Actual source code: test3.c
slepc-3.12.1 2019-11-08
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 SLP solver with a user-provided EPS.\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*);
31: /*
32: User-defined application context
33: */
34: typedef struct {
35: PetscScalar kappa; /* ratio between stiffness of spring and attached mass */
36: PetscReal h; /* mesh spacing */
37: } ApplicationCtx;
39: int main(int argc,char **argv)
40: {
41: NEP nep;
42: EPS eps;
43: KSP ksp;
44: PC pc;
45: Mat F,J;
46: ApplicationCtx ctx;
47: PetscInt n=128;
48: PetscBool terse;
51: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
52: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
53: PetscPrintf(PETSC_COMM_WORLD,"\n1-D Nonlinear Eigenproblem, n=%D\n\n",n);
54: ctx.h = 1.0/(PetscReal)n;
55: ctx.kappa = 1.0;
57: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
58: Create a standalone EPS with appropriate settings
59: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
61: EPSCreate(PETSC_COMM_WORLD,&eps);
62: EPSSetType(eps,EPSGD);
63: EPSSetFromOptions(eps);
65: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
66: Create a standalone KSP with appropriate settings
67: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
69: KSPCreate(PETSC_COMM_WORLD,&ksp);
70: KSPSetType(ksp,KSPBCGS);
71: KSPGetPC(ksp,&pc);
72: PCSetType(pc,PCSOR);
73: KSPSetFromOptions(ksp);
75: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
76: Prepare nonlinear eigensolver context
77: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
79: NEPCreate(PETSC_COMM_WORLD,&nep);
81: /* Create Function and Jacobian matrices; set evaluation routines */
82: MatCreate(PETSC_COMM_WORLD,&F);
83: MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n);
84: MatSetFromOptions(F);
85: MatSeqAIJSetPreallocation(F,3,NULL);
86: MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
87: MatSetUp(F);
88: NEPSetFunction(nep,F,F,FormFunction,&ctx);
90: MatCreate(PETSC_COMM_WORLD,&J);
91: MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n);
92: MatSetFromOptions(J);
93: MatSeqAIJSetPreallocation(J,3,NULL);
94: MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
95: MatSetUp(J);
96: NEPSetJacobian(nep,J,FormJacobian,&ctx);
98: NEPSetType(nep,NEPSLP);
99: NEPSLPSetEPS(nep,eps);
100: NEPSLPSetKSP(nep,ksp);
101: NEPSetFromOptions(nep);
103: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
104: Solve the eigensystem
105: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
107: NEPSolve(nep);
109: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
110: Display solution and clean up
111: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
113: /* show detailed info unless -terse option is given by user */
114: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
115: if (terse) {
116: NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
117: } else {
118: PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
119: NEPReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
120: NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
121: PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
122: }
124: NEPDestroy(&nep);
125: EPSDestroy(&eps);
126: KSPDestroy(&ksp);
127: MatDestroy(&F);
128: MatDestroy(&J);
129: SlepcFinalize();
130: return ierr;
131: }
133: /* ------------------------------------------------------------------- */
134: /*
135: FormFunction - Computes Function matrix T(lambda)
137: Input Parameters:
138: . nep - the NEP context
139: . lambda - the scalar argument
140: . ctx - optional user-defined context, as set by NEPSetFunction()
142: Output Parameters:
143: . fun - Function matrix
144: . B - optionally different preconditioning matrix
145: */
146: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
147: {
149: ApplicationCtx *user = (ApplicationCtx*)ctx;
150: PetscScalar A[3],c,d;
151: PetscReal h;
152: PetscInt i,n,j[3],Istart,Iend;
153: PetscBool FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;
156: /*
157: Compute Function entries and insert into matrix
158: */
159: MatGetSize(fun,&n,NULL);
160: MatGetOwnershipRange(fun,&Istart,&Iend);
161: if (Istart==0) FirstBlock=PETSC_TRUE;
162: if (Iend==n) LastBlock=PETSC_TRUE;
163: h = user->h;
164: c = user->kappa/(lambda-user->kappa);
165: d = n;
167: /*
168: Interior grid points
169: */
170: for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
171: j[0] = i-1; j[1] = i; j[2] = i+1;
172: A[0] = A[2] = -d-lambda*h/6.0; A[1] = 2.0*(d-lambda*h/3.0);
173: MatSetValues(fun,1,&i,3,j,A,INSERT_VALUES);
174: }
176: /*
177: Boundary points
178: */
179: if (FirstBlock) {
180: i = 0;
181: j[0] = 0; j[1] = 1;
182: A[0] = 2.0*(d-lambda*h/3.0); A[1] = -d-lambda*h/6.0;
183: MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
184: }
186: if (LastBlock) {
187: i = n-1;
188: j[0] = n-2; j[1] = n-1;
189: A[0] = -d-lambda*h/6.0; A[1] = d-lambda*h/3.0+lambda*c;
190: MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
191: }
193: /*
194: Assemble matrix
195: */
196: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
197: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
198: if (fun != B) {
199: MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY);
200: MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY);
201: }
202: return(0);
203: }
205: /* ------------------------------------------------------------------- */
206: /*
207: FormJacobian - Computes Jacobian matrix T'(lambda)
209: Input Parameters:
210: . nep - the NEP context
211: . lambda - the scalar argument
212: . ctx - optional user-defined context, as set by NEPSetJacobian()
214: Output Parameters:
215: . jac - Jacobian matrix
216: . B - optionally different preconditioning matrix
217: */
218: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
219: {
221: ApplicationCtx *user = (ApplicationCtx*)ctx;
222: PetscScalar A[3],c;
223: PetscReal h;
224: PetscInt i,n,j[3],Istart,Iend;
225: PetscBool FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;
228: /*
229: Compute Jacobian entries and insert into matrix
230: */
231: MatGetSize(jac,&n,NULL);
232: MatGetOwnershipRange(jac,&Istart,&Iend);
233: if (Istart==0) FirstBlock=PETSC_TRUE;
234: if (Iend==n) LastBlock=PETSC_TRUE;
235: h = user->h;
236: c = user->kappa/(lambda-user->kappa);
238: /*
239: Interior grid points
240: */
241: for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
242: j[0] = i-1; j[1] = i; j[2] = i+1;
243: A[0] = A[2] = -h/6.0; A[1] = -2.0*h/3.0;
244: MatSetValues(jac,1,&i,3,j,A,INSERT_VALUES);
245: }
247: /*
248: Boundary points
249: */
250: if (FirstBlock) {
251: i = 0;
252: j[0] = 0; j[1] = 1;
253: A[0] = -2.0*h/3.0; A[1] = -h/6.0;
254: MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
255: }
257: if (LastBlock) {
258: i = n-1;
259: j[0] = n-2; j[1] = n-1;
260: A[0] = -h/6.0; A[1] = -h/3.0-c*c;
261: MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
262: }
264: /*
265: Assemble matrix
266: */
267: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
268: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
269: return(0);
270: }
272: /*TEST
274: test:
275: suffix: 1
276: args: -nep_target 21 -terse
277: requires: !single
279: TEST*/