Actual source code: test3.c

      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 SLP solver with a user-provided EPS.\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:   EPS            eps;
     43:   KSP            ksp;
     44:   PC             pc;
     45:   Mat            F,J;
     46:   ApplicationCtx ctx;
     47:   PetscInt       n=128;
     48:   PetscReal      deftol;
     49:   PetscBool      terse,flag,ts;

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

     58:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     59:         Create a standalone EPS with appropriate settings
     60:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     62:   PetscCall(EPSCreate(PETSC_COMM_WORLD,&eps));
     63:   PetscCall(EPSSetType(eps,EPSGD));
     64:   PetscCall(EPSSetFromOptions(eps));

     66:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     67:         Create a standalone KSP with appropriate settings
     68:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     70:   PetscCall(KSPCreate(PETSC_COMM_WORLD,&ksp));
     71:   PetscCall(KSPSetType(ksp,KSPBCGS));
     72:   PetscCall(KSPGetPC(ksp,&pc));
     73:   PetscCall(PCSetType(pc,PCBJACOBI));
     74:   PetscCall(KSPSetFromOptions(ksp));

     76:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     77:                Prepare nonlinear eigensolver context
     78:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     80:   PetscCall(NEPCreate(PETSC_COMM_WORLD,&nep));

     82:   /* Create Function and Jacobian matrices; set evaluation routines */
     83:   PetscCall(MatCreate(PETSC_COMM_WORLD,&F));
     84:   PetscCall(MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n));
     85:   PetscCall(MatSetFromOptions(F));
     86:   PetscCall(MatSeqAIJSetPreallocation(F,3,NULL));
     87:   PetscCall(MatMPIAIJSetPreallocation(F,3,NULL,1,NULL));
     88:   PetscCall(NEPSetFunction(nep,F,F,FormFunction,&ctx));

     90:   PetscCall(MatCreate(PETSC_COMM_WORLD,&J));
     91:   PetscCall(MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n));
     92:   PetscCall(MatSetFromOptions(J));
     93:   PetscCall(MatSeqAIJSetPreallocation(J,3,NULL));
     94:   PetscCall(MatMPIAIJSetPreallocation(F,3,NULL,1,NULL));
     95:   PetscCall(NEPSetJacobian(nep,J,FormJacobian,&ctx));

     97:   /* Set options */
     98:   PetscCall(NEPSetType(nep,NEPSLP));
     99:   PetscCall(NEPSLPSetEPS(nep,eps));
    100:   PetscCall(NEPSLPSetKSP(nep,ksp));
    101:   PetscCall(NEPSetFromOptions(nep));

    103:   /* Print some options */
    104:   PetscCall(PetscObjectTypeCompare((PetscObject)nep,NEPSLP,&flag));
    105:   if (flag) {
    106:     PetscCall(NEPGetTwoSided(nep,&ts));
    107:     if (ts) {
    108:       PetscCall(NEPSLPGetDeflationThreshold(nep,&deftol));
    109:       PetscCall(PetscPrintf(PETSC_COMM_WORLD," Two-sided solve with deflation threshold=%g\n",(double)deftol));
    110:     }
    111:   }

    113:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    114:                       Solve the eigensystem
    115:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    117:   PetscCall(NEPSolve(nep));

    119:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    120:                     Display solution and clean up
    121:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    123:   /* show detailed info unless -terse option is given by user */
    124:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    125:   if (terse) PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL));
    126:   else {
    127:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    128:     PetscCall(NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD));
    129:     PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
    130:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    131:   }

    133:   PetscCall(NEPDestroy(&nep));
    134:   PetscCall(EPSDestroy(&eps));
    135:   PetscCall(KSPDestroy(&ksp));
    136:   PetscCall(MatDestroy(&F));
    137:   PetscCall(MatDestroy(&J));
    138:   PetscCall(SlepcFinalize());
    139:   return 0;
    140: }

    142: /* ------------------------------------------------------------------- */
    143: /*
    144:    FormFunction - Computes Function matrix  T(lambda)

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

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

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

    175:   /*
    176:      Interior grid points
    177:   */
    178:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
    179:     j[0] = i-1; j[1] = i; j[2] = i+1;
    180:     A[0] = A[2] = -d-lambda*h/6.0; A[1] = 2.0*(d-lambda*h/3.0);
    181:     PetscCall(MatSetValues(fun,1,&i,3,j,A,INSERT_VALUES));
    182:   }

    184:   /*
    185:      Boundary points
    186:   */
    187:   if (FirstBlock) {
    188:     i = 0;
    189:     j[0] = 0; j[1] = 1;
    190:     A[0] = 2.0*(d-lambda*h/3.0); A[1] = -d-lambda*h/6.0;
    191:     PetscCall(MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES));
    192:   }

    194:   if (LastBlock) {
    195:     i = n-1;
    196:     j[0] = n-2; j[1] = n-1;
    197:     A[0] = -d-lambda*h/6.0; A[1] = d-lambda*h/3.0+lambda*c;
    198:     PetscCall(MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES));
    199:   }

    201:   /*
    202:      Assemble matrix
    203:   */
    204:   PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
    205:   PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
    206:   if (fun != B) {
    207:     PetscCall(MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY));
    208:     PetscCall(MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY));
    209:   }
    210:   PetscFunctionReturn(PETSC_SUCCESS);
    211: }

    213: /* ------------------------------------------------------------------- */
    214: /*
    215:    FormJacobian - Computes Jacobian matrix  T'(lambda)

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

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

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

    245:   /*
    246:      Interior grid points
    247:   */
    248:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
    249:     j[0] = i-1; j[1] = i; j[2] = i+1;
    250:     A[0] = A[2] = -h/6.0; A[1] = -2.0*h/3.0;
    251:     PetscCall(MatSetValues(jac,1,&i,3,j,A,INSERT_VALUES));
    252:   }

    254:   /*
    255:      Boundary points
    256:   */
    257:   if (FirstBlock) {
    258:     i = 0;
    259:     j[0] = 0; j[1] = 1;
    260:     A[0] = -2.0*h/3.0; A[1] = -h/6.0;
    261:     PetscCall(MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES));
    262:   }

    264:   if (LastBlock) {
    265:     i = n-1;
    266:     j[0] = n-2; j[1] = n-1;
    267:     A[0] = -h/6.0; A[1] = -h/3.0-c*c;
    268:     PetscCall(MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES));
    269:   }

    271:   /*
    272:      Assemble matrix
    273:   */
    274:   PetscCall(MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY));
    275:   PetscCall(MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY));
    276:   PetscFunctionReturn(PETSC_SUCCESS);
    277: }

    279: /*TEST

    281:    test:
    282:       args: -nep_target 21 -terse
    283:       requires: !single
    284:       test:
    285:          suffix: 1
    286:       test:
    287:          suffix: 1_ts
    288:          args: -nep_two_sided

    290: TEST*/