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 NArnoldi solver with a user-provided KSP.\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 : " -initv ... set an initial vector.\n\n";
17 :
18 : /*
19 : Solve parabolic partial differential equation with time delay tau
20 :
21 : u_t = u_xx + a*u(t) + b*u(t-tau)
22 : u(0,t) = u(pi,t) = 0
23 :
24 : with a = 20 and b(x) = -4.1+x*(1-exp(x-pi)).
25 :
26 : Discretization leads to a DDE of dimension n
27 :
28 : -u' = A*u(t) + B*u(t-tau)
29 :
30 : which results in the nonlinear eigenproblem
31 :
32 : (-lambda*I + A + exp(-tau*lambda)*B)*u = 0
33 : */
34 :
35 : #include <slepcnep.h>
36 :
37 1 : int main(int argc,char **argv)
38 : {
39 1 : NEP nep;
40 1 : KSP ksp;
41 1 : PC pc;
42 1 : Mat Id,A,B,mats[3];
43 1 : FN f1,f2,f3,funs[3];
44 1 : Vec v0;
45 1 : PetscScalar coeffs[2],b,*pv;
46 1 : PetscInt n=128,nev,Istart,Iend,i,lag;
47 1 : PetscReal tau=0.001,h,a=20,xi;
48 1 : PetscBool terse,initv=PETSC_FALSE;
49 1 : const char *prefix;
50 :
51 1 : PetscFunctionBeginUser;
52 1 : PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
53 1 : PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
54 1 : PetscCall(PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL));
55 1 : PetscCall(PetscOptionsGetBool(NULL,NULL,"-initv",&initv,NULL));
56 1 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%" PetscInt_FMT ", tau=%g\n\n",n,(double)tau));
57 1 : h = PETSC_PI/(PetscReal)(n+1);
58 :
59 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
60 : Create a standalone KSP with appropriate settings
61 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
62 :
63 1 : PetscCall(KSPCreate(PETSC_COMM_WORLD,&ksp));
64 1 : PetscCall(KSPSetType(ksp,KSPBCGS));
65 1 : PetscCall(KSPGetPC(ksp,&pc));
66 1 : PetscCall(PCSetType(pc,PCBJACOBI));
67 1 : PetscCall(KSPSetFromOptions(ksp));
68 :
69 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
70 : Create nonlinear eigensolver context
71 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
72 :
73 1 : PetscCall(NEPCreate(PETSC_COMM_WORLD,&nep));
74 :
75 : /* Identity matrix */
76 1 : PetscCall(MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,1.0,&Id));
77 1 : PetscCall(MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE));
78 :
79 : /* A = 1/h^2*tridiag(1,-2,1) + a*I */
80 1 : PetscCall(MatCreate(PETSC_COMM_WORLD,&A));
81 1 : PetscCall(MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n));
82 1 : PetscCall(MatSetFromOptions(A));
83 1 : PetscCall(MatGetOwnershipRange(A,&Istart,&Iend));
84 129 : for (i=Istart;i<Iend;i++) {
85 128 : if (i>0) PetscCall(MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES));
86 128 : if (i<n-1) PetscCall(MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES));
87 128 : PetscCall(MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES));
88 : }
89 1 : PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
90 1 : PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
91 1 : PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE));
92 :
93 : /* B = diag(b(xi)) */
94 1 : PetscCall(MatCreate(PETSC_COMM_WORLD,&B));
95 1 : PetscCall(MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n));
96 1 : PetscCall(MatSetFromOptions(B));
97 1 : PetscCall(MatGetOwnershipRange(B,&Istart,&Iend));
98 129 : for (i=Istart;i<Iend;i++) {
99 128 : xi = (i+1)*h;
100 128 : b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
101 128 : PetscCall(MatSetValues(B,1,&i,1,&i,&b,INSERT_VALUES));
102 : }
103 1 : PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
104 1 : PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
105 1 : PetscCall(MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE));
106 :
107 : /* Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda) */
108 1 : PetscCall(FNCreate(PETSC_COMM_WORLD,&f1));
109 1 : PetscCall(FNSetType(f1,FNRATIONAL));
110 1 : coeffs[0] = -1.0; coeffs[1] = 0.0;
111 1 : PetscCall(FNRationalSetNumerator(f1,2,coeffs));
112 :
113 1 : PetscCall(FNCreate(PETSC_COMM_WORLD,&f2));
114 1 : PetscCall(FNSetType(f2,FNRATIONAL));
115 1 : coeffs[0] = 1.0;
116 1 : PetscCall(FNRationalSetNumerator(f2,1,coeffs));
117 :
118 1 : PetscCall(FNCreate(PETSC_COMM_WORLD,&f3));
119 1 : PetscCall(FNSetType(f3,FNEXP));
120 1 : PetscCall(FNSetScale(f3,-tau,1.0));
121 :
122 : /* Set the split operator */
123 1 : mats[0] = A; funs[0] = f2;
124 1 : mats[1] = Id; funs[1] = f1;
125 1 : mats[2] = B; funs[2] = f3;
126 1 : PetscCall(NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN));
127 :
128 : /* Customize nonlinear solver; set runtime options */
129 1 : PetscCall(NEPSetOptionsPrefix(nep,"check_"));
130 1 : PetscCall(NEPAppendOptionsPrefix(nep,"myprefix_"));
131 1 : PetscCall(NEPGetOptionsPrefix(nep,&prefix));
132 1 : PetscCall(PetscPrintf(PETSC_COMM_WORLD,"NEP prefix is currently: %s\n\n",prefix));
133 1 : PetscCall(NEPSetType(nep,NEPNARNOLDI));
134 1 : PetscCall(NEPNArnoldiSetKSP(nep,ksp));
135 1 : if (initv) { /* initial vector */
136 1 : PetscCall(MatCreateVecs(A,&v0,NULL));
137 1 : PetscCall(VecGetArray(v0,&pv));
138 129 : for (i=Istart;i<Iend;i++) pv[i-Istart] = PetscSinReal((4.0*PETSC_PI*i)/n);
139 1 : PetscCall(VecRestoreArray(v0,&pv));
140 1 : PetscCall(NEPSetInitialSpace(nep,1,&v0));
141 1 : PetscCall(VecDestroy(&v0));
142 : }
143 1 : PetscCall(NEPSetFromOptions(nep));
144 :
145 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
146 : Solve the eigensystem
147 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
148 :
149 1 : PetscCall(NEPSolve(nep));
150 1 : PetscCall(NEPGetDimensions(nep,&nev,NULL,NULL));
151 1 : PetscCall(PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));
152 1 : PetscCall(NEPNArnoldiGetLagPreconditioner(nep,&lag));
153 1 : PetscCall(PetscPrintf(PETSC_COMM_WORLD," N-Arnoldi lag parameter: %" PetscInt_FMT "\n",lag));
154 :
155 : /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
156 : Display solution and clean up
157 : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
158 :
159 : /* show detailed info unless -terse option is given by user */
160 1 : PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
161 1 : if (terse) PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL));
162 : else {
163 0 : PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
164 0 : PetscCall(NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD));
165 0 : PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
166 0 : PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
167 : }
168 1 : PetscCall(NEPDestroy(&nep));
169 1 : PetscCall(KSPDestroy(&ksp));
170 1 : PetscCall(MatDestroy(&Id));
171 1 : PetscCall(MatDestroy(&A));
172 1 : PetscCall(MatDestroy(&B));
173 1 : PetscCall(FNDestroy(&f1));
174 1 : PetscCall(FNDestroy(&f2));
175 1 : PetscCall(FNDestroy(&f3));
176 1 : PetscCall(SlepcFinalize());
177 : return 0;
178 : }
179 :
180 : /*TEST
181 :
182 : test:
183 : suffix: 1
184 : args: -check_myprefix_nep_view -check_myprefix_nep_monitor_conv -initv -terse
185 : filter: grep -v "tolerance" | sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g" -e "s/+0i//g"
186 : requires: double
187 :
188 : TEST*/
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