Date: 2021-02-01T14:42:17+00:00

Actual source code: test3.c
slepc-3.14.2 2021-02-01
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2020, 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;

     52:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
     53:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     54:   PetscPrintf(PETSC_COMM_WORLD,"\n1-D Nonlinear Eigenproblem, n=%D\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:   EPSCreate(PETSC_COMM_WORLD,&eps);
     63:   EPSSetType(eps,EPSGD);
     64:   EPSSetFromOptions(eps);

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

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

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

     80:   NEPCreate(PETSC_COMM_WORLD,&nep);

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

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

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

    105:   /* Print some options */
    106:   PetscObjectTypeCompare((PetscObject)nep,NEPSLP,&flag);
    107:   if (flag) {
    108:     NEPGetTwoSided(nep,&ts);
    109:     if (ts) {
    110:       NEPSLPGetDeflationThreshold(nep,&deftol);
    111:       PetscPrintf(PETSC_COMM_WORLD," Two-sided solve with deflation threshold=%g\n",(double)deftol);
    112:     }
    113:   }

    115:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    116:                       Solve the eigensystem
    117:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    119:   NEPSolve(nep);

    121:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    122:                     Display solution and clean up
    123:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    125:   /* show detailed info unless -terse option is given by user */
    126:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    127:   if (terse) {
    128:     NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
    129:   } else {
    130:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    131:     NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
    132:     NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
    133:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    134:   }

    136:   NEPDestroy(&nep);
    137:   EPSDestroy(&eps);
    138:   KSPDestroy(&ksp);
    139:   MatDestroy(&F);
    140:   MatDestroy(&J);
    141:   SlepcFinalize();
    142:   return ierr;
    143: }

    145: /* ------------------------------------------------------------------- */
    146: /*
    147:    FormFunction - Computes Function matrix  T(lambda)

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

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

    168:   /*
    169:      Compute Function entries and insert into matrix
    170:   */
    171:   MatGetSize(fun,&n,NULL);
    172:   MatGetOwnershipRange(fun,&Istart,&Iend);
    173:   if (Istart==0) FirstBlock=PETSC_TRUE;
    174:   if (Iend==n) LastBlock=PETSC_TRUE;
    175:   h = user->h;
    176:   c = user->kappa/(lambda-user->kappa);
    177:   d = n;

    179:   /*
    180:      Interior grid points
    181:   */
    182:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
    183:     j[0] = i-1; j[1] = i; j[2] = i+1;
    184:     A[0] = A[2] = -d-lambda*h/6.0; A[1] = 2.0*(d-lambda*h/3.0);
    185:     MatSetValues(fun,1,&i,3,j,A,INSERT_VALUES);
    186:   }

    188:   /*
    189:      Boundary points
    190:   */
    191:   if (FirstBlock) {
    192:     i = 0;
    193:     j[0] = 0; j[1] = 1;
    194:     A[0] = 2.0*(d-lambda*h/3.0); A[1] = -d-lambda*h/6.0;
    195:     MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
    196:   }

    198:   if (LastBlock) {
    199:     i = n-1;
    200:     j[0] = n-2; j[1] = n-1;
    201:     A[0] = -d-lambda*h/6.0; A[1] = d-lambda*h/3.0+lambda*c;
    202:     MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
    203:   }

    205:   /*
    206:      Assemble matrix
    207:   */
    208:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    209:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    210:   if (fun != B) {
    211:     MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY);
    212:     MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY);
    213:   }
    214:   return(0);
    215: }

    217: /* ------------------------------------------------------------------- */
    218: /*
    219:    FormJacobian - Computes Jacobian matrix  T'(lambda)

    221:    Input Parameters:
    222: .  nep    - the NEP context
    223: .  lambda - the scalar argument
    224: .  ctx    - optional user-defined context, as set by NEPSetJacobian()

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

    240:   /*
    241:      Compute Jacobian entries and insert into matrix
    242:   */
    243:   MatGetSize(jac,&n,NULL);
    244:   MatGetOwnershipRange(jac,&Istart,&Iend);
    245:   if (Istart==0) FirstBlock=PETSC_TRUE;
    246:   if (Iend==n) LastBlock=PETSC_TRUE;
    247:   h = user->h;
    248:   c = user->kappa/(lambda-user->kappa);

    250:   /*
    251:      Interior grid points
    252:   */
    253:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
    254:     j[0] = i-1; j[1] = i; j[2] = i+1;
    255:     A[0] = A[2] = -h/6.0; A[1] = -2.0*h/3.0;
    256:     MatSetValues(jac,1,&i,3,j,A,INSERT_VALUES);
    257:   }

    259:   /*
    260:      Boundary points
    261:   */
    262:   if (FirstBlock) {
    263:     i = 0;
    264:     j[0] = 0; j[1] = 1;
    265:     A[0] = -2.0*h/3.0; A[1] = -h/6.0;
    266:     MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
    267:   }

    269:   if (LastBlock) {
    270:     i = n-1;
    271:     j[0] = n-2; j[1] = n-1;
    272:     A[0] = -h/6.0; A[1] = -h/3.0-c*c;
    273:     MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
    274:   }

    276:   /*
    277:      Assemble matrix
    278:   */
    279:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
    280:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
    281:   return(0);
    282: }

    284: /*TEST

    286:    test:
    287:       args: -nep_target 21 -terse
    288:       requires: !single
    289:       test:
    290:          suffix: 1
    291:       test:
    292:          suffix: 1_ts
    293:          args: -nep_two_sided

    295: TEST*/