Date: 2026-03-09T09:12:24+00:00

Actual source code: loaded_string.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: */
     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[] = "Finite element model of a loaded vibrating string.\n\n"
     23:   "The command line options are:\n"
     24:   "  -n <n>, dimension of the matrices.\n"
     25:   "  -kappa <kappa>, stiffness of elastic spring.\n"
     26:   "  -mass <m>, mass of the attached load.\n\n";

     28: #include <slepcnep.h>

     30: #define NMAT 3

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

     42:   PetscFunctionBeginUser;
     43:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

     45:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     46:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-kappa",&kappa,NULL));
     47:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-mass",&m,NULL));
     48:   sigma = kappa/m;
     49:   PetscCall(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:     PetscCall(MatCreate(PETSC_COMM_WORLD,&A[i]));
     58:     PetscCall(MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n,n));
     59:     PetscCall(MatSetFromOptions(A[i]));
     60:   }

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

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

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

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

     86:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     87:                        Create the problem functions
     88:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

    102:   /* f3=lambda/(lambda-sigma) */
    103:   PetscCall(FNCreate(PETSC_COMM_WORLD,&f[2]));
    104:   PetscCall(FNSetType(f[2],FNRATIONAL));
    105:   numer[0] = 1.0; numer[1] = 0.0;
    106:   denom[0] = 1.0; denom[1] = -sigma;
    107:   PetscCall(FNRationalSetNumerator(f[2],2,numer));
    108:   PetscCall(FNRationalSetDenominator(f[2],2,denom));

    110:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    111:                 Create the eigensolver and solve the problem
    112:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

    120:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    121:                     Display solution and clean up
    122:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    124:   /* show detailed info unless -terse option is given by user */
    125:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    126:   if (terse) PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL));
    127:   else {
    128:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    129:     PetscCall(NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD));
    130:     PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
    131:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    132:   }
    133:   PetscCall(NEPDestroy(&nep));
    134:   for (i=0;i<NMAT;i++) {
    135:     PetscCall(MatDestroy(&A[i]));
    136:     PetscCall(FNDestroy(&f[i]));
    137:   }
    138:   PetscCall(SlepcFinalize());
    139:   return 0;
    140: }

    142: /*TEST

    144:    test:
    145:       suffix: 1
    146:       args: -nep_type rii -nep_target 4 -terse
    147:       requires: !single
    148:       filter: sed -e "s/[+-]0\.0*i//g"

    150:    testset:
    151:       args: -nep_type interpol -rg_type interval -rg_interval_endpoints 5,700,-.1,.1 -nep_nev 7 -nep_target 5 -nep_interpol_interpolation_degree 12 -nep_refine simple -terse
    152:       requires: !single
    153:       output_file: output/loaded_string_2.out
    154:       test:
    155:          suffix: 2
    156:          args: -nep_refine_scheme {{schur explicit}}
    157:       test:
    158:          suffix: 2_mbe
    159:          args: -nep_refine_scheme mbe -nep_refine_ksp_type preonly -nep_refine_pc_type lu

    161:    testset:
    162:       nsize: 2
    163:       args: -nep_type interpol -rg_type interval -rg_interval_endpoints 5,700,-.1,.1 -nep_nev 7 -nep_target 5 -nep_interpol_interpolation_degree 12 -nep_refine simple -nep_refine_partitions 2 -nep_interpol_st_ksp_type bcgs -nep_interpol_st_pc_type bjacobi -terse
    164:       requires: !single
    165:       output_file: output/loaded_string_2.out
    166:       timeoutfactor: 2
    167:       test:
    168:          suffix: 3_explicit
    169:          args: -nep_refine_scheme explicit
    170:       test:
    171:          suffix: 3_mbe
    172:          args: -nep_refine_scheme mbe -nep_refine_ksp_type preonly -nep_refine_pc_type cholesky

    174:    test:
    175:       suffix: 4
    176:       nsize: 4
    177:       args: -nep_type interpol -rg_type interval -rg_interval_endpoints 5,700,-.1,.1 -nep_nev 7 -nep_target 5 -nep_interpol_interpolation_degree 10 -nep_refine simple -nep_refine_partitions 2 -nep_refine_scheme explicit -nep_interpol_st_ksp_type bcgs -nep_interpol_st_pc_type bjacobi -terse -log_exclude nep,pep,fn
    178:       requires: !single
    179:       output_file: output/loaded_string_2.out
    180:       timeoutfactor: 4

    182:    test:
    183:       suffix: 5
    184:       args: -nep_type nleigs -rg_type interval -rg_interval_endpoints 4,700,-.1,.1 -nep_nev 8 -nep_target 5 -terse
    185:       filter: sed -e "s/[+-]0\.0*i//g"
    186:       requires: !single

    188:    test:
    189:       suffix: 6
    190:       args: -nep_type nleigs -rg_type interval -rg_interval_endpoints 100,700 -nep_nev 5 -nep_tol 1e-9 -nep_target 140 -nep_nleigs_interpolation_degree 15 -nep_general -terse
    191:       requires: !complex !single

    193:    test:
    194:       suffix: 6_complex
    195:       args: -nep_type nleigs -rg_type interval -rg_interval_endpoints 100,700,-.1,.1 -nep_nev 5 -nep_tol 1e-9 -nep_target 140 -nep_nleigs_interpolation_degree 15 -nep_general -terse
    196:       filter: sed -e "s/[+-]0\.0*i//g"
    197:       requires: complex !single
    198:       output_file: output/loaded_string_6.out

    200:    test:
    201:       suffix: 7
    202:       args: -nep_type interpol -rg_type interval -rg_interval_endpoints 5,700 -nep_nev 5 -nep_target 100 -nep_interpol_interpolation_degree 20 -nep_ncv 20 -n 20 -nep_refine simple -nep_refine_its 1 -terse
    203:       requires: !complex double

    205:    test:
    206:       suffix: 7_complex
    207:       args: -nep_type interpol -rg_type interval -rg_interval_endpoints 5,700,-.1,.1 -nep_nev 5 -nep_target 100 -nep_interpol_interpolation_degree 20 -nep_ncv 20 -n 20 -nep_refine simple -nep_refine_its 1 -terse
    208:       requires: complex double
    209:       output_file: output/loaded_string_7.out

    211:    testset:
    212:       args: -nep_target 10 -nep_nev 3 -nep_tol 5e-10 -terse
    213:       requires: !single
    214:       output_file: output/loaded_string_8.out
    215:       filter: sed -e "s/[+-]0\.0*i//g"
    216:       test:
    217:          suffix: 8
    218:          args: -nep_type {{rii slp narnoldi}}
    219:       test:
    220:          suffix: 8_rii_thres
    221:          args: -nep_type rii -nep_rii_deflation_threshold 5e-10
    222:       test:
    223:          suffix: 8_slp_thres
    224:          args: -nep_type slp -nep_slp_deflation_threshold 5e-10

    226:       test:
    227:          suffix: 8_slp_two_thres
    228:          args: -nep_type slp -nep_slp_deflation_threshold 5e-10 -nep_two_sided

    230:    test:
    231:       suffix: 9
    232:       args: -nep_type ciss -rg_type ellipse -rg_ellipse_center 500 -rg_ellipse_radius 500 -rg_ellipse_vscale .1 -nep_ciss_moments 4 -nep_ciss_blocksize 5 -terse
    233:       requires: complex double

    235: TEST*/