Date: 2026-05-01T10:02:07+00:00

Actual source code: damped_beam.c

      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:   PetscFunctionBeginUser;
     39:   PetscCall(SlepcInitialize(&argc,&argv,NULL,help));

     41:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     42:   nele = n/2;
     43:   n    = 2*nele;
     44:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nSimply supported beam damped in the middle, n=%" PetscInt_FMT " (nele=%" PetscInt_FMT ")\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:   PetscCall(MatCreate(PETSC_COMM_WORLD,&Ko));
     66:   PetscCall(MatSetSizes(Ko,PETSC_DECIDE,PETSC_DECIDE,n+2,n+2));
     67:   PetscCall(MatSetBlockSize(Ko,2));
     68:   PetscCall(MatSetFromOptions(Ko));

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

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

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

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

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

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

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

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

    139:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    140:                     Display solution and clean up
    141:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

    165: /*TEST

    167:    testset:
    168:       args: -pep_nev 2 -pep_ncv 12 -pep_target 0 -terse
    169:       requires: !single
    170:       output_file: output/damped_beam_1.out
    171:       test:
    172:          suffix: 1
    173:          args: -pep_type {{toar linear}} -st_type sinvert
    174:       test:
    175:          suffix: 1_qarnoldi
    176:          args: -pep_type qarnoldi -pep_qarnoldi_locking 0 -st_type sinvert
    177:       test:
    178:          suffix: 1_jd
    179:          args: -pep_type jd
    180:          filter: sed -e "s/23066i/23065i/"

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

    196: TEST*/