Actual source code: ex7.c
2: static char help[] = "Solves u`` + u^{2} = f with Newton-like methods. Using\n\
3: matrix-free techniques with user-provided explicit preconditioner matrix.\n\n";
5: #include <petscsnes.h>
7: extern PetscErrorCode FormJacobian(SNES, Vec, Mat, Mat, void *);
8: extern PetscErrorCode FormJacobianNoMatrix(SNES, Vec, Mat, Mat, void *);
9: extern PetscErrorCode FormFunction(SNES, Vec, Vec, void *);
10: extern PetscErrorCode FormFunctioni(void *, PetscInt, Vec, PetscScalar *);
11: extern PetscErrorCode OtherFunctionForDifferencing(void *, Vec, Vec);
12: extern PetscErrorCode FormInitialGuess(SNES, Vec);
13: extern PetscErrorCode Monitor(SNES, PetscInt, PetscReal, void *);
15: typedef struct {
16: PetscViewer viewer;
17: } MonitorCtx;
19: typedef struct {
20: PetscBool variant;
21: } AppCtx;
23: int main(int argc, char **argv)
24: {
25: SNES snes; /* SNES context */
26: SNESType type = SNESNEWTONLS; /* default nonlinear solution method */
27: Vec x, r, F, U; /* vectors */
28: Mat J, B; /* Jacobian matrix-free, explicit preconditioner */
29: AppCtx user; /* user-defined work context */
30: PetscScalar h, xp = 0.0, v;
31: PetscInt its, n = 5, i;
32: PetscBool puremf = PETSC_FALSE;
35: PetscInitialize(&argc, &argv, (char *)0, help);
36: PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL);
37: PetscOptionsHasName(NULL, NULL, "-variant", &user.variant);
38: h = 1.0 / (n - 1);
40: /* Set up data structures */
41: VecCreateSeq(PETSC_COMM_SELF, n, &x);
42: PetscObjectSetName((PetscObject)x, "Approximate Solution");
43: VecDuplicate(x, &r);
44: VecDuplicate(x, &F);
45: VecDuplicate(x, &U);
46: PetscObjectSetName((PetscObject)U, "Exact Solution");
48: /* create explicit matrix preconditioner */
49: MatCreateSeqAIJ(PETSC_COMM_SELF, n, n, 3, NULL, &B);
51: /* Store right-hand-side of PDE and exact solution */
52: for (i = 0; i < n; i++) {
53: v = 6.0 * xp + PetscPowScalar(xp + 1.e-12, 6.0); /* +1.e-12 is to prevent 0^6 */
54: VecSetValues(F, 1, &i, &v, INSERT_VALUES);
55: v = xp * xp * xp;
56: VecSetValues(U, 1, &i, &v, INSERT_VALUES);
57: xp += h;
58: }
60: /* Create nonlinear solver */
61: SNESCreate(PETSC_COMM_WORLD, &snes);
62: SNESSetType(snes, type);
64: /* Set various routines and options */
65: SNESSetFunction(snes, r, FormFunction, F);
66: if (user.variant) {
67: /* this approach is not normally needed, one should use the MatCreateSNESMF() below usually */
68: MatCreateMFFD(PETSC_COMM_WORLD, n, n, n, n, &J);
69: MatMFFDSetFunction(J, (PetscErrorCode(*)(void *, Vec, Vec))SNESComputeFunction, snes);
70: MatMFFDSetFunctioni(J, FormFunctioni);
71: /* Use the matrix free operator for both the Jacobian used to define the linear system and used to define the preconditioner */
72: /* This tests MatGetDiagonal() for MATMFFD */
73: PetscOptionsHasName(NULL, NULL, "-puremf", &puremf);
74: } else {
75: /* create matrix free matrix for Jacobian */
76: MatCreateSNESMF(snes, &J);
77: /* demonstrates differencing a different function than FormFunction() to apply a matrix operator */
78: /* note we use the same context for this function as FormFunction, the F vector */
79: MatMFFDSetFunction(J, OtherFunctionForDifferencing, F);
80: }
82: /* Set various routines and options */
83: SNESSetJacobian(snes, J, puremf ? J : B, puremf ? FormJacobianNoMatrix : FormJacobian, &user);
84: SNESSetFromOptions(snes);
86: /* Solve nonlinear system */
87: FormInitialGuess(snes, x);
88: SNESSolve(snes, NULL, x);
89: SNESGetIterationNumber(snes, &its);
90: PetscPrintf(PETSC_COMM_SELF, "number of SNES iterations = %" PetscInt_FMT "\n\n", its);
92: /* Free data structures */
93: VecDestroy(&x);
94: VecDestroy(&r);
95: VecDestroy(&U);
96: VecDestroy(&F);
97: MatDestroy(&J);
98: MatDestroy(&B);
99: SNESDestroy(&snes);
100: PetscFinalize();
101: return 0;
102: }
103: /* -------------------- Evaluate Function F(x) --------------------- */
105: PetscErrorCode FormFunction(SNES snes, Vec x, Vec f, void *dummy)
106: {
107: const PetscScalar *xx, *FF;
108: PetscScalar *ff, d;
109: PetscInt i, n;
111: VecGetArrayRead(x, &xx);
112: VecGetArray(f, &ff);
113: VecGetArrayRead((Vec)dummy, &FF);
114: VecGetSize(x, &n);
115: d = (PetscReal)(n - 1);
116: d = d * d;
117: ff[0] = xx[0];
118: for (i = 1; i < n - 1; i++) ff[i] = d * (xx[i - 1] - 2.0 * xx[i] + xx[i + 1]) + xx[i] * xx[i] - FF[i];
119: ff[n - 1] = xx[n - 1] - 1.0;
120: VecRestoreArrayRead(x, &xx);
121: VecRestoreArray(f, &ff);
122: VecRestoreArrayRead((Vec)dummy, &FF);
123: return 0;
124: }
126: PetscErrorCode FormFunctioni(void *dummy, PetscInt i, Vec x, PetscScalar *s)
127: {
128: const PetscScalar *xx, *FF;
129: PetscScalar d;
130: PetscInt n;
131: SNES snes = (SNES)dummy;
132: Vec F;
134: SNESGetFunction(snes, NULL, NULL, (void **)&F);
135: VecGetArrayRead(x, &xx);
136: VecGetArrayRead(F, &FF);
137: VecGetSize(x, &n);
138: d = (PetscReal)(n - 1);
139: d = d * d;
140: if (i == 0) {
141: *s = xx[0];
142: } else if (i == n - 1) {
143: *s = xx[n - 1] - 1.0;
144: } else {
145: *s = d * (xx[i - 1] - 2.0 * xx[i] + xx[i + 1]) + xx[i] * xx[i] - FF[i];
146: }
147: VecRestoreArrayRead(x, &xx);
148: VecRestoreArrayRead(F, &FF);
149: return 0;
150: }
152: /*
154: Example function that when differenced produces the same matrix free Jacobian as FormFunction()
155: this is provided to show how a user can provide a different function
156: */
157: PetscErrorCode OtherFunctionForDifferencing(void *dummy, Vec x, Vec f)
158: {
159: FormFunction(NULL, x, f, dummy);
160: VecShift(f, 1.0);
161: return 0;
162: }
164: /* -------------------- Form initial approximation ----------------- */
166: PetscErrorCode FormInitialGuess(SNES snes, Vec x)
167: {
168: PetscScalar pfive = .50;
169: VecSet(x, pfive);
170: return 0;
171: }
172: /* -------------------- Evaluate Jacobian F'(x) -------------------- */
173: /* Evaluates a matrix that is used to precondition the matrix-free
174: jacobian. In this case, the explicit preconditioner matrix is
175: also EXACTLY the Jacobian. In general, it would be some lower
176: order, simplified apprioximation */
178: PetscErrorCode FormJacobian(SNES snes, Vec x, Mat jac, Mat B, void *dummy)
179: {
180: const PetscScalar *xx;
181: PetscScalar A[3], d;
182: PetscInt i, n, j[3];
183: AppCtx *user = (AppCtx *)dummy;
185: VecGetArrayRead(x, &xx);
186: VecGetSize(x, &n);
187: d = (PetscReal)(n - 1);
188: d = d * d;
190: i = 0;
191: A[0] = 1.0;
192: MatSetValues(B, 1, &i, 1, &i, &A[0], INSERT_VALUES);
193: for (i = 1; i < n - 1; i++) {
194: j[0] = i - 1;
195: j[1] = i;
196: j[2] = i + 1;
197: A[0] = d;
198: A[1] = -2.0 * d + 2.0 * xx[i];
199: A[2] = d;
200: MatSetValues(B, 1, &i, 3, j, A, INSERT_VALUES);
201: }
202: i = n - 1;
203: A[0] = 1.0;
204: MatSetValues(B, 1, &i, 1, &i, &A[0], INSERT_VALUES);
205: MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY);
206: MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY);
207: VecRestoreArrayRead(x, &xx);
209: if (user->variant) MatMFFDSetBase(jac, x, NULL);
210: MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY);
211: MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY);
212: return 0;
213: }
215: PetscErrorCode FormJacobianNoMatrix(SNES snes, Vec x, Mat jac, Mat B, void *dummy)
216: {
217: AppCtx *user = (AppCtx *)dummy;
219: if (user->variant) MatMFFDSetBase(jac, x, NULL);
220: MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY);
221: MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY);
222: return 0;
223: }
225: /* -------------------- User-defined monitor ----------------------- */
227: PetscErrorCode Monitor(SNES snes, PetscInt its, PetscReal fnorm, void *dummy)
228: {
229: MonitorCtx *monP = (MonitorCtx *)dummy;
230: Vec x;
231: MPI_Comm comm;
233: PetscObjectGetComm((PetscObject)snes, &comm);
234: PetscFPrintf(comm, stdout, "iter = %" PetscInt_FMT ", SNES Function norm %g \n", its, (double)fnorm);
235: SNESGetSolution(snes, &x);
236: VecView(x, monP->viewer);
237: return 0;
238: }
240: /*TEST
242: test:
243: args: -ksp_gmres_cgs_refinement_type refine_always -snes_monitor_short
245: test:
246: suffix: 2
247: args: -variant -ksp_gmres_cgs_refinement_type refine_always -snes_monitor_short
248: output_file: output/ex7_1.out
250: # uses AIJ matrix to define diagonal matrix for Jacobian preconditioning
251: test:
252: suffix: 3
253: args: -variant -pc_type jacobi -snes_view -ksp_monitor
255: # uses MATMFFD matrix to define diagonal matrix for Jacobian preconditioning
256: test:
257: suffix: 4
258: args: -variant -pc_type jacobi -puremf -snes_view -ksp_monitor
260: TEST*/