Actual source code: damped_beam.c
slepc-3.10.1 2018-10-23
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2018, 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 damped_beam problem is a QEP from the vibrarion analysis of a beam
     19:    simply supported at both ends and damped in the middle.
     20: */

     22: static char help[] = "Quadratic eigenproblem from the vibrarion analysis of a beam.\n\n"
     23:   "The command line options are:\n"
     24:   "  -n <n> ... dimension of the matrices.\n\n";

     26: #include <slepcpep.h>

     28: int main(int argc,char **argv)
     29: {
     30:   Mat            M,Mo,C,K,Ko,A[3]; /* problem matrices */
     31:   PEP            pep;              /* polynomial eigenproblem solver context */
     32:   IS             isf,isbc,is;
     33:   PetscInt       n=200,nele,Istart,Iend,i,j,mloc,nloc,bc[2];
     34:   PetscReal      width=0.05,height=0.005,glength=1.0,dlen,EI,area,rho;
     35:   PetscScalar    K1[4],K2[4],K2t[4],K3[4],M1[4],M2[4],M2t[4],M3[4],damp=5.0;
     36:   PetscBool      terse;

     39:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

     41:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     42:   nele = n/2;
     43:   n    = 2*nele;
     44:   PetscPrintf(PETSC_COMM_WORLD,"\nSimply supported beam damped in the middle, n=%D (nele=%D)\n\n",n,nele);

     46:   dlen = glength/nele;
     47:   EI   = 7e10*width*height*height*height/12.0;
     48:   area = width*height;
     49:   rho  = 0.674/(area*glength);

     51:   K1[0]  =  12;  K1[1]  =   6*dlen;  K1[2]  =   6*dlen;  K1[3]  =  4*dlen*dlen;
     52:   K2[0]  = -12;  K2[1]  =   6*dlen;  K2[2]  =  -6*dlen;  K2[3]  =  2*dlen*dlen;
     53:   K2t[0] = -12;  K2t[1] =  -6*dlen;  K2t[2] =   6*dlen;  K2t[3] =  2*dlen*dlen;
     54:   K3[0]  =  12;  K3[1]  =  -6*dlen;  K3[2]  =  -6*dlen;  K3[3]  =  4*dlen*dlen;
     55:   M1[0]  = 156;  M1[1]  =  22*dlen;  M1[2]  =  22*dlen;  M1[3]  =  4*dlen*dlen;
     56:   M2[0]  =  54;  M2[1]  = -13*dlen;  M2[2]  =  13*dlen;  M2[3]  = -3*dlen*dlen;
     57:   M2t[0] =  54;  M2t[1] =  13*dlen;  M2t[2] = -13*dlen;  M2t[3] = -3*dlen*dlen;
     58:   M3[0]  = 156;  M3[1]  = -22*dlen;  M3[2]  = -22*dlen;  M3[3]  =  4*dlen*dlen;

     60:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     61:      Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
     62:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     64:   /* K is block-tridiagonal */
     65:   MatCreate(PETSC_COMM_WORLD,&Ko);
     66:   MatSetSizes(Ko,PETSC_DECIDE,PETSC_DECIDE,n+2,n+2);
     67:   MatSetBlockSize(Ko,2);
     68:   MatSetFromOptions(Ko);
     69:   MatSetUp(Ko);

     71:   MatGetOwnershipRange(Ko,&Istart,&Iend);
     72:   for (i=Istart/2;i<Iend/2;i++) {
     73:     if (i>0) {
     74:       j = i-1;
     75:       MatSetValuesBlocked(Ko,1,&i,1,&j,K2t,ADD_VALUES);
     76:       MatSetValuesBlocked(Ko,1,&i,1,&i,K3,ADD_VALUES);
     77:     }
     78:     if (i<nele) {
     79:       j = i+1;
     80:       MatSetValuesBlocked(Ko,1,&i,1,&j,K2,ADD_VALUES);
     81:       MatSetValuesBlocked(Ko,1,&i,1,&i,K1,ADD_VALUES);
     82:     }
     83:   }
     84:   MatAssemblyBegin(Ko,MAT_FINAL_ASSEMBLY);
     85:   MatAssemblyEnd(Ko,MAT_FINAL_ASSEMBLY);
     86:   MatScale(Ko,EI/(dlen*dlen*dlen));

     88:   /* M is block-tridiagonal */
     89:   MatCreate(PETSC_COMM_WORLD,&Mo);
     90:   MatSetSizes(Mo,PETSC_DECIDE,PETSC_DECIDE,n+2,n+2);
     91:   MatSetBlockSize(Mo,2);
     92:   MatSetFromOptions(Mo);
     93:   MatSetUp(Mo);

     95:   MatGetOwnershipRange(Mo,&Istart,&Iend);
     96:   for (i=Istart/2;i<Iend/2;i++) {
     97:     if (i>0) {
     98:       j = i-1;
     99:       MatSetValuesBlocked(Mo,1,&i,1,&j,M2t,ADD_VALUES);
    100:       MatSetValuesBlocked(Mo,1,&i,1,&i,M3,ADD_VALUES);
    101:     }
    102:     if (i<nele) {
    103:       j = i+1;
    104:       MatSetValuesBlocked(Mo,1,&i,1,&j,M2,ADD_VALUES);
    105:       MatSetValuesBlocked(Mo,1,&i,1,&i,M1,ADD_VALUES);
    106:     }
    107:   }
    108:   MatAssemblyBegin(Mo,MAT_FINAL_ASSEMBLY);
    109:   MatAssemblyEnd(Mo,MAT_FINAL_ASSEMBLY);
    110:   MatScale(Mo,rho*area*dlen/420);

    112:   /* remove rows/columns from K and M corresponding to boundary conditions */
    113:   ISCreateStride(PETSC_COMM_WORLD,Iend-Istart,Istart,1,&isf);
    114:   bc[0] = 0; bc[1] = n;
    115:   ISCreateGeneral(PETSC_COMM_SELF,2,bc,PETSC_USE_POINTER,&isbc);
    116:   ISDifference(isf,isbc,&is);
    117:   MatCreateSubMatrix(Ko,is,is,MAT_INITIAL_MATRIX,&K);
    118:   MatCreateSubMatrix(Mo,is,is,MAT_INITIAL_MATRIX,&M);
    119:   MatGetLocalSize(M,&mloc,&nloc);

    121:   /* C is zero except for the (nele,nele)-entry */
    122:   MatCreate(PETSC_COMM_WORLD,&C);
    123:   MatSetSizes(C,mloc,nloc,PETSC_DECIDE,PETSC_DECIDE);
    124:   MatSetFromOptions(C);
    125:   MatSetUp(C);

    127:   MatGetOwnershipRange(C,&Istart,&Iend);
    128:   if (nele-1>=Istart && nele-1<Iend) {
    129:     MatSetValue(C,nele-1,nele-1,damp,INSERT_VALUES);
    130:   }
    131:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    132:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

    134:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    135:                 Create the eigensolver and solve the problem
    136:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    138:   PEPCreate(PETSC_COMM_WORLD,&pep);
    139:   A[0] = K; A[1] = C; A[2] = M;
    140:   PEPSetOperators(pep,3,A);
    141:   PEPSetFromOptions(pep);
    142:   PEPSolve(pep);

    144:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    145:                     Display solution and clean up
    146:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    148:   /* show detailed info unless -terse option is given by user */
    149:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    150:   if (terse) {
    151:     PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL);
    152:   } else {
    153:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    154:     PEPReasonView(pep,PETSC_VIEWER_STDOUT_WORLD);
    155:     PEPErrorView(pep,PEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD);
    156:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    157:   }
    158:   PEPDestroy(&pep);
    159:   ISDestroy(&isf);
    160:   ISDestroy(&isbc);
    161:   ISDestroy(&is);
    162:   MatDestroy(&M);
    163:   MatDestroy(&C);
    164:   MatDestroy(&K);
    165:   MatDestroy(&Ko);
    166:   MatDestroy(&Mo);
    167:   SlepcFinalize();
    168:   return ierr;
    169: }

    171: /*TEST

    173:    testset:
    174:       args: -pep_nev 2 -pep_ncv 12 -pep_target 0 -st_type sinvert -terse
    175:       requires: !complex !single
    176:       output_file: output/damped_beam_1.out
    177:       test:
    178:          suffix: 1
    179:          args: -pep_type {{toar linear}}
    180:       test:
    181:          suffix: 1_qarnoldi
    182:          args: -pep_type qarnoldi -pep_qarnoldi_locking 0

    184:    testset:
    185:       args: -pep_nev 2 -pep_ncv 12 -pep_target 1i -terse
    186:       requires: complex !single
    187:       output_file: output/damped_beam_1.out
    188:       test:
    189:          suffix: 1_complex
    190:          args: -pep_type {{toar linear}} -st_type sinvert
    191:       test:
    192:          suffix: 1_qarnoldi_complex
    193:          args: -pep_type qarnoldi -pep_qarnoldi_locking 0 -st_type sinvert
    194:       test:
    195:          suffix: 1_jd_complex
    196:          args: -pep_type jd -pep_tol 1e-9

    198: TEST*/