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[] = "Test the NEPProjectOperator() function.\n\n"
12 : "This is based on ex22.\n"
13 : "The command line options are:\n"
14 : " -n <n>, where <n> = number of grid subdivisions.\n"
15 : " -tau <tau>, where <tau> is the delay parameter.\n";
16 :
17 : /*
18 : Solve parabolic partial differential equation with time delay tau
19 :
20 : u_t = u_xx + a*u(t) + b*u(t-tau)
21 : u(0,t) = u(pi,t) = 0
22 :
23 : with a = 20 and b(x) = -4.1+x*(1-exp(x-pi)).
24 :
25 : Discretization leads to a DDE of dimension n
26 :
27 : -u' = A*u(t) + B*u(t-tau)
28 :
29 : which results in the nonlinear eigenproblem
30 :
31 : (-lambda*I + A + exp(-tau*lambda)*B)*u = 0
32 : */
33 :
34 : #include <slepcnep.h>
35 :
36 1 : int main(int argc,char **argv)
37 : {
38 1 : NEP nep;
39 1 : Mat Id,A,B,mats[3];
40 1 : FN f1,f2,f3,funs[3];
41 1 : BV V;
42 1 : DS ds;
43 1 : Vec v;
44 1 : PetscScalar coeffs[2],b,*M;
45 1 : PetscInt n=32,Istart,Iend,i,j,k,nc;
46 1 : PetscReal tau=0.001,h,a=20,xi;
47 :
48 1 : PetscFunctionBeginUser;
49 1 : PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
50 1 : PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
51 1 : PetscCall(PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL));
52 1 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%" PetscInt_FMT ", tau=%g\n",n,(double)tau));
53 1 : h = PETSC_PI/(PetscReal)(n+1);
54 :
55 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
56 : Create nonlinear eigensolver context
57 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
58 :
59 1 : PetscCall(NEPCreate(PETSC_COMM_WORLD,&nep));
60 :
61 : /* Identity matrix */
62 1 : PetscCall(MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,1.0,&Id));
63 1 : PetscCall(MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE));
64 :
65 : /* A = 1/h^2*tridiag(1,-2,1) + a*I */
66 1 : PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
67 1 : PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n));
68 1 : PetscCall(MatSetFromOptions(A));
69 1 : PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
70 33 : for (i=Istart;i<Iend;i++) {
71 32 : if (i>0) PetscCall(MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES));
72 32 : if (i<n-1) PetscCall(MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES));
73 32 : PetscCall(MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES));
74 : }
75 1 : PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
76 1 : PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
77 1 : PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE));
78 :
79 : /* B = diag(b(xi)) */
80 1 : PetscCall(MatCreate(PETSC_COMM_WORLD,&B));
81 1 : PetscCall(MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n));
82 1 : PetscCall(MatSetFromOptions(B));
83 1 : PetscCall(MatGetOwnershipRange(B,&Istart,&Iend));
84 33 : for (i=Istart;i<Iend;i++) {
85 32 : xi = (i+1)*h;
86 32 : b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
87 32 : PetscCall(MatSetValues(B,1,&i,1,&i,&b,INSERT_VALUES));
88 : }
89 1 : PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
90 1 : PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
91 1 : PetscCall(MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE));
92 :
93 : /* Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda) */
94 1 : PetscCall(FNCreate(PETSC_COMM_WORLD,&f1));
95 1 : PetscCall(FNSetType(f1,FNRATIONAL));
96 1 : coeffs[0] = -1.0; coeffs[1] = 0.0;
97 1 : PetscCall(FNRationalSetNumerator(f1,2,coeffs));
98 :
99 1 : PetscCall(FNCreate(PETSC_COMM_WORLD,&f2));
100 1 : PetscCall(FNSetType(f2,FNRATIONAL));
101 1 : coeffs[0] = 1.0;
102 1 : PetscCall(FNRationalSetNumerator(f2,1,coeffs));
103 :
104 1 : PetscCall(FNCreate(PETSC_COMM_WORLD,&f3));
105 1 : PetscCall(FNSetType(f3,FNEXP));
106 1 : PetscCall(FNSetScale(f3,-tau,1.0));
107 :
108 : /* Set the split operator */
109 1 : mats[0] = A; funs[0] = f2;
110 1 : mats[1] = Id; funs[1] = f1;
111 1 : mats[2] = B; funs[2] = f3;
112 1 : PetscCall(NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN));
113 1 : PetscCall(NEPSetType(nep,NEPNARNOLDI));
114 1 : PetscCall(NEPSetFromOptions(nep));
115 :
116 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
117 : Project the NEP
118 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
119 :
120 1 : PetscCall(NEPSetUp(nep));
121 1 : PetscCall(NEPGetBV(nep,&V));
122 1 : PetscCall(BVGetSizes(V,NULL,NULL,&nc));
123 6 : for (i=0;i<nc;i++) {
124 5 : PetscCall(BVGetColumn(V,i,&v));
125 5 : PetscCall(VecSetValue(v,i,1.0,INSERT_VALUES));
126 5 : PetscCall(VecAssemblyBegin(v));
127 5 : PetscCall(VecAssemblyEnd(v));
128 5 : PetscCall(BVRestoreColumn(V,i,&v));
129 : }
130 1 : PetscCall(NEPGetDS(nep,&ds));
131 1 : PetscCall(DSSetType(ds,DSNEP));
132 1 : PetscCall(DSNEPSetFN(ds,3,funs));
133 1 : PetscCall(DSAllocate(ds,nc));
134 1 : PetscCall(DSSetDimensions(ds,nc,0,0));
135 1 : PetscCall(NEPProjectOperator(nep,0,nc));
136 :
137 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
138 : Display projected matrices and clean up
139 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
140 :
141 4 : for (k=0;k<3;k++) {
142 3 : PetscCall(DSGetArray(ds,DSMatExtra[k],&M));
143 3 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nMatrix E%" PetscInt_FMT " = \n",k));
144 18 : for (i=0;i<nc;i++) {
145 90 : for (j=0;j<nc;j++) PetscCall(PetscPrintf(PETSC_COMM_WORLD," %.5g",(double)PetscRealPart(M[i+j*nc])));
146 15 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n"));
147 : }
148 3 : PetscCall(DSRestoreArray(ds,DSMatExtra[k],&M));
149 : }
150 :
151 1 : PetscCall(NEPDestroy(&nep));
152 1 : PetscCall(MatDestroy(&Id));
153 1 : PetscCall(MatDestroy(&A));
154 1 : PetscCall(MatDestroy(&B));
155 1 : PetscCall(FNDestroy(&f1));
156 1 : PetscCall(FNDestroy(&f2));
157 1 : PetscCall(FNDestroy(&f3));
158 1 : PetscCall(SlepcFinalize());
159 : return 0;
160 : }
161 :
162 : /*TEST
163 :
164 : test:
165 : suffix: 1
166 : args: -nep_ncv 5
167 :
168 : TEST*/
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