Date: 2017-05-17T08:27:09+00:00

Actual source code: planar_waveguide.c
slepc-3.7.4 2017-05-17
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-2016, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.

      8:    SLEPc is free software: you can redistribute it and/or modify it under  the
      9:    terms of version 3 of the GNU Lesser General Public License as published by
     10:    the Free Software Foundation.

     12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
     13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
     14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
     15:    more details.

     17:    You  should have received a copy of the GNU Lesser General  Public  License
     18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
     19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     20: */
     21: /*
     22:    This example implements one of the problems found at
     23:        NLEVP: A Collection of Nonlinear Eigenvalue Problems,
     24:        The University of Manchester.
     25:    The details of the collection can be found at:
     26:        [1] T. Betcke et al., "NLEVP: A Collection of Nonlinear Eigenvalue
     27:            Problems", ACM Trans. Math. Software 39(2), Article 7, 2013.

     29:    The planar_waveguide problem is a quartic PEP with symmetric matrices,
     30:    arising from a finite element solution of the propagation constants in a
     31:    six-layer planar waveguide.
     32: */

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

     38: #include <slepcpep.h>

     40: #define NMAT 5
     41: #define NL   6

     45: int main(int argc,char **argv)
     46: {
     47:   Mat            A[NMAT];         /* problem matrices */
     48:   PEP            pep;             /* polynomial eigenproblem solver context */
     49:   PetscInt       n=128,nlocal,k,Istart,Iend,i,j,start_ct,end_ct;
     50:   PetscReal      w=9.92918,a=0.0,b=2.0,h,deltasq;
     51:   PetscReal      nref[NL],K2[NL],q[NL],*md,*supd,*subd;
     52:   PetscScalar    v,alpha;
     53:   PetscBool      terse;

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

     58:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
     59:   n = (n/4)*4;
     60:   PetscPrintf(PETSC_COMM_WORLD,"\nPlanar waveguide, n=%D\n\n",n+1);
     61:   h = (b-a)/n;
     62:   nlocal = (n/4)-1;

     64:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     65:           Set waveguide parameters used in construction of matrices
     66:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     68:   /* refractive indices in each layer */
     69:   nref[0] = 1.5;
     70:   nref[1] = 1.66;
     71:   nref[2] = 1.6;
     72:   nref[3] = 1.53;
     73:   nref[4] = 1.66;
     74:   nref[5] = 1.0;

     76:   for (i=0;i<NL;i++) K2[i] = w*w*nref[i]*nref[i];
     77:   deltasq = K2[0] - K2[NL-1];
     78:   for (i=0;i<NL;i++) q[i] = K2[i] - (K2[0] + K2[NL-1])/2;

     80:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     81:                      Compute the polynomial matrices
     82:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

     84:   /* initialize matrices */
     85:   for (i=0;i<NMAT;i++) {
     86:     MatCreate(PETSC_COMM_WORLD,&A[i]);
     87:     MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n+1,n+1);
     88:     MatSetFromOptions(A[i]);
     89:     MatSetUp(A[i]);
     90:   }
     91:   MatGetOwnershipRange(A[0],&Istart,&Iend);

     93:   /* A0 */
     94:   alpha = (h/6)*(deltasq*deltasq/16);
     95:   for (i=Istart;i<Iend;i++) {
     96:     v = 4.0;
     97:     if (i==0 || i==n) v = 2.0;
     98:     MatSetValue(A[0],i,i,v*alpha,INSERT_VALUES);
     99:     if (i>0) { MatSetValue(A[0],i,i-1,alpha,INSERT_VALUES); }
    100:     if (i<n) { MatSetValue(A[0],i,i+1,alpha,INSERT_VALUES); }
    101:   }

    103:   /* A1 */
    104:   if (Istart==0) { MatSetValue(A[1],0,0,-deltasq/4,INSERT_VALUES); }
    105:   if (Iend==n+1) { MatSetValue(A[1],n,n,deltasq/4,INSERT_VALUES); }

    107:   /* A2 */
    108:   alpha = 1.0/h;
    109:   for (i=Istart;i<Iend;i++) {
    110:     v = 2.0;
    111:     if (i==0 || i==n) v = 1.0;
    112:     MatSetValue(A[2],i,i,v*alpha,ADD_VALUES);
    113:     if (i>0) { MatSetValue(A[2],i,i-1,-alpha,ADD_VALUES); }
    114:     if (i<n) { MatSetValue(A[2],i,i+1,-alpha,ADD_VALUES); }
    115:   }
    116:   PetscMalloc3(n+1,&md,n+1,&supd,n+1,&subd);

    118:   md[0]   = 2.0*q[1];
    119:   supd[1] = q[1];
    120:   subd[0] = q[1];

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

    124:     end_ct = k*(nlocal+1);
    125:     start_ct = end_ct-nlocal;

    127:     for (j=start_ct;j<end_ct;j++) {
    128:       md[j] = 4*q[k];
    129:       supd[j+1] = q[k];
    130:       subd[j] = q[k];
    131:     }

    133:     if (k < 4) {  /* interface points */
    134:       md[end_ct] = 4*(q[k] + q[k+1])/2.0;
    135:       supd[end_ct+1] = q[k+1];
    136:       subd[end_ct] = q[k+1];
    137:     }

    139:   }

    141:   md[n] = 2*q[NL-2];
    142:   supd[n] = q[NL-2];
    143:   subd[n] = q[NL-2];

    145:   alpha = -h/6.0;
    146:   for (i=Istart;i<Iend;i++) {
    147:     MatSetValue(A[2],i,i,md[i]*alpha,ADD_VALUES);
    148:     if (i>0) { MatSetValue(A[2],i,i-1,subd[i-1]*alpha,ADD_VALUES); }
    149:     if (i<n) { MatSetValue(A[2],i,i+1,supd[i+1]*alpha,ADD_VALUES); }
    150:   }
    151:   PetscFree3(md,supd,subd);

    153:   /* A3 */
    154:   if (Istart==0) { MatSetValue(A[3],0,0,1.0,INSERT_VALUES); }
    155:   if (Iend==n+1) { MatSetValue(A[3],n,n,1.0,INSERT_VALUES); }

    157:   /* A4 */
    158:   alpha = (h/6);
    159:   for (i=Istart;i<Iend;i++) {
    160:     v = 4.0;
    161:     if (i==0 || i==n) v = 2.0;
    162:     MatSetValue(A[4],i,i,v*alpha,INSERT_VALUES);
    163:     if (i>0) { MatSetValue(A[4],i,i-1,alpha,INSERT_VALUES); }
    164:     if (i<n) { MatSetValue(A[4],i,i+1,alpha,INSERT_VALUES); }
    165:   }

    167:   /* assemble matrices */
    168:   for (i=0;i<NMAT;i++) {
    169:     MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY);
    170:   }
    171:   for (i=0;i<NMAT;i++) {
    172:     MatAssemblyEnd(A[i],MAT_FINAL_ASSEMBLY);
    173:   }

    175:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    176:                 Create the eigensolver and solve the problem
    177:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    179:   PEPCreate(PETSC_COMM_WORLD,&pep);
    180:   PEPSetOperators(pep,NMAT,A);
    181:   PEPSetFromOptions(pep);
    182:   PEPSolve(pep);

    184:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    185:                     Display solution and clean up
    186:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    187:
    188:   /* show detailed info unless -terse option is given by user */
    189:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
    190:   if (terse) {
    191:     PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL);
    192:   } else {
    193:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
    194:     PEPReasonView(pep,PETSC_VIEWER_STDOUT_WORLD);
    195:     PEPErrorView(pep,PEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD);
    196:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
    197:   }
    198:   PEPDestroy(&pep);
    199:   for (i=0;i<NMAT;i++) {
    200:     MatDestroy(&A[i]);
    201:   }
    202:   SlepcFinalize();
    203:   return ierr;
    204: }