Actual source code: test11.c
slepc-3.16.2 2022-02-01
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: */
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: NEPCISSExtraction ext;
44: PetscScalar coeffs[2],b;
45: PetscInt n=128,Istart,Iend,i,nsolve;
46: PetscReal tau=0.001,h,a=20,xi;
47: PetscBool flg,terse;
48: PetscErrorCode ierr;
50: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
51: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
52: PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL);
53: PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%D, tau=%g\n\n",n,(double)tau);
54: h = PETSC_PI/(PetscReal)(n+1);
56: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
57: Create nonlinear eigensolver context
58: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
60: NEPCreate(PETSC_COMM_WORLD,&nep);
62: /* Identity matrix */
63: MatCreate(PETSC_COMM_WORLD,&Id);
64: MatSetSizes(Id,PETSC_DECIDE,PETSC_DECIDE,n,n);
65: MatSetFromOptions(Id);
66: MatSetUp(Id);
67: MatGetOwnershipRange(Id,&Istart,&Iend);
68: for (i=Istart;i<Iend;i++) {
69: MatSetValue(Id,i,i,1.0,INSERT_VALUES);
70: }
71: MatAssemblyBegin(Id,MAT_FINAL_ASSEMBLY);
72: MatAssemblyEnd(Id,MAT_FINAL_ASSEMBLY);
73: MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);
75: /* A = 1/h^2*tridiag(1,-2,1) + a*I */
76: MatCreate(PETSC_COMM_WORLD,&A);
77: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
78: MatSetFromOptions(A);
79: MatSetUp(A);
80: MatGetOwnershipRange(A,&Istart,&Iend);
81: for (i=Istart;i<Iend;i++) {
82: if (i>0) { MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES); }
83: if (i<n-1) { MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES); }
84: MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES);
85: }
86: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
87: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
88: MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
90: /* B = diag(b(xi)) */
91: MatCreate(PETSC_COMM_WORLD,&B);
92: MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
93: MatSetFromOptions(B);
94: MatSetUp(B);
95: MatGetOwnershipRange(B,&Istart,&Iend);
96: for (i=Istart;i<Iend;i++) {
97: xi = (i+1)*h;
98: b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
99: MatSetValues(B,1,&i,1,&i,&b,INSERT_VALUES);
100: }
101: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
102: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
103: MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);
105: /* Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda) */
106: FNCreate(PETSC_COMM_WORLD,&f1);
107: FNSetType(f1,FNRATIONAL);
108: coeffs[0] = -1.0; coeffs[1] = 0.0;
109: FNRationalSetNumerator(f1,2,coeffs);
111: FNCreate(PETSC_COMM_WORLD,&f2);
112: FNSetType(f2,FNRATIONAL);
113: coeffs[0] = 1.0;
114: FNRationalSetNumerator(f2,1,coeffs);
116: FNCreate(PETSC_COMM_WORLD,&f3);
117: FNSetType(f3,FNEXP);
118: FNSetScale(f3,-tau,1.0);
120: /* Set the split operator */
121: mats[0] = A; funs[0] = f2;
122: mats[1] = Id; funs[1] = f1;
123: mats[2] = B; funs[2] = f3;
124: NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);
126: /* Customize nonlinear solver; set runtime options */
127: NEPSetType(nep,NEPCISS);
128: NEPSetDimensions(nep,1,24,PETSC_DEFAULT);
129: NEPSetTolerances(nep,1e-9,PETSC_DEFAULT);
130: NEPGetRG(nep,&rg);
131: RGSetType(rg,RGELLIPSE);
132: RGEllipseSetParameters(rg,10.0,9.5,0.1);
133: NEPCISSSetSizes(nep,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,1,PETSC_DEFAULT,PETSC_TRUE);
134: NEPCISSGetKSPs(nep,&nsolve,&ksp);
135: for (i=0;i<nsolve;i++) {
136: KSPSetTolerances(ksp[i],1e-12,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
137: KSPSetType(ksp[i],KSPBCGS);
138: KSPGetPC(ksp[i],&pc);
139: PCSetType(pc,PCSOR);
140: }
141: NEPSetFromOptions(nep);
143: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
144: Solve the eigensystem
145: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
147: PetscObjectTypeCompare((PetscObject)nep,NEPCISS,&flg);
148: if (flg) {
149: NEPCISSGetExtraction(nep,&ext);
150: PetscPrintf(PETSC_COMM_WORLD," Running CISS with %D KSP solvers (%s extraction)\n",nsolve,NEPCISSExtractions[ext]);
151: }
152: NEPSolve(nep);
154: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
155: Display solution and clean up
156: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
158: /* show detailed info unless -terse option is given by user */
159: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
160: if (terse) {
161: NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
162: } else {
163: PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
164: NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
165: NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
166: PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
167: }
168: NEPDestroy(&nep);
169: MatDestroy(&Id);
170: MatDestroy(&A);
171: MatDestroy(&B);
172: FNDestroy(&f1);
173: FNDestroy(&f2);
174: FNDestroy(&f3);
175: SlepcFinalize();
176: return ierr;
177: }
179: /*TEST
181: build:
182: requires: complex
184: testset:
185: args: -nep_ciss_extraction {{ritz hankel caa}} -terse
186: requires: complex !single
187: output_file: output/test11_1.out
188: filter: sed -e "s/([A-Z]* extraction)//"
189: test:
190: suffix: 1
191: args: -nep_ciss_delta 1e-10
192: test:
193: suffix: 2
194: nsize: 2
195: args: -nep_ciss_partitions 2
196: test:
197: suffix: 3
198: args: -nep_ciss_moments 4 -nep_ciss_blocksize 5 -nep_ciss_refine_inner 1 -nep_ciss_refine_blocksize 2
200: test:
201: suffix: 4
202: args: -terse -nep_view
203: requires: complex !single
204: filter: grep -v tolerance
206: TEST*/