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

Actual source code: test9.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: */
     10: /*
     11:    This example implements one of the problems found at
     12:        NLEVP: A Collection of Nonlinear Eigenvalue Problems,
     13:        The University of Manchester.
     14:    The details of the collection can be found at:
     15:        [1] T. Betcke et al., "NLEVP: A Collection of Nonlinear Eigenvalue
     16:            Problems", ACM Trans. Math. Software 39(2), Article 7, 2013.

     18:    The loaded_string problem is a rational eigenvalue problem for the
     19:    finite element model of a loaded vibrating string.
     20: */

     22: static char help[] = "Test the NLEIGS solver with FNCOMBINE.\n\n"
     23:   "This is based on loaded_string from the NLEVP collection.\n"
     24:   "The command line options are:\n"
     25:   "  -n <n>, dimension of the matrices.\n"
     26:   "  -kappa <kappa>, stiffness of elastic spring.\n"
     27:   "  -mass <m>, mass of the attached load.\n\n";

     29: #include <slepcnep.h>

     31: #define NMAT 3

     33: int main(int argc,char **argv)
     34: {
     35:   Mat            A[NMAT];         /* problem matrices */
     36:   FN             f[NMAT],g;       /* functions to define the nonlinear operator */
     37:   NEP            nep;             /* nonlinear eigensolver context */
     38:   PetscInt       n=100,Istart,Iend,i;
     39:   PetscReal      kappa=1.0,m=1.0;
     40:   PetscScalar    sigma,numer[2],denom[2];
     41:   PetscBool      terse;

     43:   SlepcInitialize(&argc,&argv,(char*)0,help);

     45:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     46:   PetscOptionsGetReal(NULL,NULL,"-kappa",&kappa,NULL);
     47:   PetscOptionsGetReal(NULL,NULL,"-mass",&m,NULL);
     48:   sigma = kappa/m;
     49:   PetscPrintf(PETSC_COMM_WORLD,"Loaded vibrating string, n=%" PetscInt_FMT " kappa=%g m=%g\n\n",n,(double)kappa,(double)m);

     51:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     52:                        Build the problem matrices
     53:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     55:   /* initialize matrices */
     56:   for (i=0;i<NMAT;i++) {
     57:     MatCreate(PETSC_COMM_WORLD,&A[i]);
     58:     MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n,n);
     59:     MatSetFromOptions(A[i]);
     60:     MatSetUp(A[i]);
     61:   }
     62:   MatGetOwnershipRange(A[0],&Istart,&Iend);

     64:   /* A0 */
     65:   for (i=Istart;i<Iend;i++) {
     66:     MatSetValue(A[0],i,i,(i==n-1)?1.0*n:2.0*n,INSERT_VALUES);
     67:     if (i>0) MatSetValue(A[0],i,i-1,-1.0*n,INSERT_VALUES);
     68:     if (i<n-1) MatSetValue(A[0],i,i+1,-1.0*n,INSERT_VALUES);
     69:   }

     71:   /* A1 */
     72:   for (i=Istart;i<Iend;i++) {
     73:     MatSetValue(A[1],i,i,(i==n-1)?2.0/(6.0*n):4.0/(6.0*n),INSERT_VALUES);
     74:     if (i>0) MatSetValue(A[1],i,i-1,1.0/(6.0*n),INSERT_VALUES);
     75:     if (i<n-1) MatSetValue(A[1],i,i+1,1.0/(6.0*n),INSERT_VALUES);
     76:   }

     78:   /* A2 */
     79:   if (Istart<=n-1 && n-1<Iend) MatSetValue(A[2],n-1,n-1,kappa,INSERT_VALUES);

     81:   /* assemble matrices */
     82:   for (i=0;i<NMAT;i++) MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY);
     83:   for (i=0;i<NMAT;i++) MatAssemblyEnd(A[i],MAT_FINAL_ASSEMBLY);

     85:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     86:                        Create the problem functions
     87:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     89:   /* f1=1 */
     90:   FNCreate(PETSC_COMM_WORLD,&f[0]);
     91:   FNSetType(f[0],FNRATIONAL);
     92:   numer[0] = 1.0;
     93:   FNRationalSetNumerator(f[0],1,numer);

     95:   /* f2=-lambda */
     96:   FNCreate(PETSC_COMM_WORLD,&f[1]);
     97:   FNSetType(f[1],FNRATIONAL);
     98:   numer[0] = -1.0; numer[1] = 0.0;
     99:   FNRationalSetNumerator(f[1],2,numer);

    101:   /* f3=lambda/(lambda-sigma)=1+sigma/(lambda-sigma) */
    102:   FNCreate(PETSC_COMM_WORLD,&g);
    103:   FNSetType(g,FNRATIONAL);
    104:   numer[0] = sigma;
    105:   denom[0] = 1.0; denom[1] = -sigma;
    106:   FNRationalSetNumerator(g,1,numer);
    107:   FNRationalSetDenominator(g,2,denom);
    108:   FNCreate(PETSC_COMM_WORLD,&f[2]);
    109:   FNSetType(f[2],FNCOMBINE);
    110:   FNCombineSetChildren(f[2],FN_COMBINE_ADD,f[0],g);

    112:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    113:                 Create the eigensolver and solve the problem
    114:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    116:   NEPCreate(PETSC_COMM_WORLD,&nep);
    117:   NEPSetSplitOperator(nep,3,A,f,SUBSET_NONZERO_PATTERN);
    118:   NEPSetProblemType(nep,NEP_RATIONAL);
    119:   NEPSetFromOptions(nep);
    120:   NEPSolve(nep);

    122:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    123:                     Display solution and clean up
    124:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    126:   /* show detailed info unless -terse option is given by user */
    127:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    128:   if (terse) 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:   }
    135:   NEPDestroy(&nep);
    136:   for (i=0;i<NMAT;i++) {
    137:     MatDestroy(&A[i]);
    138:     FNDestroy(&f[i]);
    139:   }
    140:   FNDestroy(&g);
    141:   SlepcFinalize();
    142:   return 0;
    143: }

    145: /*TEST

    147:    test:
    148:       suffix: 1
    149:       args: -nep_type nleigs -rg_type interval -rg_interval_endpoints 4,700,-.1,.1 -nep_nev 8 -nep_target 5 -terse
    150:       filter: sed -e "s/[+-]0\.0*i//g"
    151:       requires: !single

    153: TEST*/