Actual source code: test1.c
slepc-3.11.2 2019-07-30
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[] = "Simple 1-D nonlinear eigenproblem.\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; /* nonlinear eigensolver context */
42: Mat F,J; /* Function and Jacobian matrices */
43: ApplicationCtx ctx; /* user-defined context */
44: PetscInt n=128;
45: PetscBool terse;
48: SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
49: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
50: PetscPrintf(PETSC_COMM_WORLD,"\n1-D Nonlinear Eigenproblem, n=%D\n\n",n);
51: ctx.h = 1.0/(PetscReal)n;
52: ctx.kappa = 1.0;
54: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
55: Prepare nonlinear eigensolver context
56: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
58: NEPCreate(PETSC_COMM_WORLD,&nep);
60: /*
61: Create Function and Jacobian matrices; set evaluation routines
62: */
64: MatCreate(PETSC_COMM_WORLD,&F);
65: MatSetSizes(F,PETSC_DECIDE,PETSC_DECIDE,n,n);
66: MatSetFromOptions(F);
67: MatSeqAIJSetPreallocation(F,3,NULL);
68: MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
69: MatSetUp(F);
70: NEPSetFunction(nep,F,F,FormFunction,&ctx);
72: MatCreate(PETSC_COMM_WORLD,&J);
73: MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n);
74: MatSetFromOptions(J);
75: MatSeqAIJSetPreallocation(J,3,NULL);
76: MatMPIAIJSetPreallocation(F,3,NULL,1,NULL);
77: MatSetUp(J);
78: NEPSetJacobian(nep,J,FormJacobian,&ctx);
80: NEPSetFromOptions(nep);
82: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
83: Solve the eigensystem
84: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
86: NEPSolve(nep);
88: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
89: Display solution and clean up
90: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
92: /* show detailed info unless -terse option is given by user */
93: PetscOptionsHasName(NULL,NULL,"-terse",&terse);
94: if (terse) {
95: NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
96: } else {
97: PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
98: NEPReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
99: NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
100: PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
101: }
103: NEPDestroy(&nep);
104: MatDestroy(&F);
105: MatDestroy(&J);
106: SlepcFinalize();
107: return ierr;
108: }
110: /* ------------------------------------------------------------------- */
111: /*
112: FormFunction - Computes Function matrix T(lambda)
114: Input Parameters:
115: . nep - the NEP context
116: . lambda - the scalar argument
117: . ctx - optional user-defined context, as set by NEPSetFunction()
119: Output Parameters:
120: . fun - Function matrix
121: . B - optionally different preconditioning matrix
122: */
123: PetscErrorCode FormFunction(NEP nep,PetscScalar lambda,Mat fun,Mat B,void *ctx)
124: {
126: ApplicationCtx *user = (ApplicationCtx*)ctx;
127: PetscScalar A[3],c,d;
128: PetscReal h;
129: PetscInt i,n,j[3],Istart,Iend;
130: PetscBool FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;
133: /*
134: Compute Function entries and insert into matrix
135: */
136: MatGetSize(fun,&n,NULL);
137: MatGetOwnershipRange(fun,&Istart,&Iend);
138: if (Istart==0) FirstBlock=PETSC_TRUE;
139: if (Iend==n) LastBlock=PETSC_TRUE;
140: h = user->h;
141: c = user->kappa/(lambda-user->kappa);
142: d = n;
144: /*
145: Interior grid points
146: */
147: for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
148: j[0] = i-1; j[1] = i; j[2] = i+1;
149: A[0] = A[2] = -d-lambda*h/6.0; A[1] = 2.0*(d-lambda*h/3.0);
150: MatSetValues(fun,1,&i,3,j,A,INSERT_VALUES);
151: }
153: /*
154: Boundary points
155: */
156: if (FirstBlock) {
157: i = 0;
158: j[0] = 0; j[1] = 1;
159: A[0] = 2.0*(d-lambda*h/3.0); A[1] = -d-lambda*h/6.0;
160: MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
161: }
163: if (LastBlock) {
164: i = n-1;
165: j[0] = n-2; j[1] = n-1;
166: A[0] = -d-lambda*h/6.0; A[1] = d-lambda*h/3.0+lambda*c;
167: MatSetValues(fun,1,&i,2,j,A,INSERT_VALUES);
168: }
170: /*
171: Assemble matrix
172: */
173: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
174: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
175: if (fun != B) {
176: MatAssemblyBegin(fun,MAT_FINAL_ASSEMBLY);
177: MatAssemblyEnd(fun,MAT_FINAL_ASSEMBLY);
178: }
179: return(0);
180: }
182: /* ------------------------------------------------------------------- */
183: /*
184: FormJacobian - Computes Jacobian matrix T'(lambda)
186: Input Parameters:
187: . nep - the NEP context
188: . lambda - the scalar argument
189: . ctx - optional user-defined context, as set by NEPSetJacobian()
191: Output Parameters:
192: . jac - Jacobian matrix
193: . B - optionally different preconditioning matrix
194: */
195: PetscErrorCode FormJacobian(NEP nep,PetscScalar lambda,Mat jac,void *ctx)
196: {
198: ApplicationCtx *user = (ApplicationCtx*)ctx;
199: PetscScalar A[3],c;
200: PetscReal h;
201: PetscInt i,n,j[3],Istart,Iend;
202: PetscBool FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;
205: /*
206: Compute Jacobian entries and insert into matrix
207: */
208: MatGetSize(jac,&n,NULL);
209: MatGetOwnershipRange(jac,&Istart,&Iend);
210: if (Istart==0) FirstBlock=PETSC_TRUE;
211: if (Iend==n) LastBlock=PETSC_TRUE;
212: h = user->h;
213: c = user->kappa/(lambda-user->kappa);
215: /*
216: Interior grid points
217: */
218: for (i=(FirstBlock? Istart+1: Istart);i<(LastBlock? Iend-1: Iend);i++) {
219: j[0] = i-1; j[1] = i; j[2] = i+1;
220: A[0] = A[2] = -h/6.0; A[1] = -2.0*h/3.0;
221: MatSetValues(jac,1,&i,3,j,A,INSERT_VALUES);
222: }
224: /*
225: Boundary points
226: */
227: if (FirstBlock) {
228: i = 0;
229: j[0] = 0; j[1] = 1;
230: A[0] = -2.0*h/3.0; A[1] = -h/6.0;
231: MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
232: }
234: if (LastBlock) {
235: i = n-1;
236: j[0] = n-2; j[1] = n-1;
237: A[0] = -h/6.0; A[1] = -h/3.0-c*c;
238: MatSetValues(jac,1,&i,2,j,A,INSERT_VALUES);
239: }
241: /*
242: Assemble matrix
243: */
244: MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
245: MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
246: return(0);
247: }
249: /*TEST
251: test:
252: suffix: 1
253: args: -nep_type {{rii slp}} -nep_target 21 -terse
254: requires: !single
256: test:
257: suffix: 2_cuda
258: args: -nep_type {{rii slp}} -nep_target 21 -mat_type aijcusparse -terse
259: requires: cuda
260: output_file: output/test1_1.out
262: TEST*/