Date: 2023-11-27T17:18:59+00:00

Actual source code: loaded_string.c
slepc-3.20.1 2023-11-27
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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[] = "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,(char*)0,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:     PetscCall(MatSetUp(A[i]));
     61:   }
     62:   PetscCall(MatGetOwnershipRange(A[0],&Istart,&Iend));

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

     71:   /* A1 */
     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:   if (Istart<=n-1 && n-1<Iend) PetscCall(MatSetValue(A[2],n-1,n-1,kappa,INSERT_VALUES));

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

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

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

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

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

    109:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    110:                 Create the eigensolver and solve the problem
    111:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    113:   PetscCall(NEPCreate(PETSC_COMM_WORLD,&nep));
    114:   PetscCall(NEPSetSplitOperator(nep,3,A,f,SUBSET_NONZERO_PATTERN));
    115:   PetscCall(NEPSetProblemType(nep,NEP_RATIONAL));
    116:   PetscCall(NEPSetFromOptions(nep));
    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:   }
    132:   PetscCall(NEPDestroy(&nep));
    133:   for (i=0;i<NMAT;i++) {
    134:     PetscCall(MatDestroy(&A[i]));
    135:     PetscCall(FNDestroy(&f[i]));
    136:   }
    137:   PetscCall(SlepcFinalize());
    138:   return 0;
    139: }

    141: /*TEST

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

    149:    testset:
    150:       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
    151:       requires: !single
    152:       output_file: output/loaded_string_2.out
    153:       test:
    154:          suffix: 2
    155:          args: -nep_refine_scheme {{schur explicit}}
    156:       test:
    157:          suffix: 2_mbe
    158:          args: -nep_refine_scheme mbe -nep_refine_ksp_type preonly -nep_refine_pc_type lu

    160:    testset:
    161:       nsize: 2
    162:       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
    163:       requires: !single
    164:       output_file: output/loaded_string_2.out
    165:       timeoutfactor: 2
    166:       test:
    167:          suffix: 3_explicit
    168:          args: -nep_refine_scheme explicit
    169:       test:
    170:          suffix: 3_mbe
    171:          args: -nep_refine_scheme mbe -nep_refine_ksp_type preonly -nep_refine_pc_type cholesky

    173:    test:
    174:       suffix: 4
    175:       nsize: 4
    176:       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
    177:       requires: !single
    178:       output_file: output/loaded_string_2.out
    179:       timeoutfactor: 4

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

    187:    test:
    188:       suffix: 6
    189:       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
    190:       requires: !complex !single

    192:    test:
    193:       suffix: 6_complex
    194:       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
    195:       filter: sed -e "s/[+-]0\.0*i//g"
    196:       requires: complex !single
    197:       output_file: output/loaded_string_6.out

    199:    test:
    200:       suffix: 7
    201:       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
    202:       requires: !complex double

    204:    test:
    205:       suffix: 7_complex
    206:       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
    207:       requires: complex double
    208:       output_file: output/loaded_string_7.out

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

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

    229:    test:
    230:       suffix: 9
    231:       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
    232:       requires: complex double

    234: TEST*/