Actual source code: ex2.c
1: static char help[] = "Newton method to solve u'' + u^{2} = f, sequentially.\n\
2: This example employs a user-defined monitoring routine.\n\n";
4: /*
5: Include "petscdraw.h" so that we can use PETSc drawing routines.
6: Include "petscsnes.h" so that we can use SNES solvers. Note that this
7: file automatically includes:
8: petscsys.h - base PETSc routines petscvec.h - vectors
9: petscmat.h - matrices
10: petscis.h - index sets petscksp.h - Krylov subspace methods
11: petscviewer.h - viewers petscpc.h - preconditioners
12: petscksp.h - linear solvers
13: */
15: #include <petscsnes.h>
17: /*
18: User-defined routines
19: */
20: extern PetscErrorCode FormJacobian(SNES, Vec, Mat, Mat, void *);
21: extern PetscErrorCode FormFunction(SNES, Vec, Vec, void *);
22: extern PetscErrorCode FormInitialGuess(Vec);
23: extern PetscErrorCode Monitor(SNES, PetscInt, PetscReal, void *);
25: /*
26: User-defined context for monitoring
27: */
28: typedef struct {
29: PetscViewer viewer;
30: } MonitorCtx;
32: int main(int argc, char **argv)
33: {
34: SNES snes; /* SNES context */
35: Vec x, r, F, U; /* vectors */
36: Mat J; /* Jacobian matrix */
37: MonitorCtx monP; /* monitoring context */
38: PetscInt its, n = 5, i, maxit, maxf;
39: PetscMPIInt size;
40: PetscScalar h, xp, v, none = -1.0;
41: PetscReal abstol, rtol, stol, norm;
43: PetscFunctionBeginUser;
44: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
45: PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
46: PetscCheck(size == 1, PETSC_COMM_SELF, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only!");
47: PetscCall(PetscOptionsGetInt(NULL, NULL, "-n", &n, NULL));
48: h = 1.0 / (n - 1);
50: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
51: Create nonlinear solver context
52: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
54: PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes));
56: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
57: Create vector data structures; set function evaluation routine
58: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
59: /*
60: Note that we form 1 vector from scratch and then duplicate as needed.
61: */
62: PetscCall(VecCreate(PETSC_COMM_WORLD, &x));
63: PetscCall(VecSetSizes(x, PETSC_DECIDE, n));
64: PetscCall(VecSetFromOptions(x));
65: PetscCall(VecDuplicate(x, &r));
66: PetscCall(VecDuplicate(x, &F));
67: PetscCall(VecDuplicate(x, &U));
69: /*
70: Set function evaluation routine and vector
71: */
72: PetscCall(SNESSetFunction(snes, r, FormFunction, (void *)F));
74: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
75: Create matrix data structure; set Jacobian evaluation routine
76: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
78: PetscCall(MatCreate(PETSC_COMM_WORLD, &J));
79: PetscCall(MatSetSizes(J, PETSC_DECIDE, PETSC_DECIDE, n, n));
80: PetscCall(MatSetFromOptions(J));
81: PetscCall(MatSeqAIJSetPreallocation(J, 3, NULL));
83: /*
84: Set Jacobian matrix data structure and default Jacobian evaluation
85: routine. User can override with:
86: -snes_fd : default finite differencing approximation of Jacobian
87: -snes_mf : matrix-free Newton-Krylov method with no preconditioning
88: (unless user explicitly sets preconditioner)
89: -snes_mf_operator : form preconditioning matrix as set by the user,
90: but use matrix-free approx for Jacobian-vector
91: products within Newton-Krylov method
92: */
94: PetscCall(SNESSetJacobian(snes, J, J, FormJacobian, NULL));
96: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
97: Customize nonlinear solver; set runtime options
98: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
100: /*
101: Set an optional user-defined monitoring routine
102: */
103: PetscCall(PetscViewerDrawOpen(PETSC_COMM_WORLD, 0, 0, 0, 0, 400, 400, &monP.viewer));
104: PetscCall(SNESMonitorSet(snes, Monitor, &monP, 0));
106: /*
107: Set names for some vectors to facilitate monitoring (optional)
108: */
109: PetscCall(PetscObjectSetName((PetscObject)x, "Approximate Solution"));
110: PetscCall(PetscObjectSetName((PetscObject)U, "Exact Solution"));
112: /*
113: Set SNES/KSP/KSP/PC runtime options, e.g.,
114: -snes_view -snes_monitor -ksp_type <ksp> -pc_type <pc>
115: */
116: PetscCall(SNESSetFromOptions(snes));
118: /*
119: Print parameters used for convergence testing (optional) ... just
120: to demonstrate this routine; this information is also printed with
121: the option -snes_view
122: */
123: PetscCall(SNESGetTolerances(snes, &abstol, &rtol, &stol, &maxit, &maxf));
124: 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));
126: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
127: Initialize application:
128: Store right-hand side of PDE and exact solution
129: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
131: xp = 0.0;
132: for (i = 0; i < n; i++) {
133: v = 6.0 * xp + PetscPowScalar(xp + 1.e-12, 6.0); /* +1.e-12 is to prevent 0^6 */
134: PetscCall(VecSetValues(F, 1, &i, &v, INSERT_VALUES));
135: v = xp * xp * xp;
136: PetscCall(VecSetValues(U, 1, &i, &v, INSERT_VALUES));
137: xp += h;
138: }
140: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
141: Evaluate initial guess; then solve nonlinear system
142: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
143: /*
144: Note: The user should initialize the vector, x, with the initial guess
145: for the nonlinear solver prior to calling SNESSolve(). In particular,
146: to employ an initial guess of zero, the user should explicitly set
147: this vector to zero by calling VecSet().
148: */
149: PetscCall(FormInitialGuess(x));
150: PetscCall(SNESSolve(snes, NULL, x));
151: PetscCall(SNESGetIterationNumber(snes, &its));
152: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "number of SNES iterations = %" PetscInt_FMT "\n\n", its));
154: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
155: Check solution and clean up
156: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
158: /*
159: Check the error
160: */
161: PetscCall(VecAXPY(x, none, U));
162: PetscCall(VecNorm(x, NORM_2, &norm));
163: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Norm of error %g, Iterations %" PetscInt_FMT "\n", (double)norm, its));
165: /*
166: Free work space. All PETSc objects should be destroyed when they
167: are no longer needed.
168: */
169: PetscCall(VecDestroy(&x));
170: PetscCall(VecDestroy(&r));
171: PetscCall(VecDestroy(&U));
172: PetscCall(VecDestroy(&F));
173: PetscCall(MatDestroy(&J));
174: PetscCall(SNESDestroy(&snes));
175: PetscCall(PetscViewerDestroy(&monP.viewer));
176: PetscCall(PetscFinalize());
177: return 0;
178: }
179: /* ------------------------------------------------------------------- */
180: /*
181: FormInitialGuess - Computes initial guess.
183: Input/Output Parameter:
184: . x - the solution vector
185: */
186: PetscErrorCode FormInitialGuess(Vec x)
187: {
188: PetscFunctionBeginUser;
189: PetscCall(VecSet(x, 0.5));
190: PetscFunctionReturn(PETSC_SUCCESS);
191: }
192: /* ------------------------------------------------------------------- */
193: /*
194: FormFunction - Evaluates nonlinear function, F(x).
196: Input Parameters:
197: . snes - the SNES context
198: . x - input vector
199: . ctx - optional user-defined context, as set by SNESSetFunction()
201: Output Parameter:
202: . f - function vector
204: Note:
205: The user-defined context can contain any application-specific data
206: needed for the function evaluation (such as various parameters, work
207: vectors, and grid information). In this program the context is just
208: a vector containing the right-hand side of the discretized PDE.
209: */
211: PetscErrorCode FormFunction(SNES snes, Vec x, Vec f, void *ctx)
212: {
213: Vec g = (Vec)ctx;
214: const PetscScalar *xx, *gg;
215: PetscScalar *ff, d;
216: PetscInt i, n;
218: PetscFunctionBeginUser;
219: /*
220: Get pointers to vector data.
221: - For default PETSc vectors, VecGetArray() returns a pointer to
222: the data array. Otherwise, the routine is implementation dependent.
223: - You MUST call VecRestoreArray() when you no longer need access to
224: the array.
225: */
226: PetscCall(VecGetArrayRead(x, &xx));
227: PetscCall(VecGetArray(f, &ff));
228: PetscCall(VecGetArrayRead(g, &gg));
230: /*
231: Compute function
232: */
233: PetscCall(VecGetSize(x, &n));
234: d = (PetscReal)(n - 1);
235: d = d * d;
236: ff[0] = xx[0];
237: 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];
238: ff[n - 1] = xx[n - 1] - 1.0;
240: /*
241: Restore vectors
242: */
243: PetscCall(VecRestoreArrayRead(x, &xx));
244: PetscCall(VecRestoreArray(f, &ff));
245: PetscCall(VecRestoreArrayRead(g, &gg));
246: PetscFunctionReturn(PETSC_SUCCESS);
247: }
248: /* ------------------------------------------------------------------- */
249: /*
250: FormJacobian - Evaluates Jacobian matrix.
252: Input Parameters:
253: . snes - the SNES context
254: . x - input vector
255: . dummy - optional user-defined context (not used here)
257: Output Parameters:
258: . jac - Jacobian matrix
259: . B - optionally different preconditioning matrix
261: */
263: PetscErrorCode FormJacobian(SNES snes, Vec x, Mat jac, Mat B, void *dummy)
264: {
265: const PetscScalar *xx;
266: PetscScalar A[3], d;
267: PetscInt i, n, j[3];
269: PetscFunctionBeginUser;
270: /*
271: Get pointer to vector data
272: */
273: PetscCall(VecGetArrayRead(x, &xx));
275: /*
276: Compute Jacobian entries and insert into matrix.
277: - Note that in this case we set all elements for a particular
278: row at once.
279: */
280: PetscCall(VecGetSize(x, &n));
281: d = (PetscReal)(n - 1);
282: d = d * d;
284: /*
285: Interior grid points
286: */
287: for (i = 1; i < n - 1; i++) {
288: j[0] = i - 1;
289: j[1] = i;
290: j[2] = i + 1;
291: A[0] = A[2] = d;
292: A[1] = -2.0 * d + 2.0 * xx[i];
293: PetscCall(MatSetValues(B, 1, &i, 3, j, A, INSERT_VALUES));
294: }
296: /*
297: Boundary points
298: */
299: i = 0;
300: A[0] = 1.0;
302: PetscCall(MatSetValues(B, 1, &i, 1, &i, A, INSERT_VALUES));
304: i = n - 1;
305: A[0] = 1.0;
307: PetscCall(MatSetValues(B, 1, &i, 1, &i, A, INSERT_VALUES));
309: /*
310: Restore vector
311: */
312: PetscCall(VecRestoreArrayRead(x, &xx));
314: /*
315: Assemble matrix
316: */
317: PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
318: PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
319: if (jac != B) {
320: PetscCall(MatAssemblyBegin(jac, MAT_FINAL_ASSEMBLY));
321: PetscCall(MatAssemblyEnd(jac, MAT_FINAL_ASSEMBLY));
322: }
323: PetscFunctionReturn(PETSC_SUCCESS);
324: }
325: /* ------------------------------------------------------------------- */
326: /*
327: Monitor - User-defined monitoring routine that views the
328: current iterate with an x-window plot.
330: Input Parameters:
331: snes - the SNES context
332: its - iteration number
333: norm - 2-norm function value (may be estimated)
334: ctx - optional user-defined context for private data for the
335: monitor routine, as set by SNESMonitorSet()
337: Note:
338: See the manpage for PetscViewerDrawOpen() for useful runtime options,
339: such as -nox to deactivate all x-window output.
340: */
341: PetscErrorCode Monitor(SNES snes, PetscInt its, PetscReal fnorm, void *ctx)
342: {
343: MonitorCtx *monP = (MonitorCtx *)ctx;
344: Vec x;
345: SNESConvergedReason reason;
347: PetscFunctionBeginUser;
348: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "iter = %" PetscInt_FMT ", SNES Function norm %g\n", its, (double)fnorm));
349: PetscCall(SNESGetConvergedReason(snes, &reason));
350: PetscCall(SNESGetSolution(snes, &x));
351: PetscCall(VecView(x, monP->viewer));
352: PetscCall(PetscPrintf(PETSC_COMM_WORLD, " converged = %s\n", SNESConvergedReasons[reason]));
353: PetscFunctionReturn(PETSC_SUCCESS);
354: }
356: /*TEST
358: test:
359: args: -nox -snes_monitor_cancel -snes_monitor_short -snes_view -pc_type jacobi -ksp_gmres_cgs_refinement_type refine_always
361: test:
362: suffix: 2
363: args: -nox -snes_monitor_cancel -snes_monitor_short -snes_type newtontr -snes_view
364: requires: !single
366: test:
367: suffix: 3
368: 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
370: test:
371: suffix: 4
372: args: -nox -snes_monitor_cancel -snes_monitor_short -snes_type newtontrdc -snes_view
373: requires: !single
375: test:
376: suffix: 5
377: filter: grep -v atol | sed -e "s/CONVERGED_ITS/DIVERGED_MAX_IT/g" | sed -e "s/CONVERGED_FNORM_RELATIVE/DIVERGED_MAX_IT/g"
378: args: -nox -snes_type {{newtonls newtontr ncg ngmres qn anderson nrichardson ms ksponly ksptransposeonly vinewtonrsls vinewtonssls fas ms}} -snes_max_it 1
379: requires: !single
381: TEST*/