Date: 2016-09-29T11:13:07+00:00

Actual source code: loaded_string.c
slepc-3.7.3 2016-09-29
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.

      8:    SLEPc is free software: you can redistribute it and/or modify it under  the
      9:    terms of version 3 of the GNU Lesser General Public License as published by
     10:    the Free Software Foundation.

     12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     15:    more details.

     17:    You  should have received a copy of the GNU Lesser General  Public  License
     18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     20: */
     21: /*
     22:    This example implements one of the problems found at
     23:        NLEVP: A Collection of Nonlinear Eigenvalue Problems,
     24:        The University of Manchester.
     25:    The details of the collection can be found at:
     26:        [1] T. Betcke et al., "NLEVP: A Collection of Nonlinear Eigenvalue
     27:            Problems", ACM Trans. Math. Software 39(2), Article 7, 2013.

     29:    The loaded_string problem is a rational eigenvalue problem for the
     30:    finite element model of a loaded vibrating string.
     31: */

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

     39: #include <slepcnep.h>

     41: #define NMAT 3

     45: int main(int argc,char **argv)
     46: {
     47:   Mat            A[NMAT];         /* problem matrices */
     48:   FN             f[NMAT];         /* functions to define the nonlinear operator */
     49:   NEP            nep;             /* nonlinear eigensolver context */
     50:   PetscInt       n=20,Istart,Iend,i;
     51:   PetscReal      kappa=1.0,m=1.0;
     52:   PetscScalar    sigma,numer[2],denom[2];
     53:   PetscBool      terse;

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

     58:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     59:   PetscOptionsGetReal(NULL,NULL,"-kappa",&kappa,NULL);
     60:   PetscOptionsGetReal(NULL,NULL,"-mass",&m,NULL);
     61:   sigma = kappa/m;
     62:   PetscPrintf(PETSC_COMM_WORLD,"Loaded vibrating string, n=%D kappa=%g m=%g\n\n",n,(double)kappa,(double)m);

     64:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     65:                        Build the problem matrices
     66:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     68:   /* initialize matrices */
     69:   for (i=0;i<NMAT;i++) {
     70:     MatCreate(PETSC_COMM_WORLD,&A[i]);
     71:     MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n,n);
     72:     MatSetFromOptions(A[i]);
     73:     MatSetUp(A[i]);
     74:   }
     75:   MatGetOwnershipRange(A[0],&Istart,&Iend);

     77:   /* A0 */
     78:   for (i=Istart;i<Iend;i++) {
     79:     MatSetValue(A[0],i,i,(i==n-1)?1.0*n:2.0*n,INSERT_VALUES);
     80:     if (i>0) { MatSetValue(A[0],i,i-1,-1.0*n,INSERT_VALUES); }
     81:     if (i<n-1) { MatSetValue(A[0],i,i+1,-1.0*n,INSERT_VALUES); }
     82:   }

     84:   /* A1 */

     86:   for (i=Istart;i<Iend;i++) {
     87:     MatSetValue(A[1],i,i,(i==n-1)?2.0/(6.0*n):4.0/(6.0*n),INSERT_VALUES);
     88:     if (i>0) { MatSetValue(A[1],i,i-1,1.0/(6.0*n),INSERT_VALUES); }
     89:     if (i<n-1) { MatSetValue(A[1],i,i+1,1.0/(6.0*n),INSERT_VALUES); }
     90:   }

     92:   /* A2 */
     93:   if (Istart<=n-1 && n-1<Iend) {
     94:     MatSetValue(A[2],n-1,n-1,kappa,INSERT_VALUES);
     95:   }

     97:   /* assemble matrices */
     98:   for (i=0;i<NMAT;i++) {
     99:     MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY);
    100:   }
    101:   for (i=0;i<NMAT;i++) {
    102:     MatAssemblyEnd(A[i],MAT_FINAL_ASSEMBLY);
    103:   }

    105:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    106:                        Create the problem functions
    107:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    109:   /* f1=1 */
    110:   FNCreate(PETSC_COMM_WORLD,&f[0]);
    111:   FNSetType(f[0],FNRATIONAL);
    112:   numer[0] = 1.0;
    113:   FNRationalSetNumerator(f[0],1,numer);

    115:   /* f2=-lambda */
    116:   FNCreate(PETSC_COMM_WORLD,&f[1]);
    117:   FNSetType(f[1],FNRATIONAL);
    118:   numer[0] = -1.0; numer[1] = 0.0;
    119:   FNRationalSetNumerator(f[1],2,numer);

    121:   /* f3=lambda/(lambda-sigma) */
    122:   FNCreate(PETSC_COMM_WORLD,&f[2]);
    123:   FNSetType(f[2],FNRATIONAL);
    124:   numer[0] = 1.0; numer[1] = 0.0;
    125:   denom[0] = 1.0; denom[1] = -sigma;
    126:   FNRationalSetNumerator(f[2],2,numer);
    127:   FNRationalSetDenominator(f[2],2,denom);

    129:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    130:                 Create the eigensolver and solve the problem
    131:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    133:   NEPCreate(PETSC_COMM_WORLD,&nep);
    134:   NEPSetSplitOperator(nep,3,A,f,SUBSET_NONZERO_PATTERN);
    135:   NEPSetFromOptions(nep);
    136:   NEPSolve(nep);

    138:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    139:                     Display solution and clean up
    140:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    141:
    142:   /* show detailed info unless -terse option is given by user */
    143:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    144:   if (terse) {
    145:     NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
    146:   } else {
    147:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    148:     NEPReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
    149:     NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
    150:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    151:   }
    152:   NEPDestroy(&nep);
    153:   for (i=0;i<NMAT;i++) {
    154:     MatDestroy(&A[i]);
    155:     FNDestroy(&f[i]);
    156:   }
    157:   SlepcFinalize();
    158:   return ierr;
    159: }