Actual source code: planar_waveguide.c

slepc-3.16.1 2021-11-17
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2021, 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;

 43:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

 45:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 46:   n = (n/4)*4;
 47:   PetscPrintf(PETSC_COMM_WORLD,"\nPlanar waveguide, n=%D\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:     MatCreate(PETSC_COMM_WORLD,&A[i]);
 74:     MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n+1,n+1);
 75:     MatSetFromOptions(A[i]);
 76:     MatSetUp(A[i]);
 77:   }
 78:   MatGetOwnershipRange(A[0],&Istart,&Iend);

 80:   /* A0 */
 81:   alpha = (h/6)*(deltasq*deltasq/16);
 82:   for (i=Istart;i<Iend;i++) {
 83:     v = 4.0;
 84:     if (i==0 || i==n) v = 2.0;
 85:     MatSetValue(A[0],i,i,v*alpha,INSERT_VALUES);
 86:     if (i>0) { MatSetValue(A[0],i,i-1,alpha,INSERT_VALUES); }
 87:     if (i<n) { MatSetValue(A[0],i,i+1,alpha,INSERT_VALUES); }
 88:   }

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

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

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

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

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

114:     for (j=start_ct;j<end_ct;j++) {
115:       md[j] = 4*q[k];
116:       supd[j+1] = q[k];
117:       subd[j] = q[k];
118:     }

120:     if (k < 4) {  /* interface points */
121:       md[end_ct] = 4*(q[k] + q[k+1])/2.0;
122:       supd[end_ct+1] = q[k+1];
123:       subd[end_ct] = q[k+1];
124:     }

126:   }

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

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

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

144:   /* A4 */
145:   alpha = (h/6);
146:   for (i=Istart;i<Iend;i++) {
147:     v = 4.0;
148:     if (i==0 || i==n) v = 2.0;
149:     MatSetValue(A[4],i,i,v*alpha,INSERT_VALUES);
150:     if (i>0) { MatSetValue(A[4],i,i-1,alpha,INSERT_VALUES); }
151:     if (i<n) { MatSetValue(A[4],i,i+1,alpha,INSERT_VALUES); }
152:   }

154:   /* assemble matrices */
155:   for (i=0;i<NMAT;i++) {
156:     MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY);
157:   }
158:   for (i=0;i<NMAT;i++) {
159:     MatAssemblyEnd(A[i],MAT_FINAL_ASSEMBLY);
160:   }

162:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
163:                 Create the eigensolver and solve the problem
164:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

166:   PEPCreate(PETSC_COMM_WORLD,&pep);
167:   PEPSetOperators(pep,NMAT,A);
168:   PEPSetFromOptions(pep);
169:   PEPSolve(pep);

171:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
172:                     Display solution and clean up
173:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

175:   /* show detailed info unless -terse option is given by user */
176:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
177:   if (terse) {
178:     PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL);
179:   } else {
180:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
181:     PEPConvergedReasonView(pep,PETSC_VIEWER_STDOUT_WORLD);
182:     PEPErrorView(pep,PEP_ERROR_BACKWARD,PETSC_VIEWER_STDOUT_WORLD);
183:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
184:   }
185:   PEPDestroy(&pep);
186:   for (i=0;i<NMAT;i++) {
187:     MatDestroy(&A[i]);
188:   }
189:   SlepcFinalize();
190:   return ierr;
191: }

193: /*TEST

195:    test:
196:       suffix: 1
197:       args: -pep_type {{toar linear}} -pep_nev 4 -st_type sinvert -terse
198:       requires: !single

200: TEST*/