Date: 2022-08-09T09:05:57+00:00

Actual source code: loaded_string.c
slepc-3.17.2 2022-08-09
Report Typos and Errors

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

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

     50:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     51:                        Build the problem matrices
     52:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

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

     84:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     85:                        Create the problem functions
     86:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

    108:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    109:                 Create the eigensolver and solve the problem
    110:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

    118:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    119:                     Display solution and clean up
    120:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

    140: /*TEST

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

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

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

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

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

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

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

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

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

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

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

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

    233: TEST*/