Actual source code: test6.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 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";
18: /*
19: Solve parabolic partial differential equation with time delay tau
21: u_t = u_xx + a*u(t) + b*u(t-tau)
22: u(0,t) = u(pi,t) = 0
24: with a = 20 and b(x) = -4.1+x*(1-exp(x-pi)).
26: Discretization leads to a DDE of dimension n
28: -u' = A*u(t) + B*u(t-tau)
30: which results in the nonlinear eigenproblem
32: (-lambda*I + A + exp(-tau*lambda)*B)*u = 0
33: */
35: #include <slepcnep.h>
37: int main(int argc,char **argv)
38: {
39: NEP nep;
40: KSP ksp;
41: PC pc;
42: Mat Id,A,B,mats[3];
43: FN f1,f2,f3,funs[3];
44: Vec v0;
45: PetscScalar coeffs[2],b,*pv;
46: PetscInt n=128,nev,Istart,Iend,i;
47: PetscReal tau=0.001,h,a=20,xi;
48: PetscBool terse,initv=PETSC_FALSE;
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: PetscOptionsGetBool(NULL,NULL,"-initv",&initv,NULL);
55: PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%D, tau=%g\n\n",n,(double)tau);
56: h = PETSC_PI/(PetscReal)(n+1);
58: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
59: Create a standalone KSP with appropriate settings
60: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
62: KSPCreate(PETSC_COMM_WORLD,&ksp);
63: KSPSetType(ksp,KSPBCGS);
64: KSPGetPC(ksp,&pc);
65: PCSetType(pc,PCBJACOBI);
66: KSPSetFromOptions(ksp);
68: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
69: Create nonlinear eigensolver context
70: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
72: NEPCreate(PETSC_COMM_WORLD,&nep);
74: /* Identity matrix */
75: MatCreate(PETSC_COMM_WORLD,&Id);
76: MatSetSizes(Id,PETSC_DECIDE,PETSC_DECIDE,n,n);
77: MatSetFromOptions(Id);
78: MatSetUp(Id);
79: MatGetOwnershipRange(Id,&Istart,&Iend);
80: for (i=Istart;i<Iend;i++) {
81: MatSetValue(Id,i,i,1.0,INSERT_VALUES);
82: }
83: MatAssemblyBegin(Id,MAT_FINAL_ASSEMBLY);
84: MatAssemblyEnd(Id,MAT_FINAL_ASSEMBLY);
85: MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);
87: /* A = 1/h^2*tridiag(1,-2,1) + a*I */
88: MatCreate(PETSC_COMM_WORLD,&A);
89: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
90: MatSetFromOptions(A);
91: MatSetUp(A);
92: MatGetOwnershipRange(A,&Istart,&Iend);
93: for (i=Istart;i<Iend;i++) {
94: if (i>0) { MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES); }
95: if (i<n-1) { MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES); }
96: MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES);
97: }
98: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
99: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
100: MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
102: /* B = diag(b(xi)) */
103: MatCreate(PETSC_COMM_WORLD,&B);
104: MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
105: MatSetFromOptions(B);
106: MatSetUp(B);
107: MatGetOwnershipRange(B,&Istart,&Iend);
108: for (i=Istart;i<Iend;i++) {
109: xi = (i+1)*h;
110: b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
111: MatSetValues(B,1,&i,1,&i,&b,INSERT_VALUES);
112: }
113: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
114: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
115: MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);
117: /* Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda) */
118: FNCreate(PETSC_COMM_WORLD,&f1);
119: FNSetType(f1,FNRATIONAL);
120: coeffs[0] = -1.0; coeffs[1] = 0.0;
121: FNRationalSetNumerator(f1,2,coeffs);
123: FNCreate(PETSC_COMM_WORLD,&f2);
124: FNSetType(f2,FNRATIONAL);
125: coeffs[0] = 1.0;
126: FNRationalSetNumerator(f2,1,coeffs);
128: FNCreate(PETSC_COMM_WORLD,&f3);
129: FNSetType(f3,FNEXP);
130: FNSetScale(f3,-tau,1.0);
132: /* Set the split operator */
133: mats[0] = A; funs[0] = f2;
134: mats[1] = Id; funs[1] = f1;
135: mats[2] = B; funs[2] = f3;
136: NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);
138: /* Customize nonlinear solver; set runtime options */
139: NEPSetOptionsPrefix(nep,"myprefix_");
140: NEPSetType(nep,NEPNARNOLDI);
141: NEPNArnoldiSetKSP(nep,ksp);
142: if (initv) { /* initial vector */
143: MatCreateVecs(A,&v0,NULL);
144: VecGetArray(v0,&pv);
145: for (i=Istart;i<Iend;i++) pv[i-Istart] = PetscSinReal((4.0*PETSC_PI*i)/n);
146: VecRestoreArray(v0,&pv);
147: NEPSetInitialSpace(nep,1,&v0);
148: VecDestroy(&v0);
149: }
150: NEPSetFromOptions(nep);
152: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
153: Solve the eigensystem
154: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
156: NEPSolve(nep);
157: NEPGetDimensions(nep,&nev,NULL,NULL);
158: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);
160: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
161: Display solution and clean up
162: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
164: /* show detailed info unless -terse option is given by user */
165: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
166: if (terse) {
167: NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
168: } else {
169: PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
170: NEPReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
171: NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
172: PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
173: }
174: NEPDestroy(&nep);
175: KSPDestroy(&ksp);
176: MatDestroy(&Id);
177: MatDestroy(&A);
178: MatDestroy(&B);
179: FNDestroy(&f1);
180: FNDestroy(&f2);
181: FNDestroy(&f3);
182: SlepcFinalize();
183: return ierr;
184: }
186: /*TEST
188: test:
189: suffix: 1
190: args: -myprefix_nep_view -myprefix_nep_monitor_conv -initv -terse
191: filter: grep -v "tolerance" | sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g"
192: requires: double !complex !define(PETSC_USE_64BIT_INDICES)
194: TEST*/