Actual source code: test4.c
slepc-3.17.2 2022-08-09
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[] = "Test the RII solver with a user-provided KSP.\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: KSP ksp;
43: PC pc;
44: Mat F,J;
45: ApplicationCtx ctx;
46: PetscInt n=128,lag,its;
47: PetscBool terse,flg,cct,herm;
48: PetscReal thres;
50: SlepcInitialize(&argc,&argv,(char*)0,help);
51: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
52: PetscPrintf(PETSC_COMM_WORLD,"\n1-D Nonlinear Eigenproblem, n=%" PetscInt_FMT "\n\n",n);
53: ctx.h = 1.0/(PetscReal)n;
54: ctx.kappa = 1.0;
56: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
57: Create a standalone KSP with appropriate settings
58: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
60: KSPCreate(PETSC_COMM_WORLD,&ksp);
61: KSPSetType(ksp,KSPBCGS);
62: KSPGetPC(ksp,&pc);
63: PCSetType(pc,PCBJACOBI);
64: KSPSetFromOptions(ksp);
66: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
67: Prepare nonlinear eigensolver context
68: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
70: NEPCreate(PETSC_COMM_WORLD,&nep);
72: /* Create Function and Jacobian matrices; set evaluation routines */
73: MatCreate(PETSC_COMM_WORLD,&F);
74: MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n);
75: MatSetFromOptions(F);
76: MatSeqAIJSetPreallocation(F,3,NULL);
77: MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
78: MatSetUp(F);
79: NEPSetFunction(nep,F,F,FormFunction,&ctx);
81: MatCreate(PETSC_COMM_WORLD,&J);
82: MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n);
83: MatSetFromOptions(J);
84: MatSeqAIJSetPreallocation(J,3,NULL);
85: MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
86: MatSetUp(J);
87: NEPSetJacobian(nep,J,FormJacobian,&ctx);
89: NEPSetType(nep,NEPRII);
90: NEPRIISetKSP(nep,ksp);
91: NEPRIISetMaximumIterations(nep,6);
92: NEPRIISetConstCorrectionTol(nep,PETSC_TRUE);
93: NEPRIISetHermitian(nep,PETSC_TRUE);
94: NEPSetFromOptions(nep);
96: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
97: Solve the eigensystem
98: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
100: NEPSolve(nep);
101: PetscObjectTypeCompare((PetscObject)nep,NEPRII,&flg);
102: if (flg) {
103: NEPRIIGetMaximumIterations(nep,&its);
104: NEPRIIGetLagPreconditioner(nep,&lag);
105: NEPRIIGetDeflationThreshold(nep,&thres);
106: NEPRIIGetConstCorrectionTol(nep,&cct);
107: NEPRIIGetHermitian(nep,&herm);
108: PetscPrintf(PETSC_COMM_WORLD," Maximum inner iterations of RII is %" PetscInt_FMT "\n",its);
109: PetscPrintf(PETSC_COMM_WORLD," Preconditioner rebuilt every %" PetscInt_FMT " iterations\n",lag);
110: if (thres>0.0) PetscPrintf(PETSC_COMM_WORLD," Using deflation threshold=%g\n",(double)thres);
111: if (cct) PetscPrintf(PETSC_COMM_WORLD," Using a constant correction tolerance\n");
112: if (herm) PetscPrintf(PETSC_COMM_WORLD," Hermitian version of scalar equation\n");
113: PetscPrintf(PETSC_COMM_WORLD,"\n");
114: }
116: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
117: Display solution and clean up
118: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
120: /* show detailed info unless -terse option is given by user */
121: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
122: if (terse) NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
123: else {
124: PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
125: NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
126: NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
127: PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
128: }
130: NEPDestroy(&nep);
131: KSPDestroy(&ksp);
132: MatDestroy(&F);
133: MatDestroy(&J);
134: SlepcFinalize();
135: return 0;
136: }
138: /* ------------------------------------------------------------------- */
139: /*
140: FormFunction - Computes Function matrix T(lambda)
142: Input Parameters:
143: . nep - the NEP context
144: . lambda - the scalar argument
145: . ctx - optional user-defined context, as set by NEPSetFunction()
147: Output Parameters:
148: . fun - Function matrix
149: . B - optionally different preconditioning matrix
150: */
151: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
152: {
153: ApplicationCtx *user = (ApplicationCtx*)ctx;
154: PetscScalar A[3],c,d;
155: PetscReal h;
156: PetscInt i,n,j[3],Istart,Iend;
157: PetscBool FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;
160: /*
161: Compute Function entries and insert into matrix
162: */
163: MatGetSize(fun,&n,NULL);
164: MatGetOwnershipRange(fun,&Istart,&Iend);
165: if (Istart==0) FirstBlock=PETSC_TRUE;
166: if (Iend==n) LastBlock=PETSC_TRUE;
167: h = user->h;
168: c = user->kappa/(lambda-user->kappa);
169: d = n;
171: /*
172: Interior grid points
173: */
174: for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
175: j[0] = i-1; j[1] = i; j[2] = i+1;
176: A[0] = A[2] = -d-lambda*h/6.0; A[1] = 2.0*(d-lambda*h/3.0);
177: MatSetValues(fun,1,&i,3,j,A,INSERT_VALUES);
178: }
180: /*
181: Boundary points
182: */
183: if (FirstBlock) {
184: i = 0;
185: j[0] = 0; j[1] = 1;
186: A[0] = 2.0*(d-lambda*h/3.0); A[1] = -d-lambda*h/6.0;
187: MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
188: }
190: if (LastBlock) {
191: i = n-1;
192: j[0] = n-2; j[1] = n-1;
193: A[0] = -d-lambda*h/6.0; A[1] = d-lambda*h/3.0+lambda*c;
194: MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
195: }
197: /*
198: Assemble matrix
199: */
200: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
201: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
202: if (fun != B) {
203: MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY);
204: MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY);
205: }
206: PetscFunctionReturn(0);
207: }
209: /* ------------------------------------------------------------------- */
210: /*
211: FormJacobian - Computes Jacobian matrix T'(lambda)
213: Input Parameters:
214: . nep - the NEP context
215: . lambda - the scalar argument
216: . ctx - optional user-defined context, as set by NEPSetJacobian()
218: Output Parameters:
219: . jac - Jacobian matrix
220: . B - optionally different preconditioning matrix
221: */
222: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
223: {
224: ApplicationCtx *user = (ApplicationCtx*)ctx;
225: PetscScalar A[3],c;
226: PetscReal h;
227: PetscInt i,n,j[3],Istart,Iend;
228: PetscBool FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;
231: /*
232: Compute Jacobian entries and insert into matrix
233: */
234: MatGetSize(jac,&n,NULL);
235: MatGetOwnershipRange(jac,&Istart,&Iend);
236: if (Istart==0) FirstBlock=PETSC_TRUE;
237: if (Iend==n) LastBlock=PETSC_TRUE;
238: h = user->h;
239: c = user->kappa/(lambda-user->kappa);
241: /*
242: Interior grid points
243: */
244: for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
245: j[0] = i-1; j[1] = i; j[2] = i+1;
246: A[0] = A[2] = -h/6.0; A[1] = -2.0*h/3.0;
247: MatSetValues(jac,1,&i,3,j,A,INSERT_VALUES);
248: }
250: /*
251: Boundary points
252: */
253: if (FirstBlock) {
254: i = 0;
255: j[0] = 0; j[1] = 1;
256: A[0] = -2.0*h/3.0; A[1] = -h/6.0;
257: MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
258: }
260: if (LastBlock) {
261: i = n-1;
262: j[0] = n-2; j[1] = n-1;
263: A[0] = -h/6.0; A[1] = -h/3.0-c*c;
264: MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
265: }
267: /*
268: Assemble matrix
269: */
270: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
271: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
272: PetscFunctionReturn(0);
273: }
275: /*TEST
277: test:
278: suffix: 1
279: args: -nep_target 21 -nep_rii_lag_preconditioner 2 -terse
280: requires: !single
282: TEST*/