Line data Source code
1 : /*
2 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3 : SLEPc - Scalable Library for Eigenvalue Problem Computations
4 : Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain
5 :
6 : This file is part of SLEPc.
7 : SLEPc is distributed under a 2-clause BSD license (see LICENSE).
8 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
9 : */
10 :
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";
15 :
16 : /*
17 : Solve parabolic partial differential equation with time delay tau
18 :
19 : u_t = u_xx + a*u(t) + b*u(t-tau)
20 : u(0,t) = u(pi,t) = 0
21 :
22 : with a = 20 and b(x) = -4.1+x*(1-exp(x-pi)).
23 :
24 : Discretization leads to a DDE of dimension n
25 :
26 : -u' = A*u(t) + B*u(t-tau)
27 :
28 : which results in the nonlinear eigenproblem
29 :
30 : (-lambda*I + A + exp(-tau*lambda)*B)*u = 0
31 : */
32 :
33 : #include <slepcnep.h>
34 :
35 17 : int main(int argc,char **argv)
36 : {
37 17 : NEP nep; /* nonlinear eigensolver context */
38 17 : Mat Id,A,B; /* problem matrices */
39 17 : FN f1,f2,f3; /* functions to define the nonlinear operator */
40 17 : Mat mats[3];
41 17 : FN funs[3];
42 17 : PetscScalar coeffs[2],b;
43 17 : PetscInt n=128,nev,Istart,Iend,i;
44 17 : PetscReal tau=0.001,h,a=20,xi;
45 17 : PetscBool terse;
46 :
47 17 : PetscFunctionBeginUser;
48 17 : PetscCall(SlepcInitialize(&argc,&argv,NULL,help));
49 17 : PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
50 17 : PetscCall(PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL));
51 17 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%" PetscInt_FMT ", tau=%g\n\n",n,(double)tau));
52 17 : h = PETSC_PI/(PetscReal)(n+1);
53 :
54 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
55 : Create nonlinear eigensolver context
56 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
57 :
58 17 : PetscCall(NEPCreate(PETSC_COMM_WORLD,&nep));
59 :
60 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
61 : Create problem matrices and coefficient functions. Pass them to NEP
62 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
63 :
64 : /*
65 : Identity matrix
66 : */
67 17 : PetscCall(MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,1.0,&Id));
68 17 : PetscCall(MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE));
69 :
70 : /*
71 : A = 1/h^2*tridiag(1,-2,1) + a*I
72 : */
73 17 : PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
74 17 : PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n));
75 17 : PetscCall(MatSetFromOptions(A));
76 17 : PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
77 5265 : for (i=Istart;i<Iend;i++) {
78 5248 : if (i>0) PetscCall(MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES));
79 5248 : if (i<n-1) PetscCall(MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES));
80 5248 : PetscCall(MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES));
81 : }
82 17 : PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
83 17 : PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
84 17 : PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE));
85 :
86 : /*
87 : B = diag(b(xi))
88 : */
89 17 : PetscCall(MatCreate(PETSC_COMM_WORLD,&B));
90 17 : PetscCall(MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n));
91 17 : PetscCall(MatSetFromOptions(B));
92 17 : PetscCall(MatGetOwnershipRange(B,&Istart,&Iend));
93 5265 : for (i=Istart;i<Iend;i++) {
94 5248 : xi = (i+1)*h;
95 5248 : b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
96 5248 : PetscCall(MatSetValue(B,i,i,b,INSERT_VALUES));
97 : }
98 17 : PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
99 17 : PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
100 17 : PetscCall(MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE));
101 :
102 : /*
103 : Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda)
104 : */
105 17 : PetscCall(FNCreate(PETSC_COMM_WORLD,&f1));
106 17 : PetscCall(FNSetType(f1,FNRATIONAL));
107 17 : coeffs[0] = -1.0; coeffs[1] = 0.0;
108 17 : PetscCall(FNRationalSetNumerator(f1,2,coeffs));
109 :
110 17 : PetscCall(FNCreate(PETSC_COMM_WORLD,&f2));
111 17 : PetscCall(FNSetType(f2,FNRATIONAL));
112 17 : coeffs[0] = 1.0;
113 17 : PetscCall(FNRationalSetNumerator(f2,1,coeffs));
114 :
115 17 : PetscCall(FNCreate(PETSC_COMM_WORLD,&f3));
116 17 : PetscCall(FNSetType(f3,FNEXP));
117 17 : PetscCall(FNSetScale(f3,-tau,1.0));
118 :
119 : /*
120 : Set the split operator. Note that A is passed first so that
121 : SUBSET_NONZERO_PATTERN can be used
122 : */
123 17 : mats[0] = A; funs[0] = f2;
124 17 : mats[1] = Id; funs[1] = f1;
125 17 : mats[2] = B; funs[2] = f3;
126 17 : PetscCall(NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN));
127 :
128 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
129 : Customize nonlinear solver; set runtime options
130 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
131 :
132 17 : PetscCall(NEPSetTolerances(nep,1e-9,PETSC_CURRENT));
133 17 : PetscCall(NEPSetDimensions(nep,1,PETSC_DETERMINE,PETSC_DETERMINE));
134 17 : PetscCall(NEPRIISetLagPreconditioner(nep,0));
135 :
136 : /*
137 : Set solver parameters at runtime
138 : */
139 17 : PetscCall(NEPSetFromOptions(nep));
140 :
141 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
142 : Solve the eigensystem
143 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
144 :
145 17 : PetscCall(NEPSolve(nep));
146 17 : PetscCall(NEPGetDimensions(nep,&nev,NULL,NULL));
147 17 : PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));
148 :
149 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
150 : Display solution and clean up
151 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
152 :
153 : /* show detailed info unless -terse option is given by user */
154 17 : PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
155 17 : if (terse) PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL));
156 : else {
157 0 : PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
158 0 : PetscCall(NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD));
159 0 : PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
160 0 : PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
161 : }
162 17 : PetscCall(NEPDestroy(&nep));
163 17 : PetscCall(MatDestroy(&Id));
164 17 : PetscCall(MatDestroy(&A));
165 17 : PetscCall(MatDestroy(&B));
166 17 : PetscCall(FNDestroy(&f1));
167 17 : PetscCall(FNDestroy(&f2));
168 17 : PetscCall(FNDestroy(&f3));
169 17 : PetscCall(SlepcFinalize());
170 : return 0;
171 : }
172 :
173 : /*TEST
174 :
175 : testset:
176 : suffix: 1
177 : args: -nep_type {{rii slp narnoldi}} -terse
178 : filter: sed -e "s/[+-]0\.0*i//g"
179 : requires: !single
180 :
181 : test:
182 : suffix: 1_ciss
183 : 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
184 : requires: complex !single
185 :
186 : test:
187 : suffix: 2
188 : 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
189 : filter: sed -e "s/[+-]0\.0*i//g"
190 : requires: !single
191 :
192 : testset:
193 : args: -n 512 -nep_target 10 -nep_nev 3 -terse
194 : filter: sed -e "s/[+-]0\.0*i//g"
195 : requires: !single
196 : output_file: output/ex22_3.out
197 : test:
198 : suffix: 3
199 : args: -nep_type {{rii slp narnoldi}}
200 : test:
201 : suffix: 3_simpleu
202 : args: -nep_type {{rii slp narnoldi}} -nep_deflation_simpleu
203 : test:
204 : suffix: 3_slp_thres
205 : args: -nep_type slp -nep_slp_deflation_threshold 1e-8
206 : test:
207 : suffix: 3_rii_thres
208 : args: -nep_type rii -nep_rii_deflation_threshold 1e-8
209 :
210 : test:
211 : suffix: 4
212 : 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
213 : filter: sed -e "s/[+-]0\.0*i//g"
214 : requires: x !single
215 : output_file: output/ex22_2.out
216 :
217 : TEST*/
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