Actual source code: ex7.c
1: /*$Id: ex7.c,v 1.59 2001/08/07 21:31:12 bsmith Exp $*/
3: static char help[] = "Solves u`` + u^{2} = f with Newton-like methods. Using\n\
4: matrix-free techniques with user-provided explicit preconditioner matrix.\n\n";
6: #include petscsnes.h
8: extern int FormJacobian(SNES,Vec,Mat*,Mat*,MatStructure*,void*);
9: extern int FormFunction(SNES,Vec,Vec,void*);
10: extern int FormInitialGuess(SNES,Vec);
11: extern int Monitor(SNES,int,PetscReal,void *);
13: typedef struct {
14: PetscViewer viewer;
15: } MonitorCtx;
17: typedef struct {
18: Mat precond;
19: PetscTruth variant;
20: } AppCtx;
24: int main(int argc,char **argv)
25: {
26: SNES snes; /* SNES context */
27: SNESType type = SNESLS; /* default nonlinear solution method */
28: Vec x,r,F,U,work; /* vectors */
29: Mat J,B; /* Jacobian matrix-free, explicit preconditioner */
30: MonitorCtx monP; /* monitoring context */
31: AppCtx user; /* user-defined work context */
32: PetscScalar h,xp = 0.0,v;
33: int ierr,its,n = 5,i;
35: PetscInitialize(&argc,&argv,(char *)0,help);
36: PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
37: PetscOptionsHasName(PETSC_NULL,"-variant",&user.variant);
38: h = 1.0/(n-1);
40: /* Set up data structures */
41: PetscViewerDrawOpen(PETSC_COMM_SELF,0,0,0,0,400,400,&monP.viewer);
42: VecCreateSeq(PETSC_COMM_SELF,n,&x);
43: PetscObjectSetName((PetscObject)x,"Approximate Solution");
44: VecDuplicate(x,&r);
45: VecDuplicate(x,&F);
46: VecDuplicate(x,&U);
47: PetscObjectSetName((PetscObject)U,"Exact Solution");
49: /* create explict matrix preconditioner */
50: MatCreateSeqAIJ(PETSC_COMM_SELF,n,n,3,PETSC_NULL,&B);
51: user.precond = B;
53: /* Store right-hand-side of PDE and exact solution */
54: for (i=0; i<n; i++) {
55: v = 6.0*xp + PetscPowScalar(xp+1.e-12,6.0); /* +1.e-12 is to prevent 0^6 */
56: VecSetValues(F,1,&i,&v,INSERT_VALUES);
57: v= xp*xp*xp;
58: VecSetValues(U,1,&i,&v,INSERT_VALUES);
59: xp += h;
60: }
62: /* Create nonlinear solver */
63: SNESCreate(PETSC_COMM_WORLD,&snes);
64: SNESSetType(snes,type);
66: if (user.variant) {
67: MatCreateMF(x,&J);
68: VecDuplicate(x,&work);
69: MatSNESMFSetFunction(J,work,FormFunction,F);
70: } else {
71: /* create matrix free matrix for Jacobian */
72: MatCreateSNESMF(snes,x,&J);
73: }
75: /* Set various routines and options */
76: SNESSetFunction(snes,r,FormFunction,F);
77: SNESSetJacobian(snes,J,B,FormJacobian,&user);
78: SNESSetMonitor(snes,Monitor,&monP,0);
79: SNESSetFromOptions(snes);
81: /* Solve nonlinear system */
82: FormInitialGuess(snes,x);
83: SNESSolve(snes,x,&its);
84: PetscPrintf(PETSC_COMM_SELF,"number of Newton iterations = %d\n\n",its);
86: /* Free data structures */
87: if (user.variant) {
88: VecDestroy(work);
89: }
90: VecDestroy(x); VecDestroy(r);
91: VecDestroy(U); VecDestroy(F);
92: MatDestroy(J); MatDestroy(B);
93: SNESDestroy(snes);
94: PetscViewerDestroy(monP.viewer);
95: PetscFinalize();
97: return 0;
98: }
99: /* -------------------- Evaluate Function F(x) --------------------- */
101: int FormFunction(SNES snes,Vec x,Vec f,void *dummy)
102: {
103: PetscScalar *xx,*ff,*FF,d;
104: int i,ierr,n;
106: VecGetArray(x,&xx);
107: VecGetArray(f,&ff);
108: VecGetArray((Vec) dummy,&FF);
109: VecGetSize(x,&n);
110: d = (PetscReal)(n - 1); d = d*d;
111: ff[0] = xx[0];
112: for (i=1; i<n-1; i++) {
113: ff[i] = d*(xx[i-1] - 2.0*xx[i] + xx[i+1]) + xx[i]*xx[i] - FF[i];
114: }
115: ff[n-1] = xx[n-1] - 1.0;
116: VecRestoreArray(x,&xx);
117: VecRestoreArray(f,&ff);
118: VecRestoreArray((Vec)dummy,&FF);
119: return 0;
120: }
121: /* -------------------- Form initial approximation ----------------- */
125: int FormInitialGuess(SNES snes,Vec x)
126: {
127: int ierr;
128: PetscScalar pfive = .50;
129: VecSet(&pfive,x);
130: return 0;
131: }
134: /* -------------------- Evaluate Jacobian F'(x) -------------------- */
135: /* Evaluates a matrix that is used to precondition the matrix-free
136: jacobian. In this case, the explict preconditioner matrix is
137: also EXACTLY the Jacobian. In general, it would be some lower
138: order, simplified apprioximation */
140: int FormJacobian(SNES snes,Vec x,Mat *jac,Mat *B,MatStructure*flag,void *dummy)
141: {
142: PetscScalar *xx,A[3],d;
143: int i,n,j[3],ierr,iter;
144: AppCtx *user = (AppCtx*) dummy;
146: SNESGetIterationNumber(snes,&iter);
148: if (iter%2 ==0) { /* Compute new preconditioner matrix */
149: printf("iter=%d, computing new preconditioning matrix\n",iter+1);
150: *B = user->precond;
151: VecGetArray(x,&xx);
152: VecGetSize(x,&n);
153: d = (PetscReal)(n - 1); d = d*d;
155: i = 0; A[0] = 1.0;
156: MatSetValues(*B,1,&i,1,&i,&A[0],INSERT_VALUES);
157: for (i=1; i<n-1; i++) {
158: j[0] = i - 1; j[1] = i; j[2] = i + 1;
159: A[0] = d; A[1] = -2.0*d + 2.0*xx[i]; A[2] = d;
160: MatSetValues(*B,1,&i,3,j,A,INSERT_VALUES);
161: }
162: i = n-1; A[0] = 1.0;
163: MatSetValues(*B,1,&i,1,&i,&A[0],INSERT_VALUES);
164: MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);
165: MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);
166: VecRestoreArray(x,&xx);
167: *flag = SAME_NONZERO_PATTERN;
168: } else { /* reuse preconditioner from last iteration */
169: printf("iter=%d, using old preconditioning matrix\n",iter+1);
170: *flag = SAME_PRECONDITIONER;
171: }
172: if (user->variant) {
173: MatSNESMFSetBase(*jac,x);
174: }
175: MatAssemblyBegin(*jac,MAT_FINAL_ASSEMBLY);
176: MatAssemblyEnd(*jac,MAT_FINAL_ASSEMBLY);
177: return 0;
178: }
179: /* -------------------- User-defined monitor ----------------------- */
183: int Monitor(SNES snes,int its,PetscReal fnorm,void *dummy)
184: {
185: int ierr;
186: MonitorCtx *monP = (MonitorCtx*) dummy;
187: Vec x;
188: MPI_Comm comm;
190: PetscObjectGetComm((PetscObject)snes,&comm);
191: PetscFPrintf(comm,stdout,"iter = %d, SNES Function norm %g \n",its,fnorm);
192: SNESGetSolution(snes,&x);
193: VecView(x,monP->viewer);
194: return 0;
195: }