Actual source code: test15.c
slepc-3.18.3 2023-03-24
1: /*
2: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
3: SLEPc - Scalable Library for Eigenvalue Problem Computations
4: Copyright (c) 2002-, 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);
63: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
64: PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL);
65: PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%" PetscInt_FMT ", 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: MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,1.0,&Id);
76: MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);
78: /* A = 1/h^2*tridiag(1,-2,1) + a*I */
79: MatCreate(PETSC_COMM_WORLD,&A);
80: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
81: MatSetFromOptions(A);
82: MatSetUp(A);
83: MatGetOwnershipRange(A,&Istart,&Iend);
84: for (i=Istart;i<Iend;i++) {
85: if (i>0) MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES);
86: if (i<n-1) MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES);
87: MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES);
88: }
89: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
90: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
91: MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
93: /* B = diag(b(xi)) */
94: MatCreate(PETSC_COMM_WORLD,&B);
95: MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
96: MatSetFromOptions(B);
97: MatSetUp(B);
98: MatGetOwnershipRange(B,&Istart,&Iend);
99: for (i=Istart;i<Iend;i++) {
100: xi = (i+1)*h;
101: b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
102: MatSetValues(B,1,&i,1,&i,&b,INSERT_VALUES);
103: }
104: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
105: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
106: MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);
108: /* Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda) */
109: FNCreate(PETSC_COMM_WORLD,&f1);
110: FNSetType(f1,FNRATIONAL);
111: coeffs[0] = -1.0; coeffs[1] = 0.0;
112: FNRationalSetNumerator(f1,2,coeffs);
114: FNCreate(PETSC_COMM_WORLD,&f2);
115: FNSetType(f2,FNRATIONAL);
116: coeffs[0] = 1.0;
117: FNRationalSetNumerator(f2,1,coeffs);
119: FNCreate(PETSC_COMM_WORLD,&f3);
120: FNSetType(f3,FNEXP);
121: FNSetScale(f3,-tau,1.0);
123: /* Set the split operator */
124: mats[0] = A; funs[0] = f2;
125: mats[1] = Id; funs[1] = f1;
126: mats[2] = B; funs[2] = f3;
127: NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);
129: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
130: Customize nonlinear solver; set runtime options
131: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
133: NEPSetType(nep,NEPNLEIGS);
134: NEPGetRG(nep,&rg);
135: RGSetType(rg,RGINTERVAL);
136: #if defined(PETSC_USE_COMPLEX)
137: RGIntervalSetEndpoints(rg,5,20,-0.001,0.001);
138: #else
139: RGIntervalSetEndpoints(rg,5,20,-0.0,0.0);
140: #endif
141: NEPSetTarget(nep,15.0);
142: NEPSetWhichEigenpairs(nep,NEP_TARGET_MAGNITUDE);
144: /*
145: Set solver options. In particular, we must allocate sufficient
146: storage for all eigenpairs that may converge (ncv). This is
147: application-dependent.
148: */
149: mpd = 40;
150: NEPSetDimensions(nep,2*mpd,3*mpd,mpd);
151: NEPSetTolerances(nep,PETSC_DEFAULT,2000);
152: PetscNew(&ctx);
153: ctx->lastnconv = 0;
154: ctx->nreps = 0;
155: NEPSetStoppingTestFunction(nep,MyStoppingTest,(void*)ctx,NULL);
157: NEPSetFromOptions(nep);
159: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
160: Solve the eigensystem
161: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
163: NEPSolve(nep);
165: /* show detailed info unless -terse option is given by user */
166: PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
167: PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_INFO_DETAIL);
168: NEPConvergedReasonView(nep,viewer);
169: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
170: if (!terse) NEPErrorView(nep,NEP_ERROR_BACKWARD,viewer);
171: PetscViewerPopFormat(viewer);
173: NEPDestroy(&nep);
174: MatDestroy(&Id);
175: MatDestroy(&A);
176: MatDestroy(&B);
177: FNDestroy(&f1);
178: FNDestroy(&f2);
179: FNDestroy(&f3);
180: PetscFree(ctx);
181: SlepcFinalize();
182: return 0;
183: }
185: /*
186: Function for user-defined stopping test.
188: Ignores the value of nev. It only takes into account the number of
189: eigenpairs that have converged in recent outer iterations (restarts);
190: if no new eigenvalues have converged in the last few restarts,
191: we stop the iteration, assuming that no more eigenvalues are present
192: inside the region.
193: */
194: PetscErrorCode MyStoppingTest(NEP nep,PetscInt its,PetscInt max_it,PetscInt nconv,PetscInt nev,NEPConvergedReason *reason,void *ptr)
195: {
196: CTX_DELAY *ctx = (CTX_DELAY*)ptr;
199: /* check usual termination conditions, but ignoring the case nconv>=nev */
200: NEPStoppingBasic(nep,its,max_it,nconv,PETSC_MAX_INT,reason,NULL);
201: if (*reason==NEP_CONVERGED_ITERATING) {
202: /* check if nconv is the same as before */
203: if (nconv==ctx->lastnconv) ctx->nreps++;
204: else {
205: ctx->lastnconv = nconv;
206: ctx->nreps = 0;
207: }
208: /* check if no eigenvalues converged in last 10 restarts */
209: if (nconv && ctx->nreps>10) *reason = NEP_CONVERGED_USER;
210: }
211: return 0;
212: }
214: /*TEST
216: test:
217: suffix: 1
218: args: -terse
220: TEST*/