Date: 2020-01-13T12:01:58+00:00

Actual source code: test3.c
slepc-3.12.2 2020-01-13
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2019, 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:   PetscBool      terse;

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

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

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

     65:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     66:         Create a standalone KSP with appropriate settings
     67:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

     75:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     76:                Prepare nonlinear eigensolver context
     77:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     79:   NEPCreate(PETSC_COMM_WORLD,&nep);

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

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

     98:   NEPSetType(nep,NEPSLP);
     99:   NEPSLPSetEPS(nep,eps);
    100:   NEPSLPSetKSP(nep,ksp);
    101:   NEPSetFromOptions(nep);

    103:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    104:                       Solve the eigensystem
    105:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    107:   NEPSolve(nep);

    109:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    110:                     Display solution and clean up
    111:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    113:   /* show detailed info unless -terse option is given by user */
    114:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    115:   if (terse) {
    116:     NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
    117:   } else {
    118:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    119:     NEPReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
    120:     NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
    121:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    122:   }

    124:   NEPDestroy(&nep);
    125:   EPSDestroy(&eps);
    126:   KSPDestroy(&ksp);
    127:   MatDestroy(&F);
    128:   MatDestroy(&J);
    129:   SlepcFinalize();
    130:   return ierr;
    131: }

    133: /* ------------------------------------------------------------------- */
    134: /*
    135:    FormFunction - Computes Function matrix  T(lambda)

    137:    Input Parameters:
    138: .  nep    - the NEP context
    139: .  lambda - the scalar argument
    140: .  ctx    - optional user-defined context, as set by NEPSetFunction()

    142:    Output Parameters:
    143: .  fun - Function matrix
    144: .  B   - optionally different preconditioning matrix
    145: */
    146: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
    147: {
    149:   ApplicationCtx *user = (ApplicationCtx*)ctx;
    150:   PetscScalar    A[3],c,d;
    151:   PetscReal      h;
    152:   PetscInt       i,n,j[3],Istart,Iend;
    153:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;

    156:   /*
    157:      Compute Function entries and insert into matrix
    158:   */
    159:   MatGetSize(fun,&n,NULL);
    160:   MatGetOwnershipRange(fun,&Istart,&Iend);
    161:   if (Istart==0) FirstBlock=PETSC_TRUE;
    162:   if (Iend==n) LastBlock=PETSC_TRUE;
    163:   h = user->h;
    164:   c = user->kappa/(lambda-user->kappa);
    165:   d = n;

    167:   /*
    168:      Interior grid points
    169:   */
    170:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
    171:     j[0] = i-1; j[1] = i; j[2] = i+1;
    172:     A[0] = A[2] = -d-lambda*h/6.0; A[1] = 2.0*(d-lambda*h/3.0);
    173:     MatSetValues(fun,1,&i,3,j,A,INSERT_VALUES);
    174:   }

    176:   /*
    177:      Boundary points
    178:   */
    179:   if (FirstBlock) {
    180:     i = 0;
    181:     j[0] = 0; j[1] = 1;
    182:     A[0] = 2.0*(d-lambda*h/3.0); A[1] = -d-lambda*h/6.0;
    183:     MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
    184:   }

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

    193:   /*
    194:      Assemble matrix
    195:   */
    196:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
    197:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
    198:   if (fun != B) {
    199:     MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY);
    200:     MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY);
    201:   }
    202:   return(0);
    203: }

    205: /* ------------------------------------------------------------------- */
    206: /*
    207:    FormJacobian - Computes Jacobian matrix  T'(lambda)

    209:    Input Parameters:
    210: .  nep    - the NEP context
    211: .  lambda - the scalar argument
    212: .  ctx    - optional user-defined context, as set by NEPSetJacobian()

    214:    Output Parameters:
    215: .  jac - Jacobian matrix
    216: .  B   - optionally different preconditioning matrix
    217: */
    218: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
    219: {
    221:   ApplicationCtx *user = (ApplicationCtx*)ctx;
    222:   PetscScalar    A[3],c;
    223:   PetscReal      h;
    224:   PetscInt       i,n,j[3],Istart,Iend;
    225:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;

    228:   /*
    229:      Compute Jacobian entries and insert into matrix
    230:   */
    231:   MatGetSize(jac,&n,NULL);
    232:   MatGetOwnershipRange(jac,&Istart,&Iend);
    233:   if (Istart==0) FirstBlock=PETSC_TRUE;
    234:   if (Iend==n) LastBlock=PETSC_TRUE;
    235:   h = user->h;
    236:   c = user->kappa/(lambda-user->kappa);

    238:   /*
    239:      Interior grid points
    240:   */
    241:   for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
    242:     j[0] = i-1; j[1] = i; j[2] = i+1;
    243:     A[0] = A[2] = -h/6.0; A[1] = -2.0*h/3.0;
    244:     MatSetValues(jac,1,&i,3,j,A,INSERT_VALUES);
    245:   }

    247:   /*
    248:      Boundary points
    249:   */
    250:   if (FirstBlock) {
    251:     i = 0;
    252:     j[0] = 0; j[1] = 1;
    253:     A[0] = -2.0*h/3.0; A[1] = -h/6.0;
    254:     MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
    255:   }

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

    264:   /*
    265:      Assemble matrix
    266:   */
    267:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
    268:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
    269:   return(0);
    270: }

    272: /*TEST

    274:    test:
    275:       suffix: 1
    276:       args: -nep_target 21 -terse
    277:       requires: !single

    279: TEST*/