Date: 2026-05-01T10:02:06+00:00

Actual source code: planar_waveguide.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 planar_waveguide problem is a quartic PEP with symmetric matrices,
     19:    arising from a finite element solution of the propagation constants in a
     20:    six-layer planar waveguide.
     21: */

     23: static char help[] = "FEM solution of the propagation constants in a six-layer planar waveguide.\n\n"
     24:   "The command line options are:\n"
     25:   "  -n <n>, the dimension of the matrices.\n\n";

     27: #include <slepcpep.h>

     29: #define NMAT 5
     30: #define NL   6

     32: int main(int argc,char **argv)
     33: {
     34:   Mat            A[NMAT];         /* problem matrices */
     35:   PEP            pep;             /* polynomial eigenproblem solver context */
     36:   PetscInt       n=128,nlocal,k,Istart,Iend,i,j,start_ct,end_ct;
     37:   PetscReal      w=9.92918,a=0.0,b=2.0,h,deltasq;
     38:   PetscReal      nref[NL],K2[NL],q[NL],*md,*supd,*subd;
     39:   PetscScalar    v,alpha;
     40:   PetscBool      terse;

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

     45:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
     46:   n = (n/4)*4;
     47:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nPlanar waveguide, n=%" PetscInt_FMT "\n\n",n+1));
     48:   h = (b-a)/n;
     49:   nlocal = (n/4)-1;

     51:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     52:           Set waveguide parameters used in construction of matrices
     53:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     55:   /* refractive indices in each layer */
     56:   nref[0] = 1.5;
     57:   nref[1] = 1.66;
     58:   nref[2] = 1.6;
     59:   nref[3] = 1.53;
     60:   nref[4] = 1.66;
     61:   nref[5] = 1.0;

     63:   for (i=0;i<NL;i++) K2[i] = w*w*nref[i]*nref[i];
     64:   deltasq = K2[0] - K2[NL-1];
     65:   for (i=0;i<NL;i++) q[i] = K2[i] - (K2[0] + K2[NL-1])/2;

     67:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     68:                      Compute the polynomial matrices
     69:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     71:   /* initialize matrices */
     72:   for (i=0;i<NMAT;i++) {
     73:     PetscCall(MatCreate(PETSC_COMM_WORLD,&A[i]));
     74:     PetscCall(MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n+1,n+1));
     75:     PetscCall(MatSetFromOptions(A[i]));
     76:   }
     77:   PetscCall(MatGetOwnershipRange(A[0],&Istart,&Iend));

     79:   /* A0 */
     80:   alpha = (h/6)*(deltasq*deltasq/16);
     81:   for (i=Istart;i<Iend;i++) {
     82:     v = 4.0;
     83:     if (i==0 || i==n) v = 2.0;
     84:     PetscCall(MatSetValue(A[0],i,i,v*alpha,INSERT_VALUES));
     85:     if (i>0) PetscCall(MatSetValue(A[0],i,i-1,alpha,INSERT_VALUES));
     86:     if (i<n) PetscCall(MatSetValue(A[0],i,i+1,alpha,INSERT_VALUES));
     87:   }

     89:   /* A1 */
     90:   if (Istart==0) PetscCall(MatSetValue(A[1],0,0,-deltasq/4,INSERT_VALUES));
     91:   if (Iend==n+1) PetscCall(MatSetValue(A[1],n,n,deltasq/4,INSERT_VALUES));

     93:   /* A2 */
     94:   alpha = 1.0/h;
     95:   for (i=Istart;i<Iend;i++) {
     96:     v = 2.0;
     97:     if (i==0 || i==n) v = 1.0;
     98:     PetscCall(MatSetValue(A[2],i,i,v*alpha,ADD_VALUES));
     99:     if (i>0) PetscCall(MatSetValue(A[2],i,i-1,-alpha,ADD_VALUES));
    100:     if (i<n) PetscCall(MatSetValue(A[2],i,i+1,-alpha,ADD_VALUES));
    101:   }
    102:   PetscCall(PetscMalloc3(n+1,&md,n+1,&supd,n+1,&subd));

    104:   md[0]   = 2.0*q[1];
    105:   supd[1] = q[1];
    106:   subd[0] = q[1];

    108:   for (k=1;k<=NL-2;k++) {

    110:     end_ct = k*(nlocal+1);
    111:     start_ct = end_ct-nlocal;

    113:     for (j=start_ct;j<end_ct;j++) {
    114:       md[j] = 4*q[k];
    115:       supd[j+1] = q[k];
    116:       subd[j] = q[k];
    117:     }

    119:     if (k < 4) {  /* interface points */
    120:       md[end_ct] = 4*(q[k] + q[k+1])/2.0;
    121:       supd[end_ct+1] = q[k+1];
    122:       subd[end_ct] = q[k+1];
    123:     }

    125:   }

    127:   md[n] = 2*q[NL-2];
    128:   supd[n] = q[NL-2];
    129:   subd[n] = q[NL-2];

    131:   alpha = -h/6.0;
    132:   for (i=Istart;i<Iend;i++) {
    133:     PetscCall(MatSetValue(A[2],i,i,md[i]*alpha,ADD_VALUES));
    134:     if (i>0) PetscCall(MatSetValue(A[2],i,i-1,subd[i-1]*alpha,ADD_VALUES));
    135:     if (i<n) PetscCall(MatSetValue(A[2],i,i+1,supd[i+1]*alpha,ADD_VALUES));
    136:   }
    137:   PetscCall(PetscFree3(md,supd,subd));

    139:   /* A3 */
    140:   if (Istart==0) PetscCall(MatSetValue(A[3],0,0,1.0,INSERT_VALUES));
    141:   if (Iend==n+1) PetscCall(MatSetValue(A[3],n,n,1.0,INSERT_VALUES));

    143:   /* A4 */
    144:   alpha = (h/6);
    145:   for (i=Istart;i<Iend;i++) {
    146:     v = 4.0;
    147:     if (i==0 || i==n) v = 2.0;
    148:     PetscCall(MatSetValue(A[4],i,i,v*alpha,INSERT_VALUES));
    149:     if (i>0) PetscCall(MatSetValue(A[4],i,i-1,alpha,INSERT_VALUES));
    150:     if (i<n) PetscCall(MatSetValue(A[4],i,i+1,alpha,INSERT_VALUES));
    151:   }

    153:   /* assemble matrices */
    154:   for (i=0;i<NMAT;i++) PetscCall(MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY));
    155:   for (i=0;i<NMAT;i++) PetscCall(MatAssemblyEnd(A[i],MAT_FINAL_ASSEMBLY));

    157:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    158:                 Create the eigensolver and solve the problem
    159:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    161:   PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep));
    162:   PetscCall(PEPSetOperators(pep,NMAT,A));
    163:   PetscCall(PEPSetFromOptions(pep));
    164:   PetscCall(PEPSolve(pep));

    166:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    167:                     Display solution and clean up
    168:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    170:   /* show detailed info unless -terse option is given by user */
    171:   PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
    172:   if (terse) PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL));
    173:   else {
    174:     PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
    175:     PetscCall(PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD));
    176:     PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD));
    177:     PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
    178:   }
    179:   PetscCall(PEPDestroy(&pep));
    180:   for (i=0;i<NMAT;i++) PetscCall(MatDestroy(&A[i]));
    181:   PetscCall(SlepcFinalize());
    182:   return 0;
    183: }

    185: /*TEST

    187:    test:
    188:       suffix: 1
    189:       args: -pep_type {{toar linear}} -pep_nev 4 -st_type sinvert -terse
    190:       requires: !single

    192: TEST*/