Date: 2022-08-09T09:05:55+00:00

Actual source code: test4.c
slepc-3.17.2 2022-08-09
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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;

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

     56:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     57:         Create a standalone KSP with appropriate settings
     58:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

     66:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     67:                Prepare nonlinear eigensolver context
     68:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     70:   NEPCreate(PETSC_COMM_WORLD,&nep);

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

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

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

     96:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     97:                       Solve the eigensystem
     98:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

    116:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    117:                     Display solution and clean up
    118:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

    138: /* ------------------------------------------------------------------- */
    139: /*
    140:    FormFunction - Computes Function matrix  T(lambda)

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

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

    160:   /*
    161:      Compute Function entries and insert into matrix
    162:   */
    163:   MatGetSize(fun,&n,NULL);
    164:   MatGetOwnershipRange(fun,&Istart,&Iend);
    165:   if (Istart==0) FirstBlock=PETSC_TRUE;
    166:   if (Iend==n) LastBlock=PETSC_TRUE;
    167:   h = user->h;
    168:   c = user->kappa/(lambda-user->kappa);
    169:   d = n;

    171:   /*
    172:      Interior grid points
    173:   */
    174:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
    175:     j[0] = i-1; j[1] = i; j[2] = i+1;
    176:     A[0] = A[2] = -d-lambda*h/6.0; A[1] = 2.0*(d-lambda*h/3.0);
    177:     MatSetValues(fun,1,&i,3,j,A,INSERT_VALUES);
    178:   }

    180:   /*
    181:      Boundary points
    182:   */
    183:   if (FirstBlock) {
    184:     i = 0;
    185:     j[0] = 0; j[1] = 1;
    186:     A[0] = 2.0*(d-lambda*h/3.0); A[1] = -d-lambda*h/6.0;
    187:     MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
    188:   }

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

    197:   /*
    198:      Assemble matrix
    199:   */
    200:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    201:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    202:   if (fun != B) {
    203:     MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY);
    204:     MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY);
    205:   }
    206:   PetscFunctionReturn(0);
    207: }

    209: /* ------------------------------------------------------------------- */
    210: /*
    211:    FormJacobian - Computes Jacobian matrix  T'(lambda)

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

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

    231:   /*
    232:      Compute Jacobian entries and insert into matrix
    233:   */
    234:   MatGetSize(jac,&n,NULL);
    235:   MatGetOwnershipRange(jac,&Istart,&Iend);
    236:   if (Istart==0) FirstBlock=PETSC_TRUE;
    237:   if (Iend==n) LastBlock=PETSC_TRUE;
    238:   h = user->h;
    239:   c = user->kappa/(lambda-user->kappa);

    241:   /*
    242:      Interior grid points
    243:   */
    244:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
    245:     j[0] = i-1; j[1] = i; j[2] = i+1;
    246:     A[0] = A[2] = -h/6.0; A[1] = -2.0*h/3.0;
    247:     MatSetValues(jac,1,&i,3,j,A,INSERT_VALUES);
    248:   }

    250:   /*
    251:      Boundary points
    252:   */
    253:   if (FirstBlock) {
    254:     i = 0;
    255:     j[0] = 0; j[1] = 1;
    256:     A[0] = -2.0*h/3.0; A[1] = -h/6.0;
    257:     MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
    258:   }

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

    267:   /*
    268:      Assemble matrix
    269:   */
    270:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
    271:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
    272:   PetscFunctionReturn(0);
    273: }

    275: /*TEST

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

    282: TEST*/