Date: 2023-09-05T10:18:34+00:00

Actual source code: wiresaw.c
slepc-3.19.2 2023-09-05
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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 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,(char*)0,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));
     60:   PetscCall(MatSetUp(K));

     62:   PetscCall(MatGetOwnershipRange(K,&Istart,&Iend));
     63:   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));

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

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

     75:   PetscCall(MatGetOwnershipRange(D,&Istart,&Iend));
     76:   for (j=Istart;j<Iend;j++) {
     77:     for (k=0;k<n;k++) {
     78:       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));
     79:     }
     80:   }

     82:   PetscCall(MatAssemblyBegin(D,MAT_FINAL_ASSEMBLY));
     83:   PetscCall(MatAssemblyEnd(D,MAT_FINAL_ASSEMBLY));
     84:   PetscCall(MatScale(D,0.5));

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

     97:   /* add damping */
     98:   if (eta>0.0) {
     99:     PetscCall(MatAXPY(K,eta,D,DIFFERENT_NONZERO_PATTERN)); /* K = K + eta*D */
    100:     PetscCall(MatShift(D,eta)); /* D = D + eta*eye(n) */
    101:   }

    103:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    104:                 Create the eigensolver and solve the problem
    105:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

    115:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    116:                     Display solution and clean up
    117:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    119:   /* show detailed info unless -terse option is given by user */
    120:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    121:   if (terse) PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL));
    122:   else {
    123:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    124:     PetscCall(PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD));
    125:     PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD));
    126:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    127:   }
    128:   PetscCall(PEPDestroy(&pep));
    129:   PetscCall(MatDestroy(&M));
    130:   PetscCall(MatDestroy(&D));
    131:   PetscCall(MatDestroy(&K));
    132:   PetscCall(SlepcFinalize());
    133:   return 0;
    134: }

    136: /*TEST

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

    152: TEST*/