Date: 2026-03-31T13:23:04+00:00

Actual source code: wiresaw.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 two 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:    WIRESAW1 is a gyroscopic QEP from vibration analysis of a wiresaw,
     19:    where the parameter V represents the speed of the wire. When the
     20:    parameter eta is nonzero, then it turns into the WIRESAW2 problem
     21:    (with added viscous damping, e.g. eta=0.8).

     23:        [2] S. Wei and I. Kao, "Vibration analysis of wire and frequency
     24:            response in the modern wiresaw manufacturing process", J. Sound
     25:            Vib. 213(5):1383-1395, 2000.
     26: */

     28: static char help[] = "Vibration analysis of a wiresaw.\n\n"
     29:   "The command line options are:\n"
     30:   "  -n <n> ... dimension of the matrices (default 10).\n"
     31:   "  -v <value> ... velocity of the wire (default 0.01).\n"
     32:   "  -eta <value> ... viscous damping (default 0.0).\n\n";

     34: #include <slepcpep.h>

     36: int main(int argc,char **argv)
     37: {
     38:   Mat            M,D,K,A[3];      /* problem matrices */
     39:   PEP            pep;             /* polynomial eigenproblem solver context */
     40:   PetscInt       n=10,Istart,Iend,j,k;
     41:   PetscReal      v=0.01,eta=0.0;
     42:   PetscBool      terse;

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

     47:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     48:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-v",&v,NULL));
     49:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-eta",&eta,NULL));
     50:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nVibration analysis of a wiresaw, n=%" PetscInt_FMT " v=%g eta=%g\n\n",n,(double)v,(double)eta));

     52:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     53:      Compute the matrices that define the eigensystem, (k^2*M+k*D+K)x=0
     54:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     56:   /* K is a diagonal matrix */
     57:   PetscCall(MatCreate(PETSC_COMM_WORLD,&K));
     58:   PetscCall(MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,n,n));
     59:   PetscCall(MatSetFromOptions(K));

     61:   PetscCall(MatGetOwnershipRange(K,&Istart,&Iend));
     62:   for (j=Istart;j<Iend;j++) PetscCall(MatSetValue(K,j,j,(j+1)*(j+1)*PETSC_PI*PETSC_PI*(1.0-v*v),INSERT_VALUES));

     64:   PetscCall(MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY));
     65:   PetscCall(MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY));
     66:   PetscCall(MatScale(K,0.5));

     68:   /* D is a tridiagonal */
     69:   PetscCall(MatCreate(PETSC_COMM_WORLD,&D));
     70:   PetscCall(MatSetSizes(D,PETSC_DECIDE,PETSC_DECIDE,n,n));
     71:   PetscCall(MatSetFromOptions(D));

     73:   PetscCall(MatGetOwnershipRange(D,&Istart,&Iend));
     74:   for (j=Istart;j<Iend;j++) {
     75:     for (k=0;k<n;k++) {
     76:       if ((j+k)%2) PetscCall(MatSetValue(D,j,k,8.0*(j+1)*(k+1)*v/((j+1)*(j+1)-(k+1)*(k+1)),INSERT_VALUES));
     77:     }
     78:   }

     80:   PetscCall(MatAssemblyBegin(D,MAT_FINAL_ASSEMBLY));
     81:   PetscCall(MatAssemblyEnd(D,MAT_FINAL_ASSEMBLY));
     82:   PetscCall(MatScale(D,0.5));

     84:   /* M is a diagonal matrix */
     85:   PetscCall(MatCreate(PETSC_COMM_WORLD,&M));
     86:   PetscCall(MatSetSizes(M,PETSC_DECIDE,PETSC_DECIDE,n,n));
     87:   PetscCall(MatSetFromOptions(M));
     88:   PetscCall(MatGetOwnershipRange(M,&Istart,&Iend));
     89:   for (j=Istart;j<Iend;j++) PetscCall(MatSetValue(M,j,j,1.0,INSERT_VALUES));
     90:   PetscCall(MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY));
     91:   PetscCall(MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY));
     92:   PetscCall(MatScale(M,0.5));

     94:   /* add damping */
     95:   if (eta>0.0) {
     96:     PetscCall(MatAXPY(K,eta,D,DIFFERENT_NONZERO_PATTERN)); /* K = K + eta*D */
     97:     PetscCall(MatShift(D,eta)); /* D = D + eta*eye(n) */
     98:   }

    100:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    101:                 Create the eigensolver and solve the problem
    102:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    104:   PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep));
    105:   A[0] = K; A[1] = D; A[2] = M;
    106:   PetscCall(PEPSetOperators(pep,3,A));
    107:   if (eta==0.0) PetscCall(PEPSetProblemType(pep,PEP_GYROSCOPIC));
    108:   else PetscCall(PEPSetProblemType(pep,PEP_GENERAL));
    109:   PetscCall(PEPSetFromOptions(pep));
    110:   PetscCall(PEPSolve(pep));

    112:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    113:                     Display solution and clean up
    114:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    116:   /* show detailed info unless -terse option is given by user */
    117:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    118:   if (terse) PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL));
    119:   else {
    120:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    121:     PetscCall(PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD));
    122:     PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD));
    123:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    124:   }
    125:   PetscCall(PEPDestroy(&pep));
    126:   PetscCall(MatDestroy(&M));
    127:   PetscCall(MatDestroy(&D));
    128:   PetscCall(MatDestroy(&K));
    129:   PetscCall(SlepcFinalize());
    130:   return 0;
    131: }

    133: /*TEST

    135:    testset:
    136:       args: -pep_nev 4 -terse
    137:       requires: double
    138:       output_file: output/wiresaw_1.out
    139:       test:
    140:          suffix: 1
    141:          args: -pep_type {{toar qarnoldi}}
    142:       test:
    143:          suffix: 1_linear_h1
    144:          args: -pep_type linear -pep_linear_explicitmatrix -pep_linear_linearization 1,0 -pep_linear_st_ksp_type bcgs -pep_linear_st_pc_type kaczmarz
    145:       test:
    146:          suffix: 1_linear_h2
    147:          args: -pep_type linear -pep_linear_explicitmatrix -pep_linear_linearization 0,1
    148:       test:
    149:          suffix: 1_linear_other
    150:          args: -pep_type linear -pep_linear_explicitmatrix -pep_linear_linearization .3,.7

    152:    testset:
    153:       args: -pep_nev 4 -eta 0.1 -terse
    154:       requires: double
    155:       output_file: output/wiresaw_2.out
    156:       test:
    157:          suffix: 2
    158:          args: -pep_type {{toar qarnoldi}}
    159:       test:
    160:          suffix: 2_linear
    161:          args: -pep_type linear -pep_linear_explicitmatrix -pep_linear_linearization {{1,0 0,1}} -pep_linear_st_ksp_type bcgs -pep_linear_st_pc_type kaczmarz
    162:       test:
    163:          suffix: 2_linear_other
    164:          args: -pep_type linear -pep_linear_explicitmatrix -pep_linear_linearization .3,.7

    166: TEST*/