Actual source code: test16.c
slepc-3.21.2 2024-09-25
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 use of NEPSetEigenvalueComparison().\n\n"
12: "This is a simplified version of ex20.\n"
13: "The command line options are:\n"
14: " -n <n>, where <n> = number of grid subdivisions.\n";
16: /*
17: Solve 1-D PDE
18: -u'' = lambda*u
19: on [0,1] subject to
20: u(0)=0, u'(1)=u(1)*lambda*kappa/(kappa-lambda)
21: */
23: #include <slepcnep.h>
25: /*
26: User-defined routines
27: */
28: PetscErrorCode FormFunction(NEP,PetscScalar,Mat,Mat,void*);
29: PetscErrorCode FormJacobian(NEP,PetscScalar,Mat,void*);
30: PetscErrorCode MyEigenSort(PetscScalar,PetscScalar,PetscScalar,PetscScalar,PetscInt*,void*);
32: /*
33: User-defined application context
34: */
35: typedef struct {
36: PetscScalar kappa; /* ratio between stiffness of spring and attached mass */
37: PetscReal h; /* mesh spacing */
38: } ApplicationCtx;
40: int main(int argc,char **argv)
41: {
42: NEP nep; /* nonlinear eigensolver context */
43: Mat F,J; /* Function and Jacobian matrices */
44: ApplicationCtx ctx; /* user-defined context */
45: PetscScalar target;
46: RG rg;
47: PetscInt n=128;
48: PetscBool terse;
50: PetscFunctionBeginUser;
51: PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
52: PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
53: PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\n1-D Nonlinear Eigenproblem, n=%" PetscInt_FMT "\n\n",n));
54: ctx.h = 1.0/(PetscReal)n;
55: ctx.kappa = 1.0;
57: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
58: Prepare nonlinear eigensolver context
59: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
61: PetscCall(NEPCreate(PETSC_COMM_WORLD,&nep));
63: PetscCall(MatCreate(PETSC_COMM_WORLD,&F));
64: PetscCall(MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n));
65: PetscCall(MatSetFromOptions(F));
66: PetscCall(MatSeqAIJSetPreallocation(F,3,NULL));
67: PetscCall(MatMPIAIJSetPreallocation(F,3,NULL,1,NULL));
68: PetscCall(NEPSetFunction(nep,F,F,FormFunction,&ctx));
70: PetscCall(MatCreate(PETSC_COMM_WORLD,&J));
71: PetscCall(MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n));
72: PetscCall(MatSetFromOptions(J));
73: PetscCall(MatSeqAIJSetPreallocation(J,3,NULL));
74: PetscCall(MatMPIAIJSetPreallocation(F,3,NULL,1,NULL));
75: PetscCall(NEPSetJacobian(nep,J,FormJacobian,&ctx));
77: PetscCall(NEPSetType(nep,NEPNLEIGS));
78: PetscCall(NEPGetRG(nep,&rg));
79: PetscCall(RGSetType(rg,RGINTERVAL));
80: #if defined(PETSC_USE_COMPLEX)
81: PetscCall(RGIntervalSetEndpoints(rg,2.0,400.0,-0.001,0.001));
82: #else
83: PetscCall(RGIntervalSetEndpoints(rg,2.0,400.0,0,0));
84: #endif
85: PetscCall(NEPSetTarget(nep,25.0));
86: PetscCall(NEPSetEigenvalueComparison(nep,MyEigenSort,&target));
87: PetscCall(NEPSetTolerances(nep,PETSC_SMALL,PETSC_DEFAULT));
88: PetscCall(NEPSetFromOptions(nep));
89: PetscCall(NEPGetTarget(nep,&target));
91: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
92: Solve the eigensystem and display the solution
93: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
95: PetscCall(NEPSolve(nep));
97: /* show detailed info unless -terse option is given by user */
98: PetscCall(PetscOptionsHasName(NULL,NULL,"-terse",&terse));
99: if (terse) PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL));
100: else {
101: PetscCall(PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL));
102: PetscCall(NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD));
103: PetscCall(NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD));
104: PetscCall(PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD));
105: }
107: PetscCall(NEPDestroy(&nep));
108: PetscCall(MatDestroy(&F));
109: PetscCall(MatDestroy(&J));
110: PetscCall(SlepcFinalize());
111: return 0;
112: }
114: /* ------------------------------------------------------------------- */
115: /*
116: FormFunction - Computes Function matrix T(lambda)
118: Input Parameters:
119: . nep - the NEP context
120: . lambda - the scalar argument
121: . ctx - optional user-defined context, as set by NEPSetFunction()
123: Output Parameters:
124: . fun - Function matrix
125: . B - optionally different preconditioning matrix
126: */
127: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
128: {
129: ApplicationCtx *user = (ApplicationCtx*)ctx;
130: PetscScalar A[3],c,d;
131: PetscReal h;
132: PetscInt i,n,j[3],Istart,Iend;
133: PetscBool FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;
135: PetscFunctionBeginUser;
136: /*
137: Compute Function entries and insert into matrix
138: */
139: PetscCall(MatGetSize(fun,&n,NULL));
140: PetscCall(MatGetOwnershipRange(fun,&Istart,&Iend));
141: if (Istart==0) FirstBlock=PETSC_TRUE;
142: if (Iend==n) LastBlock=PETSC_TRUE;
143: h = user->h;
144: c = user->kappa/(lambda-user->kappa);
145: d = n;
147: /*
148: Interior grid points
149: */
150: for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
151: j[0] = i-1; j[1] = i; j[2] = i+1;
152: A[0] = A[2] = -d-lambda*h/6.0; A[1] = 2.0*(d-lambda*h/3.0);
153: PetscCall(MatSetValues(fun,1,&i,3,j,A,INSERT_VALUES));
154: }
156: /*
157: Boundary points
158: */
159: if (FirstBlock) {
160: i = 0;
161: j[0] = 0; j[1] = 1;
162: A[0] = 2.0*(d-lambda*h/3.0); A[1] = -d-lambda*h/6.0;
163: PetscCall(MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES));
164: }
166: if (LastBlock) {
167: i = n-1;
168: j[0] = n-2; j[1] = n-1;
169: A[0] = -d-lambda*h/6.0; A[1] = d-lambda*h/3.0+lambda*c;
170: PetscCall(MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES));
171: }
173: /*
174: Assemble matrix
175: */
176: PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY));
177: PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY));
178: if (fun != B) {
179: PetscCall(MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY));
180: PetscCall(MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY));
181: }
182: PetscFunctionReturn(PETSC_SUCCESS);
183: }
185: /* ------------------------------------------------------------------- */
186: /*
187: FormJacobian - Computes Jacobian matrix T'(lambda)
189: Input Parameters:
190: . nep - the NEP context
191: . lambda - the scalar argument
192: . ctx - optional user-defined context, as set by NEPSetJacobian()
194: Output Parameters:
195: . jac - Jacobian matrix
196: . B - optionally different preconditioning matrix
197: */
198: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
199: {
200: ApplicationCtx *user = (ApplicationCtx*)ctx;
201: PetscScalar A[3],c;
202: PetscReal h;
203: PetscInt i,n,j[3],Istart,Iend;
204: PetscBool FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;
206: PetscFunctionBeginUser;
207: /*
208: Compute Jacobian entries and insert into matrix
209: */
210: PetscCall(MatGetSize(jac,&n,NULL));
211: PetscCall(MatGetOwnershipRange(jac,&Istart,&Iend));
212: if (Istart==0) FirstBlock=PETSC_TRUE;
213: if (Iend==n) LastBlock=PETSC_TRUE;
214: h = user->h;
215: c = user->kappa/(lambda-user->kappa);
217: /*
218: Interior grid points
219: */
220: for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
221: j[0] = i-1; j[1] = i; j[2] = i+1;
222: A[0] = A[2] = -h/6.0; A[1] = -2.0*h/3.0;
223: PetscCall(MatSetValues(jac,1,&i,3,j,A,INSERT_VALUES));
224: }
226: /*
227: Boundary points
228: */
229: if (FirstBlock) {
230: i = 0;
231: j[0] = 0; j[1] = 1;
232: A[0] = -2.0*h/3.0; A[1] = -h/6.0;
233: PetscCall(MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES));
234: }
236: if (LastBlock) {
237: i = n-1;
238: j[0] = n-2; j[1] = n-1;
239: A[0] = -h/6.0; A[1] = -h/3.0-c*c;
240: PetscCall(MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES));
241: }
243: /*
244: Assemble matrix
245: */
246: PetscCall(MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY));
247: PetscCall(MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY));
248: PetscFunctionReturn(PETSC_SUCCESS);
249: }
251: /*
252: Function for user-defined eigenvalue ordering criterion.
254: Given two eigenvalues ar+i*ai and br+i*bi, the subroutine must choose
255: one of them as the preferred one according to the criterion.
256: In this example, eigenvalues are sorted with respect to the target,
257: but those on the right of the target are preferred.
258: */
259: PetscErrorCode MyEigenSort(PetscScalar ar,PetscScalar ai,PetscScalar br,PetscScalar bi,PetscInt *r,void *ctx)
260: {
261: PetscReal a,b;
262: PetscScalar target = *(PetscScalar*)ctx;
264: PetscFunctionBeginUser;
265: if (PetscRealPart(ar-target)<0.0 && PetscRealPart(br-target)>0.0) *r = 1;
266: else {
267: a = SlepcAbsEigenvalue(ar-target,ai);
268: b = SlepcAbsEigenvalue(br-target,bi);
269: if (a>b) *r = 1;
270: else if (a<b) *r = -1;
271: else *r = 0;
272: }
273: PetscFunctionReturn(PETSC_SUCCESS);
274: }
276: /*TEST
278: test:
279: suffix: 1
280: args: -nep_nev 4 -nep_ncv 8 -terse
281: requires: double !complex
283: TEST*/