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:    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;

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

     46:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     47:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-kappa",&kappa,NULL));
     48:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-mass",&m,NULL));
     49:   sigma = kappa/m;
     50:   PetscCall(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:     PetscCall(MatCreate(PETSC_COMM_WORLD,&A[i]));
     58:     PetscCall(MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n,n));
     59:     PetscCall(MatSetFromOptions(A[i]));
     60:   }
     61:   PetscCall(MatGetOwnershipRange(A[0],&Istart,&Iend));

     63:   /* A0 */
     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:   for (i=Istart;i<Iend;i++) {
     72:     PetscCall(MatSetValue(A[1],i,i,(i==n-1)?2.0/(6.0*n):4.0/(6.0*n),INSERT_VALUES));
     73:     if (i>0) PetscCall(MatSetValue(A[1],i,i-1,1.0/(6.0*n),INSERT_VALUES));
     74:     if (i<n-1) PetscCall(MatSetValue(A[1],i,i+1,1.0/(6.0*n),INSERT_VALUES));
     75:   }

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

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

     84:   /* build matrices for the QEP */
     85:   PetscCall(MatAXPY(A[2],1.0,A[0],DIFFERENT_NONZERO_PATTERN));
     86:   PetscCall(MatAXPY(A[2],sigma,A[1],SAME_NONZERO_PATTERN));
     87:   PetscCall(MatScale(A[2],-1.0));
     88:   PetscCall(MatScale(A[0],sigma));
     89:   M = A[1];
     90:   A[1] = A[2];
     91:   A[2] = M;

     93:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     94:                 Create the eigensolver and solve the problem
     95:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

    102:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    103:                     Display solution and clean up
    104:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

    121: /*TEST

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

    128: TEST*/