istart==0) FirstBlock=PETSC_TRUE;
    238:   if (Iend==n) LastBlock=PETSC_TRUE;
    239:   h = user->h;
    240:   c = user->kappa/(lambda-user->kappa);

    242:   /*
    243:      Interior grid points
    244:   */
    245:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
    246:     j[0] = i-1; j[1] = i; j[2] = i+1;
    247:     A[0] = A[2] = -h/6.0; A[1] = -2.0*h/3.0;
    248:     MatSetValues(jac,1,&i,3,j,A,INSERT_VALUES);
    249:   }

    251:   /*
    252:      Boundary points
    253:   */
    254:   if (FirstBlock) {
    255:     i = 0;
    256:     j[0] = 0; j[1] = 1;
    257:     A[0] = -2.0*h/3.0; A[1] = -h/6.0;
    258:     MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
    259:   }

    261:   if (LastBlock) {
    262:     i = n-1;
    263:     j[0] = n-2; j[1] = n-1;
    264:     A[0] = -h/6.0; A[1] = -h/3.0-c*c;
    265:     MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
    266:   }

    268:   /*
    269:      Assemble matrix
    270:   */
    271:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
    272:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
    273:   return 0;
    274: }

    276: /*TEST

    278:    test:
    279:       suffix: 1
    280:       args: -nep_target 21 -nep_rii_lag_preconditioner 2 -terse
    281:       requires: !single

    283: TEST*/