Actual source code: test6.c
slepc-3.14.0 2020-09-30
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-2020, 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,lag;
47: PetscReal tau=0.001,h,a=20,xi;
48: PetscBool terse,initv=PETSC_FALSE;
49: const char *prefix;
52: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
53: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
54: PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL);
55: PetscOptionsGetBool(NULL,NULL,"-initv",&initv,NULL);
56: PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%D, tau=%g\n\n",n,(double)tau);
57: h = PETSC_PI/(PetscReal)(n+1);
59: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
60: Create a standalone KSP with appropriate settings
61: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
63: KSPCreate(PETSC_COMM_WORLD,&ksp);
64: KSPSetType(ksp,KSPBCGS);
65: KSPGetPC(ksp,&pc);
66: PCSetType(pc,PCBJACOBI);
67: KSPSetFromOptions(ksp);
69: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
70: Create nonlinear eigensolver context
71: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
73: NEPCreate(PETSC_COMM_WORLD,&nep);
75: /* Identity matrix */
76: MatCreate(PETSC_COMM_WORLD,&Id);
77: MatSetSizes(Id,PETSC_DECIDE,PETSC_DECIDE,n,n);
78: MatSetFromOptions(Id);
79: MatSetUp(Id);
80: MatGetOwnershipRange(Id,&Istart,&Iend);
81: for (i=Istart;i<Iend;i++) {
82: MatSetValue(Id,i,i,1.0,INSERT_VALUES);
83: }
84: MatAssemblyBegin(Id,MAT_FINAL_ASSEMBLY);
85: MatAssemblyEnd(Id,MAT_FINAL_ASSEMBLY);
86: MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);
88: /* A = 1/h^2*tridiag(1,-2,1) + a*I */
89: MatCreate(PETSC_COMM_WORLD,&A);
90: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
91: MatSetFromOptions(A);
92: MatSetUp(A);
93: MatGetOwnershipRange(A,&Istart,&Iend);
94: for (i=Istart;i<Iend;i++) {
95: if (i>0) { MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES); }
96: if (i<n-1) { MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES); }
97: MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES);
98: }
99: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
100: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
101: MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
103: /* B = diag(b(xi)) */
104: MatCreate(PETSC_COMM_WORLD,&B);
105: MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
106: MatSetFromOptions(B);
107: MatSetUp(B);
108: MatGetOwnershipRange(B,&Istart,&Iend);
109: for (i=Istart;i<Iend;i++) {
110: xi = (i+1)*h;
111: b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
112: MatSetValues(B,1,&i,1,&i,&b,INSERT_VALUES);
113: }
114: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
115: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
116: MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);
118: /* Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda) */
119: FNCreate(PETSC_COMM_WORLD,&f1);
120: FNSetType(f1,FNRATIONAL);
121: coeffs[0] = -1.0; coeffs[1] = 0.0;
122: FNRationalSetNumerator(f1,2,coeffs);
124: FNCreate(PETSC_COMM_WORLD,&f2);
125: FNSetType(f2,FNRATIONAL);
126: coeffs[0] = 1.0;
127: FNRationalSetNumerator(f2,1,coeffs);
129: FNCreate(PETSC_COMM_WORLD,&f3);
130: FNSetType(f3,FNEXP);
131: FNSetScale(f3,-tau,1.0);
133: /* Set the split operator */
134: mats[0] = A; funs[0] = f2;
135: mats[1] = Id; funs[1] = f1;
136: mats[2] = B; funs[2] = f3;
137: NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);
139: /* Customize nonlinear solver; set runtime options */
140: NEPSetOptionsPrefix(nep,"check_");
141: NEPAppendOptionsPrefix(nep,"myprefix_");
142: NEPGetOptionsPrefix(nep,&prefix);
143: PetscPrintf(PETSC_COMM_WORLD,"NEP prefix is currently: %s\n\n",prefix);
144: NEPSetType(nep,NEPNARNOLDI);
145: NEPNArnoldiSetKSP(nep,ksp);
146: if (initv) { /* initial vector */
147: MatCreateVecs(A,&v0,NULL);
148: VecGetArray(v0,&pv);
149: for (i=Istart;i<Iend;i++) pv[i-Istart] = PetscSinReal((4.0*PETSC_PI*i)/n);
150: VecRestoreArray(v0,&pv);
151: NEPSetInitialSpace(nep,1,&v0);
152: VecDestroy(&v0);
153: }
154: NEPSetFromOptions(nep);
156: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
157: Solve the eigensystem
158: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
160: NEPSolve(nep);
161: NEPGetDimensions(nep,&nev,NULL,NULL);
162: PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);
163: NEPNArnoldiGetLagPreconditioner(nep,&lag);
164: PetscPrintf(PETSC_COMM_WORLD," N-Arnoldi lag parameter: %D\n",lag);
166: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
167: Display solution and clean up
168: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
170: /* show detailed info unless -terse option is given by user */
171: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
172: if (terse) {
173: NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
174: } else {
175: PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
176: NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
177: NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
178: PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
179: }
180: NEPDestroy(&nep);
181: KSPDestroy(&ksp);
182: MatDestroy(&Id);
183: MatDestroy(&A);
184: MatDestroy(&B);
185: FNDestroy(&f1);
186: FNDestroy(&f2);
187: FNDestroy(&f3);
188: SlepcFinalize();
189: return ierr;
190: }
192: /*TEST
194: test:
195: suffix: 1
196: args: -check_myprefix_nep_view -check_myprefix_nep_monitor_conv -initv -terse
197: filter: grep -v "tolerance" | sed -e "s/[0-9]\.[0-9]*e[+-]\([0-9]*\)/removed/g" -e "s/+0i//g"
198: requires: double
200: TEST*/