Actual source code: planar_waveguide.c
slepc-3.11.2 2019-07-30
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2019, 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: PEPReasonView(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: !complex !single
200: TEST*/