Actual source code: test15.c
slepc-3.14.1 2020-12-08
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[] = "Illustrates the use of a user-defined stopping test.\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: /*
37: User-defined routines
38: */
39: PetscErrorCode MyStoppingTest(NEP,PetscInt,PetscInt,PetscInt,PetscInt,NEPConvergedReason*,void*);
41: typedef struct {
42: PetscInt lastnconv; /* last value of nconv; used in stopping test */
43: PetscInt nreps; /* number of repetitions of nconv; used in stopping test */
44: } CTX_DELAY;
46: int main(int argc,char **argv)
47: {
48: NEP nep;
49: Mat Id,A,B;
50: FN f1,f2,f3;
51: RG rg;
52: CTX_DELAY *ctx;
53: Mat mats[3];
54: FN funs[3];
55: PetscScalar coeffs[2],b;
56: PetscInt n=128,Istart,Iend,i,mpd;
57: PetscReal tau=0.001,h,a=20,xi;
58: PetscBool terse;
59: PetscViewer viewer;
62: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
63: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
64: PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL);
65: PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%D, tau=%g\n\n",n,(double)tau);
66: h = PETSC_PI/(PetscReal)(n+1);
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: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
139: Customize nonlinear solver; set runtime options
140: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
142: NEPSetType(nep,NEPNLEIGS);
143: NEPGetRG(nep,&rg);
144: RGSetType(rg,RGINTERVAL);
145: #if defined(PETSC_USE_COMPLEX)
146: RGIntervalSetEndpoints(rg,5,20,-0.001,0.001);
147: #else
148: RGIntervalSetEndpoints(rg,5,20,-0.0,0.0);
149: #endif
150: NEPSetTarget(nep,15.0);
151: NEPSetWhichEigenpairs(nep,NEP_TARGET_MAGNITUDE);
153: /*
154: Set solver options. In particular, we must allocate sufficient
155: storage for all eigenpairs that may converge (ncv). This is
156: application-dependent.
157: */
158: mpd = 40;
159: NEPSetDimensions(nep,2*mpd,3*mpd,mpd);
160: NEPSetTolerances(nep,PETSC_DEFAULT,2000);
161: PetscNew(&ctx);
162: ctx->lastnconv = 0;
163: ctx->nreps = 0;
164: NEPSetStoppingTestFunction(nep,MyStoppingTest,(void*)ctx,NULL);
166: NEPSetFromOptions(nep);
168: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
169: Solve the eigensystem
170: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
172: NEPSolve(nep);
174: /* show detailed info unless -terse option is given by user */
175: PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
176: PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
177: NEPConvergedReasonView(nep,viewer);
178: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
179: if (!terse) {
180: NEPErrorView(nep,NEP_ERROR_BACKWARD,viewer);
181: }
182: PetscViewerPopFormat(viewer);
184: NEPDestroy(&nep);
185: MatDestroy(&Id);
186: MatDestroy(&A);
187: MatDestroy(&B);
188: FNDestroy(&f1);
189: FNDestroy(&f2);
190: FNDestroy(&f3);
191: PetscFree(ctx);
192: SlepcFinalize();
193: return ierr;
194: }
196: /*
197: Function for user-defined stopping test.
199: Ignores the value of nev. It only takes into account the number of
200: eigenpairs that have converged in recent outer iterations (restarts);
201: if no new eigenvalues have converged in the last few restarts,
202: we stop the iteration, assuming that no more eigenvalues are present
203: inside the region.
204: */
205: PetscErrorCode MyStoppingTest(NEP nep,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,NEPConvergedReason *reason,void *ptr)
206: {
208: CTX_DELAY *ctx = (CTX_DELAY*)ptr;
211: /* check usual termination conditions, but ignoring the case nconv>=nev */
212: NEPStoppingBasic(nep,its,max_it,nconv,PETSC_MAX_INT,reason,NULL);
213: if (*reason==NEP_CONVERGED_ITERATING) {
214: /* check if nconv is the same as before */
215: if (nconv==ctx->lastnconv) ctx->nreps++;
216: else {
217: ctx->lastnconv = nconv;
218: ctx->nreps = 0;
219: }
220: /* check if no eigenvalues converged in last 10 restarts */
221: if (nconv && ctx->nreps>10) *reason = NEP_CONVERGED_USER;
222: }
223: return(0);
224: }
226: /*TEST
228: test:
229: suffix: 1
230: args: -terse
232: TEST*/