Actual source code: ex2.c
2: static char help[] = "Newton method to solve u'' + u^{2} = f, sequentially.\n\
3: This example employs a user-defined monitoring routine.\n\n";
5: /*
6: Include "petscdraw.h" so that we can use PETSc drawing routines.
7: Include "petscsnes.h" so that we can use SNES solvers. Note that this
8: file automatically includes:
9: petscsys.h - base PETSc routines petscvec.h - vectors
10: petscmat.h - matrices
11: petscis.h - index sets petscksp.h - Krylov subspace methods
12: petscviewer.h - viewers petscpc.h - preconditioners
13: petscksp.h - linear solvers
14: */
16: #include <petscsnes.h>
18: /*
19: User-defined routines
20: */
21: extern PetscErrorCode FormJacobian(SNES, Vec, Mat, Mat, void *);
22: extern PetscErrorCode FormFunction(SNES, Vec, Vec, void *);
23: extern PetscErrorCode FormInitialGuess(Vec);
24: extern PetscErrorCode Monitor(SNES, PetscInt, PetscReal, void *);
26: /*
27: User-defined context for monitoring
28: */
29: typedef struct {
30: PetscViewer viewer;
31: } MonitorCtx;
33: int main(int argc, char **argv)
34: {
35: SNES snes; /* SNES context */
36: Vec x, r, F, U; /* vectors */
37: Mat J; /* Jacobian matrix */
38: MonitorCtx monP; /* monitoring context */
39: PetscInt its, n = 5, i, maxit, maxf;
40: PetscMPIInt size;
41: PetscScalar h, xp, v, none = -1.0;
42: PetscReal abstol, rtol, stol, norm;
44: PetscFunctionBeginUser;
45: PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
46: PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
47: PetscCheck(size == 1, PETSC_COMM_SELF, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");
48: PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL));
49: h = 1.0 / (n - 1);
51: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
52: Create nonlinear solver context
53: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
55: PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes));
57: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
58: Create vector data structures; set function evaluation routine
59: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
60: /*
61: Note that we form 1 vector from scratch and then duplicate as needed.
62: */
63: PetscCall(VecCreate(PETSC_COMM_WORLD, &x));
64: PetscCall(VecSetSizes(x, PETSC_DECIDE, n));
65: PetscCall(VecSetFromOptions(x));
66: PetscCall(VecDuplicate(x, &r));
67: PetscCall(VecDuplicate(x, &F));
68: PetscCall(VecDuplicate(x, &U));
70: /*
71: Set function evaluation routine and vector
72: */
73: PetscCall(SNESSetFunction(snes, r, FormFunction, (void *)F));
75: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
76: Create matrix data structure; set Jacobian evaluation routine
77: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
79: PetscCall(MatCreate(PETSC_COMM_WORLD, &J));
80: PetscCall(MatSetSizes(J, PETSC_DECIDE, PETSC_DECIDE, n, n));
81: PetscCall(MatSetFromOptions(J));
82: PetscCall(MatSeqAIJSetPreallocation(J, 3, NULL));
84: /*
85: Set Jacobian matrix data structure and default Jacobian evaluation
86: routine. User can override with:
87: -snes_fd : default finite differencing approximation of Jacobian
88: -snes_mf : matrix-free Newton-Krylov method with no preconditioning
89: (unless user explicitly sets preconditioner)
90: -snes_mf_operator : form preconditioning matrix as set by the user,
91: but use matrix-free approx for Jacobian-vector
92: products within Newton-Krylov method
93: */
95: PetscCall(SNESSetJacobian(snes, J, J, FormJacobian, NULL));
97: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
98: Customize nonlinear solver; set runtime options
99: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
101: /*
102: Set an optional user-defined monitoring routine
103: */
104: PetscCall(PetscViewerDrawOpen(PETSC_COMM_WORLD, 0, 0, 0, 0, 400, 400, &monP.viewer));
105: PetscCall(SNESMonitorSet(snes, Monitor, &monP, 0));
107: /*
108: Set names for some vectors to facilitate monitoring (optional)
109: */
110: PetscCall(PetscObjectSetName((PetscObject)x, "Approximate Solution"));
111: PetscCall(PetscObjectSetName((PetscObject)U, "Exact Solution"));
113: /*
114: Set SNES/KSP/KSP/PC runtime options, e.g.,
115: -snes_view -snes_monitor -ksp_type <ksp> -pc_type <pc>
116: */
117: PetscCall(SNESSetFromOptions(snes));
119: /*
120: Print parameters used for convergence testing (optional) ... just
121: to demonstrate this routine; this information is also printed with
122: the option -snes_view
123: */
124: PetscCall(SNESGetTolerances(snes, &abstol, &rtol, &stol, &maxit, &maxf));
125: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "atol=%g, rtol=%g, stol=%g, maxit=%" PetscInt_FMT ", maxf=%" PetscInt_FMT "\n", (double)abstol, (double)rtol, (double)stol, maxit, maxf));
127: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
128: Initialize application:
129: Store right-hand-side of PDE and exact solution
130: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
132: xp = 0.0;
133: for (i = 0; i < n; i++) {
134: v = 6.0 * xp + PetscPowScalar(xp + 1.e-12, 6.0); /* +1.e-12 is to prevent 0^6 */
135: PetscCall(VecSetValues(F, 1, &i, &v, INSERT_VALUES));
136: v = xp * xp * xp;
137: PetscCall(VecSetValues(U, 1, &i, &v, INSERT_VALUES));
138: xp += h;
139: }
141: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
142: Evaluate initial guess; then solve nonlinear system
143: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
144: /*
145: Note: The user should initialize the vector, x, with the initial guess
146: for the nonlinear solver prior to calling SNESSolve(). In particular,
147: to employ an initial guess of zero, the user should explicitly set
148: this vector to zero by calling VecSet().
149: */
150: PetscCall(FormInitialGuess(x));
151: PetscCall(SNESSolve(snes, NULL, x));
152: PetscCall(SNESGetIterationNumber(snes, &its));
153: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "number of SNES iterations = %" PetscInt_FMT "\n\n", its));
155: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
156: Check solution and clean up
157: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
159: /*
160: Check the error
161: */
162: PetscCall(VecAXPY(x, none, U));
163: PetscCall(VecNorm(x, NORM_2, &norm));
164: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Norm of error %g, Iterations %" PetscInt_FMT "\n", (double)norm, its));
166: /*
167: Free work space. All PETSc objects should be destroyed when they
168: are no longer needed.
169: */
170: PetscCall(VecDestroy(&x));
171: PetscCall(VecDestroy(&r));
172: PetscCall(VecDestroy(&U));
173: PetscCall(VecDestroy(&F));
174: PetscCall(MatDestroy(&J));
175: PetscCall(SNESDestroy(&snes));
176: PetscCall(PetscViewerDestroy(&monP.viewer));
177: PetscCall(PetscFinalize());
178: return 0;
179: }
180: /* ------------------------------------------------------------------- */
181: /*
182: FormInitialGuess - Computes initial guess.
184: Input/Output Parameter:
185: . x - the solution vector
186: */
187: PetscErrorCode FormInitialGuess(Vec x)
188: {
189: PetscScalar pfive = .50;
190: PetscFunctionBeginUser;
191: PetscCall(VecSet(x, pfive));
192: PetscFunctionReturn(PETSC_SUCCESS);
193: }
194: /* ------------------------------------------------------------------- */
195: /*
196: FormFunction - Evaluates nonlinear function, F(x).
198: Input Parameters:
199: . snes - the SNES context
200: . x - input vector
201: . ctx - optional user-defined context, as set by SNESSetFunction()
203: Output Parameter:
204: . f - function vector
206: Note:
207: The user-defined context can contain any application-specific data
208: needed for the function evaluation (such as various parameters, work
209: vectors, and grid information). In this program the context is just
210: a vector containing the right-hand-side of the discretized PDE.
211: */
213: PetscErrorCode FormFunction(SNES snes, Vec x, Vec f, void *ctx)
214: {
215: Vec g = (Vec)ctx;
216: const PetscScalar *xx, *gg;
217: PetscScalar *ff, d;
218: PetscInt i, n;
220: PetscFunctionBeginUser;
221: /*
222: Get pointers to vector data.
223: - For default PETSc vectors, VecGetArray() returns a pointer to
224: the data array. Otherwise, the routine is implementation dependent.
225: - You MUST call VecRestoreArray() when you no longer need access to
226: the array.
227: */
228: PetscCall(VecGetArrayRead(x, &xx));
229: PetscCall(VecGetArray(f, &ff));
230: PetscCall(VecGetArrayRead(g, &gg));
232: /*
233: Compute function
234: */
235: PetscCall(VecGetSize(x, &n));
236: d = (PetscReal)(n - 1);
237: d = d * d;
238: ff[0] = xx[0];
239: for (i = 1; i < n - 1; i++) ff[i] = d * (xx[i - 1] - 2.0 * xx[i] + xx[i + 1]) + xx[i] * xx[i] - gg[i];
240: ff[n - 1] = xx[n - 1] - 1.0;
242: /*
243: Restore vectors
244: */
245: PetscCall(VecRestoreArrayRead(x, &xx));
246: PetscCall(VecRestoreArray(f, &ff));
247: PetscCall(VecRestoreArrayRead(g, &gg));
248: PetscFunctionReturn(PETSC_SUCCESS);
249: }
250: /* ------------------------------------------------------------------- */
251: /*
252: FormJacobian - Evaluates Jacobian matrix.
254: Input Parameters:
255: . snes - the SNES context
256: . x - input vector
257: . dummy - optional user-defined context (not used here)
259: Output Parameters:
260: . jac - Jacobian matrix
261: . B - optionally different preconditioning matrix
263: */
265: PetscErrorCode FormJacobian(SNES snes, Vec x, Mat jac, Mat B, void *dummy)
266: {
267: const PetscScalar *xx;
268: PetscScalar A[3], d;
269: PetscInt i, n, j[3];
271: PetscFunctionBeginUser;
272: /*
273: Get pointer to vector data
274: */
275: PetscCall(VecGetArrayRead(x, &xx));
277: /*
278: Compute Jacobian entries and insert into matrix.
279: - Note that in this case we set all elements for a particular
280: row at once.
281: */
282: PetscCall(VecGetSize(x, &n));
283: d = (PetscReal)(n - 1);
284: d = d * d;
286: /*
287: Interior grid points
288: */
289: for (i = 1; i < n - 1; i++) {
290: j[0] = i - 1;
291: j[1] = i;
292: j[2] = i + 1;
293: A[0] = A[2] = d;
294: A[1] = -2.0 * d + 2.0 * xx[i];
295: PetscCall(MatSetValues(B, 1, &i, 3, j, A, INSERT_VALUES));
296: }
298: /*
299: Boundary points
300: */
301: i = 0;
302: A[0] = 1.0;
304: PetscCall(MatSetValues(B, 1, &i, 1, &i, A, INSERT_VALUES));
306: i = n - 1;
307: A[0] = 1.0;
309: PetscCall(MatSetValues(B, 1, &i, 1, &i, A, INSERT_VALUES));
311: /*
312: Restore vector
313: */
314: PetscCall(VecRestoreArrayRead(x, &xx));
316: /*
317: Assemble matrix
318: */
319: PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
320: PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
321: if (jac != B) {
322: PetscCall(MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY));
323: PetscCall(MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY));
324: }
325: PetscFunctionReturn(PETSC_SUCCESS);
326: }
327: /* ------------------------------------------------------------------- */
328: /*
329: Monitor - User-defined monitoring routine that views the
330: current iterate with an x-window plot.
332: Input Parameters:
333: snes - the SNES context
334: its - iteration number
335: norm - 2-norm function value (may be estimated)
336: ctx - optional user-defined context for private data for the
337: monitor routine, as set by SNESMonitorSet()
339: Note:
340: See the manpage for PetscViewerDrawOpen() for useful runtime options,
341: such as -nox to deactivate all x-window output.
342: */
343: PetscErrorCode Monitor(SNES snes, PetscInt its, PetscReal fnorm, void *ctx)
344: {
345: MonitorCtx *monP = (MonitorCtx *)ctx;
346: Vec x;
348: PetscFunctionBeginUser;
349: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "iter = %" PetscInt_FMT ", SNES Function norm %g\n", its, (double)fnorm));
350: PetscCall(SNESGetSolution(snes, &x));
351: PetscCall(VecView(x, monP->viewer));
352: PetscFunctionReturn(PETSC_SUCCESS);
353: }
355: /*TEST
357: test:
358: args: -nox -snes_monitor_cancel -snes_monitor_short -snes_view -pc_type jacobi -ksp_gmres_cgs_refinement_type refine_always
360: test:
361: suffix: 2
362: args: -nox -snes_monitor_cancel -snes_monitor_short -snes_type newtontr -snes_view
363: requires: !single
365: test:
366: suffix: 3
367: args: -nox -malloc no -options_left no -snes_monitor_cancel -snes_monitor_short -snes_view -pc_type jacobi -ksp_gmres_cgs_refinement_type refine_always
369: test:
370: suffix: 4
371: args: -nox -snes_monitor_cancel -snes_monitor_short -snes_type newtontrdc -snes_view
372: requires: !single
374: TEST*/