Date: 2022-10-01T06:40:30+00:00

Actual source code: loaded_string.c
slepc-3.18.0 2022-10-01
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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:    This example solves the loaded_string problem by first transforming
     21:    it to a quadratic eigenvalue problem.
     22: */

     24: static char help[] = "Finite element model of a loaded vibrating string.\n\n"
     25:   "The command line options are:\n"
     26:   "  -n <n>, dimension of the matrices.\n"
     27:   "  -kappa <kappa>, stiffness of elastic spring.\n"
     28:   "  -mass <m>, mass of the attached load.\n\n";

     30: #include <slepcpep.h>

     32: #define NMAT 3

     34: int main(int argc,char **argv)
     35: {
     36:   Mat            A[3],M;      /* problem matrices */
     37:   PEP            pep;         /* polynomial eigenproblem solver context */
     38:   PetscInt       n=100,Istart,Iend,i;
     39:   PetscBool      terse;
     40:   PetscReal      kappa=1.0,m=1.0;
     41:   PetscScalar    sigma;

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

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

     52:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     53:      Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
     54:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
     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:   /* build matrices for the QEP */
     86:   MatAXPY(A[2],1.0,A[0],DIFFERENT_NONZERO_PATTERN);
     87:   MatAXPY(A[2],sigma,A[1],SAME_NONZERO_PATTERN);
     88:   MatScale(A[2],-1.0);
     89:   MatScale(A[0],sigma);
     90:   M = A[1];
     91:   A[1] = A[2];
     92:   A[2] = M;

     94:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     95:                 Create the eigensolver and solve the problem
     96:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     98:   PEPCreate(PETSC_COMM_WORLD,&pep);
     99:   PEPSetOperators(pep,3,A);
    100:   PEPSetFromOptions(pep);
    101:   PEPSolve(pep);

    103:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    104:                     Display solution and clean up
    105:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    107:   /* show detailed info unless -terse option is given by user */
    108:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    109:   if (terse) PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL);
    110:   else {
    111:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    112:     PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD);
    113:     PEPErrorView(pep,PEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD);
    114:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    115:   }
    116:   PEPDestroy(&pep);
    117:   for (i=0;i<NMAT;i++) MatDestroy(&A[i]);
    118:   SlepcFinalize();
    119:   return 0;
    120: }

    122: /*TEST

    124:    test:
    125:       suffix: 1
    126:       args: -pep_hyperbolic -pep_interval 4,900 -pep_type stoar -st_type sinvert -st_pc_type cholesky -terse
    127:       requires: !single

    129: TEST*/