Actual source code: ex22.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: */
11: static char help[] = "Delay differential equation.\n\n"
12: "The command line options are:\n"
13: " -n <n>, where <n> = number of grid subdivisions.\n"
14: " -tau <tau>, where <tau> is the delay parameter.\n\n";
16: /*
17: Solve parabolic partial differential equation with time delay tau
19: u_t = u_xx + a*u(t) + b*u(t-tau)
20: u(0,t) = u(pi,t) = 0
22: with a = 20 and b(x) = -4.1+x*(1-exp(x-pi)).
24: Discretization leads to a DDE of dimension n
26: -u' = A*u(t) + B*u(t-tau)
28: which results in the nonlinear eigenproblem
30: (-lambda*I + A + exp(-tau*lambda)*B)*u = 0
31: */
33: #include <slepcnep.h>
35: int main(int argc,char **argv)
36: {
37: NEP nep; /* nonlinear eigensolver context */
38: Mat Id,A,B; /* problem matrices */
39: FN f1,f2,f3; /* functions to define the nonlinear operator */
40: Mat mats[3];
41: FN funs[3];
42: PetscScalar coeffs[2],b;
43: PetscInt n=128,nev,Istart,Iend,i;
44: PetscReal tau=0.001,h,a=20,xi;
45: PetscBool terse;
48: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
49: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
50: PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL);
51: PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%D, tau=%g\n\n",n,(double)tau);
52: h = PETSC_PI/(PetscReal)(n+1);
54: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
55: Create nonlinear eigensolver context
56: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
58: NEPCreate(PETSC_COMM_WORLD,&nep);
60: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
61: Create problem matrices and coefficient functions. Pass them to NEP
62: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
64: /*
65: Identity matrix
66: */
67: MatCreate(PETSC_COMM_WORLD,&Id);
68: MatSetSizes(Id,PETSC_DECIDE,PETSC_DECIDE,n,n);
69: MatSetFromOptions(Id);
70: MatSetUp(Id);
71: MatGetOwnershipRange(Id,&Istart,&Iend);
72: for (i=Istart;i<Iend;i++) {
73: MatSetValue(Id,i,i,1.0,INSERT_VALUES);
74: }
75: MatAssemblyBegin(Id,MAT_FINAL_ASSEMBLY);
76: MatAssemblyEnd(Id,MAT_FINAL_ASSEMBLY);
77: MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);
79: /*
80: A = 1/h^2*tridiag(1,-2,1) + a*I
81: */
82: MatCreate(PETSC_COMM_WORLD,&A);
83: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
84: MatSetFromOptions(A);
85: MatSetUp(A);
86: MatGetOwnershipRange(A,&Istart,&Iend);
87: for (i=Istart;i<Iend;i++) {
88: if (i>0) { MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES); }
89: if (i<n-1) { MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES); }
90: MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES);
91: }
92: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
93: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
94: MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
96: /*
97: B = diag(b(xi))
98: */
99: MatCreate(PETSC_COMM_WORLD,&B);
100: MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
101: MatSetFromOptions(B);
102: MatSetUp(B);
103: MatGetOwnershipRange(B,&Istart,&Iend);
104: for (i=Istart;i<Iend;i++) {
105: xi = (i+1)*h;
106: b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
107: MatSetValue(B,i,i,b,INSERT_VALUES);
108: }
109: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
110: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
111: MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);
113: /*
114: Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda)
115: */
116: FNCreate(PETSC_COMM_WORLD,&f1);
117: FNSetType(f1,FNRATIONAL);
118: coeffs[0] = -1.0; coeffs[1] = 0.0;
119: FNRationalSetNumerator(f1,2,coeffs);
121: FNCreate(PETSC_COMM_WORLD,&f2);
122: FNSetType(f2,FNRATIONAL);
123: coeffs[0] = 1.0;
124: FNRationalSetNumerator(f2,1,coeffs);
126: FNCreate(PETSC_COMM_WORLD,&f3);
127: FNSetType(f3,FNEXP);
128: FNSetScale(f3,-tau,1.0);
130: /*
131: Set the split operator. Note that A is passed first so that
132: SUBSET_NONZERO_PATTERN can be used
133: */
134: mats[0] = A; funs[0] = f2;
135: mats[1] = Id; funs[1] = f1;
136: mats[2] = B; funs[2] = f3;
137: NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);
139: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
140: Customize nonlinear solver; set runtime options
141: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
143: NEPSetTolerances(nep,1e-9,PETSC_DEFAULT);
144: NEPSetDimensions(nep,1,PETSC_DEFAULT,PETSC_DEFAULT);
145: NEPRIISetLagPreconditioner(nep,0);
147: /*
148: Set solver parameters at runtime
149: */
150: NEPSetFromOptions(nep);
152: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
153: Solve the eigensystem
154: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
156: NEPSolve(nep);
157: NEPGetDimensions(nep,&nev,NULL,NULL);
158: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);
160: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
161: Display solution and clean up
162: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
164: /* show detailed info unless -terse option is given by user */
165: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
166: if (terse) {
167: NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
168: } else {
169: PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
170: NEPReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
171: NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
172: PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
173: }
174: NEPDestroy(&nep);
175: MatDestroy(&Id);
176: MatDestroy(&A);
177: MatDestroy(&B);
178: FNDestroy(&f1);
179: FNDestroy(&f2);
180: FNDestroy(&f3);
181: SlepcFinalize();
182: return ierr;
183: }
185: /*TEST
187: testset:
188: args: -terse
189: requires: !single
190: output_file: output/ex22_1.out
191: test:
192: suffix: 1
193: args: -nep_type {{rii slp narnoldi}}
195: test:
196: suffix: 1_ciss
197: args: -nep_type ciss -rg_type ellipse -rg_ellipse_center 10 -rg_ellipse_radius 9.5 -nep_ncv 24 -terse
198: requires: complex
200: test:
201: suffix: 2
202: args: -nep_type interpol -nep_interpol_pep_extract {{none norm residual}} -rg_type interval -rg_interval_endpoints 5,20,-.1,.1 -nep_nev 3 -nep_target 5 -terse
203: requires: !single
205: test:
206: suffix: 3
207: args: -n 512 -nep_target 10 -nep_nev 3 -nep_type {{rii slp narnoldi}} -terse
208: requires: !single
210: TEST*/