Date: 2015-09-03T15:05:49+00:00

Actual source code: damped_beam.c
slepc-3.6.1 2015-09-03
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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 damped_beam problem is a QEP from the vibrarion analysis of a beam
     30:    simply supported at both ends and damped in the middle.
     31: */

     33: static char help[] = "NLEVP problem: damped_beam.\n\n"
     34:   "The command line options are:\n"
     35:   "  -n <n> ... dimension of the matrices.\n\n";

     37: #include <slepcpep.h>

     41: int main(int argc,char **argv)
     42: {
     43:   Mat            M,Mo,C,K,Ko,A[3]; /* problem matrices */
     44:   PEP            pep;              /* polynomial eigenproblem solver context */
     45:   IS             isf,isbc,is;
     46:   PetscInt       n=200,nele,Istart,Iend,i,j,mloc,nloc,bc[2];
     47:   PetscReal      width=0.05,height=0.005,glength=1.0,dlen,EI,area,rho;
     48:   PetscScalar    K1[4],K2[4],K2t[4],K3[4],M1[4],M2[4],M2t[4],M3[4],damp=5.0;
     49:   PetscBool      terse;

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

     54:   PetscOptionsGetInt(NULL,"-n",&n,NULL);
     55:   nele = n/2;
     56:   n    = 2*nele;
     57:   PetscPrintf(PETSC_COMM_WORLD,"\nSimply supported beam damped in the middle, n=%D (nele=%D)\n\n",n,nele);

     59:   dlen = glength/nele;
     60:   EI   = 7e10*width*height*height*height/12.0;
     61:   area = width*height;
     62:   rho  = 0.674/(area*glength);

     64:   K1[0]  =  12;  K1[1]  =   6*dlen;  K1[2]  =   6*dlen;  K1[3]  =  4*dlen*dlen;
     65:   K2[0]  = -12;  K2[1]  =   6*dlen;  K2[2]  =  -6*dlen;  K2[3]  =  2*dlen*dlen;
     66:   K2t[0] = -12;  K2t[1] =  -6*dlen;  K2t[2] =   6*dlen;  K2t[3] =  2*dlen*dlen;
     67:   K3[0]  =  12;  K3[1]  =  -6*dlen;  K3[2]  =  -6*dlen;  K3[3]  =  4*dlen*dlen;
     68:   M1[0]  = 156;  M1[1]  =  22*dlen;  M1[2]  =  22*dlen;  M1[3]  =  4*dlen*dlen;
     69:   M2[0]  =  54;  M2[1]  = -13*dlen;  M2[2]  =  13*dlen;  M2[3]  = -3*dlen*dlen;
     70:   M2t[0] =  54;  M2t[1] =  13*dlen;  M2t[2] = -13*dlen;  M2t[3] = -3*dlen*dlen;
     71:   M3[0]  = 156;  M3[1]  = -22*dlen;  M3[2]  = -22*dlen;  M3[3]  =  4*dlen*dlen;

     73:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     74:      Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
     75:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     77:   /* K is block-tridiagonal */
     78:   MatCreate(PETSC_COMM_WORLD,&Ko);
     79:   MatSetSizes(Ko,PETSC_DECIDE,PETSC_DECIDE,n+2,n+2);
     80:   MatSetBlockSize(Ko,2);
     81:   MatSetFromOptions(Ko);
     82:   MatSetUp(Ko);
     83:
     84:   MatGetOwnershipRange(Ko,&Istart,&Iend);
     85:   for (i=Istart/2;i<Iend/2;i++) {
     86:     if (i>0) {
     87:       j = i-1;
     88:       MatSetValuesBlocked(Ko,1,&i,1,&j,K2t,ADD_VALUES);
     89:       MatSetValuesBlocked(Ko,1,&i,1,&i,K3,ADD_VALUES);
     90:     }
     91:     if (i<nele) {
     92:       j = i+1;
     93:       MatSetValuesBlocked(Ko,1,&i,1,&j,K2,ADD_VALUES);
     94:       MatSetValuesBlocked(Ko,1,&i,1,&i,K1,ADD_VALUES);
     95:     }
     96:   }
     97:   MatAssemblyBegin(Ko,MAT_FINAL_ASSEMBLY);
     98:   MatAssemblyEnd(Ko,MAT_FINAL_ASSEMBLY);
     99:   MatScale(Ko,EI/(dlen*dlen*dlen));

    101:   /* M is block-tridiagonal */
    102:   MatCreate(PETSC_COMM_WORLD,&Mo);
    103:   MatSetSizes(Mo,PETSC_DECIDE,PETSC_DECIDE,n+2,n+2);
    104:   MatSetBlockSize(Mo,2);
    105:   MatSetFromOptions(Mo);
    106:   MatSetUp(Mo);

    108:   MatGetOwnershipRange(Mo,&Istart,&Iend);
    109:   for (i=Istart/2;i<Iend/2;i++) {
    110:     if (i>0) {
    111:       j = i-1;
    112:       MatSetValuesBlocked(Mo,1,&i,1,&j,M2t,ADD_VALUES);
    113:       MatSetValuesBlocked(Mo,1,&i,1,&i,M3,ADD_VALUES);
    114:     }
    115:     if (i<nele) {
    116:       j = i+1;
    117:       MatSetValuesBlocked(Mo,1,&i,1,&j,M2,ADD_VALUES);
    118:       MatSetValuesBlocked(Mo,1,&i,1,&i,M1,ADD_VALUES);
    119:     }
    120:   }
    121:   MatAssemblyBegin(Mo,MAT_FINAL_ASSEMBLY);
    122:   MatAssemblyEnd(Mo,MAT_FINAL_ASSEMBLY);
    123:   MatScale(Mo,rho*area*dlen/420);

    125:   /* remove rows/columns from K and M corresponding to boundary conditions */
    126:   ISCreateStride(PETSC_COMM_WORLD,Iend-Istart,Istart,1,&isf);
    127:   bc[0] = 0; bc[1] = n;
    128:   ISCreateGeneral(PETSC_COMM_SELF,2,bc,PETSC_USE_POINTER,&isbc);
    129:   ISDifference(isf,isbc,&is);
    130:   MatGetSubMatrix(Ko,is,is,MAT_INITIAL_MATRIX,&K);
    131:   MatGetSubMatrix(Mo,is,is,MAT_INITIAL_MATRIX,&M);
    132:   MatGetLocalSize(M,&mloc,&nloc);

    134:   /* C is zero except for the (nele,nele)-entry */
    135:   MatCreate(PETSC_COMM_WORLD,&C);
    136:   MatSetSizes(C,mloc,nloc,PETSC_DECIDE,PETSC_DECIDE);
    137:   MatSetFromOptions(C);
    138:   MatSetUp(C);
    139:
    140:   MatGetOwnershipRange(C,&Istart,&Iend);
    141:   if (nele-1>=Istart && nele-1<Iend) {
    142:     MatSetValue(C,nele-1,nele-1,damp,INSERT_VALUES);
    143:   }
    144:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    145:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    146:
    147:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    148:                 Create the eigensolver and solve the problem
    149:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    151:   PEPCreate(PETSC_COMM_WORLD,&pep);
    152:   A[0] = K; A[1] = C; A[2] = M;
    153:   PEPSetOperators(pep,3,A);
    154:   PEPSetFromOptions(pep);
    155:   PEPSolve(pep);

    157:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    158:                     Display solution and clean up
    159:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    160:
    161:   /* show detailed info unless -terse option is given by user */
    162:   PetscOptionsHasName(NULL,"-terse",&terse);
    163:   if (terse) {
    164:     PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL);
    165:   } else {
    166:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    167:     PEPReasonView(pep,PETSC_VIEWER_STDOUT_WORLD);
    168:     PEPErrorView(pep,PEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD);
    169:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    170:   }
    171:   PEPDestroy(&pep);
    172:   ISDestroy(&isf);
    173:   ISDestroy(&isbc);
    174:   ISDestroy(&is);
    175:   MatDestroy(&M);
    176:   MatDestroy(&C);
    177:   MatDestroy(&K);
    178:   MatDestroy(&Ko);
    179:   MatDestroy(&Mo);
    180:   SlepcFinalize();
    181:   return 0;
    182: }