Actual source code: test11.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[] = "Test the CISS solver with the problem of ex22.\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;
38: Mat Id,A,B,mats[3];
39: FN f1,f2,f3,funs[3];
40: RG rg;
41: KSP *ksp;
42: PC pc;
43: PetscScalar coeffs[2],b;
44: PetscInt n=128,Istart,Iend,i,nsolve;
45: PetscReal tau=0.001,h,a=20,xi;
46: PetscBool terse;
49: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
50: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
51: PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL);
52: PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%D, tau=%g\n\n",n,(double)tau);
53: h = PETSC_PI/(PetscReal)(n+1);
55: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
56: Create nonlinear eigensolver context
57: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
59: NEPCreate(PETSC_COMM_WORLD,&nep);
61: /* Identity matrix */
62: MatCreate(PETSC_COMM_WORLD,&Id);
63: MatSetSizes(Id,PETSC_DECIDE,PETSC_DECIDE,n,n);
64: MatSetFromOptions(Id);
65: MatSetUp(Id);
66: MatGetOwnershipRange(Id,&Istart,&Iend);
67: for (i=Istart;i<Iend;i++) {
68: MatSetValue(Id,i,i,1.0,INSERT_VALUES);
69: }
70: MatAssemblyBegin(Id,MAT_FINAL_ASSEMBLY);
71: MatAssemblyEnd(Id,MAT_FINAL_ASSEMBLY);
72: MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);
74: /* A = 1/h^2*tridiag(1,-2,1) + a*I */
75: MatCreate(PETSC_COMM_WORLD,&A);
76: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
77: MatSetFromOptions(A);
78: MatSetUp(A);
79: MatGetOwnershipRange(A,&Istart,&Iend);
80: for (i=Istart;i<Iend;i++) {
81: if (i>0) { MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES); }
82: if (i<n-1) { MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES); }
83: MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES);
84: }
85: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
86: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
87: MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
89: /* B = diag(b(xi)) */
90: MatCreate(PETSC_COMM_WORLD,&B);
91: MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
92: MatSetFromOptions(B);
93: MatSetUp(B);
94: MatGetOwnershipRange(B,&Istart,&Iend);
95: for (i=Istart;i<Iend;i++) {
96: xi = (i+1)*h;
97: b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
98: MatSetValues(B,1,&i,1,&i,&b,INSERT_VALUES);
99: }
100: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
101: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
102: MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);
104: /* Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda) */
105: FNCreate(PETSC_COMM_WORLD,&f1);
106: FNSetType(f1,FNRATIONAL);
107: coeffs[0] = -1.0; coeffs[1] = 0.0;
108: FNRationalSetNumerator(f1,2,coeffs);
110: FNCreate(PETSC_COMM_WORLD,&f2);
111: FNSetType(f2,FNRATIONAL);
112: coeffs[0] = 1.0;
113: FNRationalSetNumerator(f2,1,coeffs);
115: FNCreate(PETSC_COMM_WORLD,&f3);
116: FNSetType(f3,FNEXP);
117: FNSetScale(f3,-tau,1.0);
119: /* Set the split operator */
120: mats[0] = A; funs[0] = f2;
121: mats[1] = Id; funs[1] = f1;
122: mats[2] = B; funs[2] = f3;
123: NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);
125: /* Customize nonlinear solver; set runtime options */
126: NEPSetType(nep,NEPCISS);
127: NEPSetDimensions(nep,1,24,PETSC_DEFAULT);
128: NEPSetTolerances(nep,1e-9,PETSC_DEFAULT);
129: NEPGetRG(nep,&rg);
130: RGSetType(rg,RGELLIPSE);
131: RGEllipseSetParameters(rg,10.0,9.5,0.1);
132: NEPCISSSetSizes(nep,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,1,PETSC_DEFAULT,PETSC_TRUE);
133: NEPCISSGetKSPs(nep,&nsolve,&ksp);
134: for (i=0;i<nsolve;i++) {
135: KSPSetTolerances(ksp[i],1e-12,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
136: KSPSetType(ksp[i],KSPBCGS);
137: KSPGetPC(ksp[i],&pc);
138: PCSetType(pc,PCSOR);
139: }
140: NEPSetFromOptions(nep);
142: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
143: Solve the eigensystem
144: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
146: PetscPrintf(PETSC_COMM_WORLD," Running CISS with %D KSP solvers\n",nsolve);
147: NEPSolve(nep);
149: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
150: Display solution and clean up
151: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
153: /* show detailed info unless -terse option is given by user */
154: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
155: if (terse) {
156: NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
157: } else {
158: PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
159: NEPReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
160: NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
161: PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
162: }
163: NEPDestroy(&nep);
164: MatDestroy(&Id);
165: MatDestroy(&A);
166: MatDestroy(&B);
167: FNDestroy(&f1);
168: FNDestroy(&f2);
169: FNDestroy(&f3);
170: SlepcFinalize();
171: return ierr;
172: }
174: /*TEST
176: build:
177: requires: complex
179: test:
180: suffix: 1
181: args: -terse
182: requires: complex
184: TEST*/