Date: 2016-03-29T14:59:10+00:00

Actual source code: spring.c
slepc-3.6.3 2016-03-29
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2015, 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 spring problem is a QEP from the finite element model of a damped
     30:    mass-spring system. This implementation supports only scalar parameters,
     31:    that is all masses, dampers and springs have the same constants.
     32:    Furthermore, this implementation does not consider different constants
     33:    for dampers and springs connecting adjacent masses or masses to the ground.
     34: */

     36: static char help[] = "NLEVP problem: spring.\n\n"
     37:   "The command line options are:\n"
     38:   "  -n <n> ... dimension of the matrices.\n"
     39:   "  -mu <value> ... mass (default 1).\n"
     40:   "  -tau <value> ... damping constant of the dampers (default 10).\n"
     41:   "  -kappa <value> ... damping constant of the springs (default 5).\n\n";

     43: #include <slepcpep.h>

     47: int main(int argc,char **argv)
     48: {
     49:   Mat            M,C,K,A[3];      /* problem matrices */
     50:   PEP            pep;             /* polynomial eigenproblem solver context */
     51:   PetscInt       n=5,Istart,Iend,i;
     52:   PetscReal      mu=1,tau=10,kappa=5;
     53:   PetscBool      terse;

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

     58:   PetscOptionsGetInt(NULL,"-n",&n,NULL);
     59:   PetscOptionsGetReal(NULL,"-mu",&mu,NULL);
     60:   PetscOptionsGetReal(NULL,"-tau",&tau,NULL);
     61:   PetscOptionsGetReal(NULL,"-kappa",&kappa,NULL);
     62:   PetscPrintf(PETSC_COMM_WORLD,"\nDamped mass-spring system, n=%D mu=%g tau=%g kappa=%g\n\n",n,(double)mu,(double)tau,(double)kappa);

     64:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     65:      Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
     66:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     68:   /* K is a tridiagonal */
     69:   MatCreate(PETSC_COMM_WORLD,&K);
     70:   MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,n,n);
     71:   MatSetFromOptions(K);
     72:   MatSetUp(K);
     73:
     74:   MatGetOwnershipRange(K,&Istart,&Iend);
     75:   for (i=Istart;i<Iend;i++) {
     76:     if (i>0) {
     77:       MatSetValue(K,i,i-1,-kappa,INSERT_VALUES);
     78:     }
     79:     MatSetValue(K,i,i,kappa*3.0,INSERT_VALUES);
     80:     if (i<n-1) {
     81:       MatSetValue(K,i,i+1,-kappa,INSERT_VALUES);
     82:     }
     83:   }

     85:   MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY);
     86:   MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY);

     88:   /* C is a tridiagonal */
     89:   MatCreate(PETSC_COMM_WORLD,&C);
     90:   MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,n,n);
     91:   MatSetFromOptions(C);
     92:   MatSetUp(C);
     93:
     94:   MatGetOwnershipRange(C,&Istart,&Iend);
     95:   for (i=Istart;i<Iend;i++) {
     96:     if (i>0) {
     97:       MatSetValue(C,i,i-1,-tau,INSERT_VALUES);
     98:     }
     99:     MatSetValue(C,i,i,tau*3.0,INSERT_VALUES);
    100:     if (i<n-1) {
    101:       MatSetValue(C,i,i+1,-tau,INSERT_VALUES);
    102:     }
    103:   }

    105:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    106:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    107:
    108:   /* M is a diagonal matrix */
    109:   MatCreate(PETSC_COMM_WORLD,&M);
    110:   MatSetSizes(M,PETSC_DECIDE,PETSC_DECIDE,n,n);
    111:   MatSetFromOptions(M);
    112:   MatSetUp(M);
    113:   MatGetOwnershipRange(M,&Istart,&Iend);
    114:   for (i=Istart;i<Iend;i++) {
    115:     MatSetValue(M,i,i,mu,INSERT_VALUES);
    116:   }
    117:   MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);
    118:   MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);

    120:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    121:                 Create the eigensolver and solve the problem
    122:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    124:   PEPCreate(PETSC_COMM_WORLD,&pep);
    125:   A[0] = K; A[1] = C; A[2] = M;
    126:   PEPSetOperators(pep,3,A);
    127:   PEPSetFromOptions(pep);
    128:   PEPSolve(pep);

    130:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    131:                     Display solution and clean up
    132:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    133:
    134:   /* show detailed info unless -terse option is given by user */
    135:   PetscOptionsHasName(NULL,"-terse",&terse);
    136:   if (terse) {
    137:     PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL);
    138:   } else {
    139:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    140:     PEPReasonView(pep,PETSC_VIEWER_STDOUT_WORLD);
    141:     PEPErrorView(pep,PEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD);
    142:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    143:   }
    144:   PEPDestroy(&pep);
    145:   MatDestroy(&M);
    146:   MatDestroy(&C);
    147:   MatDestroy(&K);
    148:   SlepcFinalize();
    149:   return 0;
    150: }