Actual source code: ex22.c
slepc-3.18.2 2023-01-26
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-, 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);
49: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
50: PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL);
51: PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%" PetscInt_FMT ", 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: MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,1.0,&Id);
68: MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);
70: /*
71: A = 1/h^2*tridiag(1,-2,1) + a*I
72: */
73: MatCreate(PETSC_COMM_WORLD,&A);
74: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
75: MatSetFromOptions(A);
76: MatSetUp(A);
77: MatGetOwnershipRange(A,&Istart,&Iend);
78: for (i=Istart;i<Iend;i++) {
79: if (i>0) MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES);
80: if (i<n-1) MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES);
81: MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES);
82: }
83: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
84: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
85: MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
87: /*
88: B = diag(b(xi))
89: */
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: MatSetValue(B,i,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: /*
105: Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda)
106: */
107: FNCreate(PETSC_COMM_WORLD,&f1);
108: FNSetType(f1,FNRATIONAL);
109: coeffs[0] = -1.0; coeffs[1] = 0.0;
110: FNRationalSetNumerator(f1,2,coeffs);
112: FNCreate(PETSC_COMM_WORLD,&f2);
113: FNSetType(f2,FNRATIONAL);
114: coeffs[0] = 1.0;
115: FNRationalSetNumerator(f2,1,coeffs);
117: FNCreate(PETSC_COMM_WORLD,&f3);
118: FNSetType(f3,FNEXP);
119: FNSetScale(f3,-tau,1.0);
121: /*
122: Set the split operator. Note that A is passed first so that
123: SUBSET_NONZERO_PATTERN can be used
124: */
125: mats[0] = A; funs[0] = f2;
126: mats[1] = Id; funs[1] = f1;
127: mats[2] = B; funs[2] = f3;
128: NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);
130: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
131: Customize nonlinear solver; set runtime options
132: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
134: NEPSetTolerances(nep,1e-9,PETSC_DEFAULT);
135: NEPSetDimensions(nep,1,PETSC_DEFAULT,PETSC_DEFAULT);
136: NEPRIISetLagPreconditioner(nep,0);
138: /*
139: Set solver parameters at runtime
140: */
141: NEPSetFromOptions(nep);
143: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
144: Solve the eigensystem
145: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
147: NEPSolve(nep);
148: NEPGetDimensions(nep,&nev,NULL,NULL);
149: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);
151: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
152: Display solution and clean up
153: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
155: /* show detailed info unless -terse option is given by user */
156: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
157: if (terse) NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
158: else {
159: PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
160: NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
161: NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
162: PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
163: }
164: NEPDestroy(&nep);
165: MatDestroy(&Id);
166: MatDestroy(&A);
167: MatDestroy(&B);
168: FNDestroy(&f1);
169: FNDestroy(&f2);
170: FNDestroy(&f3);
171: SlepcFinalize();
172: return 0;
173: }
175: /*TEST
177: testset:
178: suffix: 1
179: args: -nep_type {{rii slp narnoldi}} -terse
180: filter: sed -e "s/[+-]0\.0*i//g"
181: requires: !single
183: test:
184: suffix: 1_ciss
185: args: -nep_type ciss -nep_ciss_extraction {{ritz hankel caa}} -rg_type ellipse -rg_ellipse_center 10 -rg_ellipse_radius 9.5 -nep_ncv 24 -terse
186: requires: complex !single
188: test:
189: suffix: 2
190: 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
191: filter: sed -e "s/[+-]0\.0*i//g"
192: requires: !single
194: testset:
195: args: -n 512 -nep_target 10 -nep_nev 3 -terse
196: filter: sed -e "s/[+-]0\.0*i//g"
197: requires: !single
198: output_file: output/ex22_3.out
199: test:
200: suffix: 3
201: args: -nep_type {{rii slp narnoldi}}
202: test:
203: suffix: 3_simpleu
204: args: -nep_type {{rii slp narnoldi}} -nep_deflation_simpleu
205: test:
206: suffix: 3_slp_thres
207: args: -nep_type slp -nep_slp_deflation_threshold 1e-8
208: test:
209: suffix: 3_rii_thres
210: args: -nep_type rii -nep_rii_deflation_threshold 1e-8
212: test:
213: suffix: 4
214: args: -nep_type interpol -rg_type interval -rg_interval_endpoints 5,20,-.1,.1 -nep_nev 3 -nep_target 5 -terse -nep_monitor draw::draw_lg
215: filter: sed -e "s/[+-]0\.0*i//g"
216: requires: x !single
217: output_file: output/ex22_2.out
219: TEST*/