Date: 2026-03-31T13:23:04+00:00

Actual source code: acoustic_wave_2d.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 acoustic_wave_2d problem is a 2-D version of acoustic_wave_1d, also
     19:    scaled for real arithmetic.
     20: */

     22: static char help[] = "Quadratic eigenproblem from an acoustics application (2-D).\n\n"
     23:   "The command line options are:\n"
     24:   "  -m <m>, where <m> = grid size, the matrices have dimension m*(m-1).\n"
     25:   "  -z <z>, where <z> = impedance (default 1.0).\n\n";

     27: #include <slepcpep.h>

     29: int main(int argc,char **argv)
     30: {
     31:   Mat            M,C,K,A[3];      /* problem matrices */
     32:   PEP            pep;             /* polynomial eigenproblem solver context */
     33:   PetscInt       m=6,n,II,Istart,Iend,i,j;
     34:   PetscScalar    z=1.0;
     35:   PetscReal      h;
     36:   char           str[50];
     37:   PetscBool      terse;

     39:   PetscFunctionBeginUser;
     40:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

     42:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL));
     43:   PetscCheck(m>1,PETSC_COMM_WORLD,PETSC_ERR_USER_INPUT,"m must be at least 2");
     44:   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-z",&z,NULL));
     45:   h = 1.0/m;
     46:   n = m*(m-1);
     47:   PetscCall(SlepcSNPrintfScalar(str,sizeof(str),z,PETSC_FALSE));
     48:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nAcoustic wave 2-D, n=%" PetscInt_FMT " (m=%" PetscInt_FMT "), z=%s\n\n",n,m,str));

     50:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     51:      Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
     52:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     54:   /* K has a pattern similar to the 2D Laplacian */
     55:   PetscCall(MatCreate(PETSC_COMM_WORLD,&K));
     56:   PetscCall(MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,n,n));
     57:   PetscCall(MatSetFromOptions(K));

     59:   PetscCall(MatGetOwnershipRange(K,&Istart,&Iend));
     60:   for (II=Istart;II<Iend;II++) {
     61:     i = II/m; j = II-i*m;
     62:     if (i>0) PetscCall(MatSetValue(K,II,II-m,(j==m-1)?-0.5:-1.0,INSERT_VALUES));
     63:     if (i<m-2) PetscCall(MatSetValue(K,II,II+m,(j==m-1)?-0.5:-1.0,INSERT_VALUES));
     64:     if (j>0) PetscCall(MatSetValue(K,II,II-1,-1.0,INSERT_VALUES));
     65:     if (j<m-1) PetscCall(MatSetValue(K,II,II+1,-1.0,INSERT_VALUES));
     66:     PetscCall(MatSetValue(K,II,II,(j==m-1)?2.0:4.0,INSERT_VALUES));
     67:   }

     69:   PetscCall(MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY));
     70:   PetscCall(MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY));

     72:   /* C is the zero matrix except for a few nonzero elements on the diagonal */
     73:   PetscCall(MatCreate(PETSC_COMM_WORLD,&C));
     74:   PetscCall(MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,n,n));
     75:   PetscCall(MatSetFromOptions(C));

     77:   PetscCall(MatGetOwnershipRange(C,&Istart,&Iend));
     78:   for (i=Istart;i<Iend;i++) {
     79:     if (i%m==m-1) PetscCall(MatSetValue(C,i,i,-2*PETSC_PI*h/z,INSERT_VALUES));
     80:   }
     81:   PetscCall(MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY));
     82:   PetscCall(MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY));

     84:   /* M is a diagonal matrix */
     85:   PetscCall(MatCreate(PETSC_COMM_WORLD,&M));
     86:   PetscCall(MatSetSizes(M,PETSC_DECIDE,PETSC_DECIDE,n,n));
     87:   PetscCall(MatSetFromOptions(M));

     89:   PetscCall(MatGetOwnershipRange(M,&Istart,&Iend));
     90:   for (i=Istart;i<Iend;i++) {
     91:     if (i%m==m-1) PetscCall(MatSetValue(M,i,i,2*PETSC_PI*PETSC_PI*h*h,INSERT_VALUES));
     92:     else PetscCall(MatSetValue(M,i,i,4*PETSC_PI*PETSC_PI*h*h,INSERT_VALUES));
     93:   }
     94:   PetscCall(MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY));
     95:   PetscCall(MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY));

     97:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     98:                 Create the eigensolver and solve the problem
     99:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    101:   PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep));
    102:   A[0] = K; A[1] = C; A[2] = M;
    103:   PetscCall(PEPSetOperators(pep,3,A));
    104:   PetscCall(PEPSetFromOptions(pep));
    105:   PetscCall(PEPSolve(pep));

    107:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    108:                     Display solution and clean up
    109:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    111:   /* show detailed info unless -terse option is given by user */
    112:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    113:   if (terse) PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL));
    114:   else {
    115:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    116:     PetscCall(PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD));
    117:     PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD));
    118:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    119:   }
    120:   PetscCall(PEPDestroy(&pep));
    121:   PetscCall(MatDestroy(&M));
    122:   PetscCall(MatDestroy(&C));
    123:   PetscCall(MatDestroy(&K));
    124:   PetscCall(SlepcFinalize());
    125:   return 0;
    126: }

    128: /*TEST

    130:    testset:
    131:       args: -pep_nev 2 -pep_ncv 18 -terse
    132:       output_file: output/acoustic_wave_2d_1.out
    133:       filter: sed -e "s/2.60936i/2.60937i/g" | sed -e "s/2.60938i/2.60937i/g"
    134:       test:
    135:          suffix: 1
    136:          args: -pep_type {{qarnoldi linear}}
    137:       test:
    138:          suffix: 1_toar
    139:          args: -pep_type toar -pep_toar_locking 0

    141:    testset:
    142:       args: -pep_nev 2 -pep_ncv 18 -pep_type stoar -pep_hermitian -pep_scale scalar -st_type sinvert -terse
    143:       output_file: output/acoustic_wave_2d_2.out
    144:       test:
    145:          suffix: 2
    146:       test:
    147:          suffix: 2_lin_b
    148:          args: -pep_stoar_linearization 0,1
    149:       test:
    150:          suffix: 2_lin_ab
    151:          args: -pep_stoar_linearization 0.1,0.9

    153: TEST*/