Date: 2022-03-31T15:29:29+00:00

Actual source code: damped_beam.c
slepc-3.17.0 2022-03-31
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      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 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;

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

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

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

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

     59:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     60:      Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
     61:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

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

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

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

    131:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    132:                 Create the eigensolver and solve the problem
    133:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

    141:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    142:                     Display solution and clean up
    143:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    145:   /* show detailed info unless -terse option is given by user */
    146:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    147:   if (terse) PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL);
    148:   else {
    149:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    150:     PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD);
    151:     PEPErrorView(pep,PEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD);
    152:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    153:   }
    154:   PEPDestroy(&pep);
    155:   ISDestroy(&isf);
    156:   ISDestroy(&isbc);
    157:   ISDestroy(&is);
    158:   MatDestroy(&M);
    159:   MatDestroy(&C);
    160:   MatDestroy(&K);
    161:   MatDestroy(&Ko);
    162:   MatDestroy(&Mo);
    163:   SlepcFinalize();
    164:   return 0;
    165: }

    167: /*TEST

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

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

    197: TEST*/