Actual source code: test5.c
slepc-3.11.2 2019-07-30
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2019, 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 INTERPOL solver with a user-provided PEP.\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\n";
17: /*
18: Solve parabolic partial differential equation with time delay tau
20: u_t = u_xx + a*u(t) + b*u(t-tau)
21: u(0,t) = u(pi,t) = 0
23: with a = 20 and b(x) = -4.1+x*(1-exp(x-pi)).
25: Discretization leads to a DDE of dimension n
27: -u' = A*u(t) + B*u(t-tau)
29: which results in the nonlinear eigenproblem
31: (-lambda*I + A + exp(-tau*lambda)*B)*u = 0
32: */
34: #include <slepcnep.h>
36: int main(int argc,char **argv)
37: {
38: NEP nep;
39: PEP pep;
40: Mat Id,A,B;
41: FN f1,f2,f3;
42: RG rg;
43: Mat mats[3];
44: FN funs[3];
45: PetscScalar coeffs[2],b;
46: PetscInt n=128,nev,Istart,Iend,i,deg;
47: PetscReal tau=0.001,h,a=20,xi,tol;
48: PetscBool terse;
51: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
52: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
53: PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL);
54: PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%D, tau=%g\n\n",n,(double)tau);
55: h = PETSC_PI/(PetscReal)(n+1);
57: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
58: Create a standalone PEP and RG objects with appropriate settings
59: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
61: PEPCreate(PETSC_COMM_WORLD,&pep);
62: PEPSetType(pep,PEPTOAR);
63: PEPSetFromOptions(pep);
65: RGCreate(PETSC_COMM_WORLD,&rg);
66: RGSetType(rg,RGINTERVAL);
67: RGIntervalSetEndpoints(rg,5,20,-0.1,0.1);
68: RGSetFromOptions(rg);
70: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
71: Create nonlinear eigensolver context
72: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
74: NEPCreate(PETSC_COMM_WORLD,&nep);
76: /* Identity matrix */
77: MatCreate(PETSC_COMM_WORLD,&Id);
78: MatSetSizes(Id,PETSC_DECIDE,PETSC_DECIDE,n,n);
79: MatSetFromOptions(Id);
80: MatSetUp(Id);
81: MatGetOwnershipRange(Id,&Istart,&Iend);
82: for (i=Istart;i<Iend;i++) {
83: MatSetValue(Id,i,i,1.0,INSERT_VALUES);
84: }
85: MatAssemblyBegin(Id,MAT_FINAL_ASSEMBLY);
86: MatAssemblyEnd(Id,MAT_FINAL_ASSEMBLY);
87: MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);
89: /* A = 1/h^2*tridiag(1,-2,1) + a*I */
90: MatCreate(PETSC_COMM_WORLD,&A);
91: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
92: MatSetFromOptions(A);
93: MatSetUp(A);
94: MatGetOwnershipRange(A,&Istart,&Iend);
95: for (i=Istart;i<Iend;i++) {
96: if (i>0) { MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES); }
97: if (i<n-1) { MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES); }
98: MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES);
99: }
100: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
101: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
102: MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
104: /* B = diag(b(xi)) */
105: MatCreate(PETSC_COMM_WORLD,&B);
106: MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
107: MatSetFromOptions(B);
108: MatSetUp(B);
109: MatGetOwnershipRange(B,&Istart,&Iend);
110: for (i=Istart;i<Iend;i++) {
111: xi = (i+1)*h;
112: b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
113: MatSetValues(B,1,&i,1,&i,&b,INSERT_VALUES);
114: }
115: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
116: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
117: MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);
119: /* Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda) */
120: FNCreate(PETSC_COMM_WORLD,&f1);
121: FNSetType(f1,FNRATIONAL);
122: coeffs[0] = -1.0; coeffs[1] = 0.0;
123: FNRationalSetNumerator(f1,2,coeffs);
125: FNCreate(PETSC_COMM_WORLD,&f2);
126: FNSetType(f2,FNRATIONAL);
127: coeffs[0] = 1.0;
128: FNRationalSetNumerator(f2,1,coeffs);
130: FNCreate(PETSC_COMM_WORLD,&f3);
131: FNSetType(f3,FNEXP);
132: FNSetScale(f3,-tau,1.0);
134: /* Set the split operator */
135: mats[0] = A; funs[0] = f2;
136: mats[1] = Id; funs[1] = f1;
137: mats[2] = B; funs[2] = f3;
138: NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);
140: /* Customize nonlinear solver; set runtime options */
141: NEPSetType(nep,NEPINTERPOL);
142: NEPSetRG(nep,rg);
143: NEPInterpolSetPEP(nep,pep);
144: NEPInterpolGetInterpolation(nep,&tol,°);
145: NEPInterpolSetInterpolation(nep,tol,deg+2); /* increase degree of interpolation */
146: NEPSetFromOptions(nep);
148: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
149: Solve the eigensystem
150: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
152: NEPSolve(nep);
153: NEPGetDimensions(nep,&nev,NULL,NULL);
154: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);
156: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
157: Display solution and clean up
158: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
160: /* show detailed info unless -terse option is given by user */
161: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
162: if (terse) {
163: NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
164: } else {
165: PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
166: NEPReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
167: NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
168: PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
169: }
170: NEPDestroy(&nep);
171: PEPDestroy(&pep);
172: RGDestroy(&rg);
173: MatDestroy(&Id);
174: MatDestroy(&A);
175: MatDestroy(&B);
176: FNDestroy(&f1);
177: FNDestroy(&f2);
178: FNDestroy(&f3);
179: SlepcFinalize();
180: return ierr;
181: }
183: /*TEST
185: test:
186: suffix: 1
187: args: -nep_nev 3 -nep_target 5 -terse
188: requires: !single
190: test:
191: suffix: 2_cuda
192: args: -nep_nev 3 -nep_target 5 -mat_type aijcusparse -terse
193: requires: cuda
194: output_file: output/test5_1.out
196: TEST*/