Actual source code: ex7.c
1: static char help[] = "Nonlinear, time-dependent PDE in 2d.\n";
3: /*
4: Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
5: Include "petscts.h" so that we can use SNES solvers. Note that this
6: file automatically includes:
7: petscsys.h - base PETSc routines petscvec.h - vectors
8: petscmat.h - matrices
9: petscis.h - index sets petscksp.h - Krylov subspace methods
10: petscviewer.h - viewers petscpc.h - preconditioners
11: petscksp.h - linear solvers
12: */
13: #include <petscdm.h>
14: #include <petscdmda.h>
15: #include <petscts.h>
17: /*
18: User-defined routines
19: */
20: extern PetscErrorCode FormFunction(TS, PetscReal, Vec, Vec, void *), FormInitialSolution(DM, Vec);
21: extern PetscErrorCode MyTSMonitor(TS, PetscInt, PetscReal, Vec, void *);
22: extern PetscErrorCode MySNESMonitor(SNES, PetscInt, PetscReal, PetscViewerAndFormat *);
24: int main(int argc, char **argv)
25: {
26: TS ts; /* time integrator */
27: SNES snes;
28: Vec x, r; /* solution, residual vectors */
29: DM da;
30: PetscViewerAndFormat *vf;
32: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
33: Initialize program
34: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
35: PetscFunctionBeginUser;
36: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
37: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
38: Create distributed array (DMDA) to manage parallel grid and vectors
39: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
40: PetscCall(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_STAR, 8, 8, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, NULL, &da));
41: PetscCall(DMSetFromOptions(da));
42: PetscCall(DMSetUp(da));
44: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
45: Extract global vectors from DMDA; then duplicate for remaining
46: vectors that are the same types
47: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
48: PetscCall(DMCreateGlobalVector(da, &x));
49: PetscCall(VecDuplicate(x, &r));
51: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
52: Create timestepping solver context
53: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
54: PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
55: PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
56: PetscCall(TSSetRHSFunction(ts, NULL, FormFunction, da));
58: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
59: Create matrix data structure; set Jacobian evaluation routine
61: Set Jacobian matrix data structure and default Jacobian evaluation
62: routine. User can override with:
63: -snes_mf : matrix-free Newton-Krylov method with no preconditioning
64: (unless user explicitly sets preconditioner)
65: -snes_mf_operator : form preconditioning matrix as set by the user,
66: but use matrix-free approx for Jacobian-vector
67: products within Newton-Krylov method
69: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
71: PetscCall(TSSetMaxTime(ts, 1.0));
72: PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER));
73: PetscCall(TSMonitorSet(ts, MyTSMonitor, PETSC_VIEWER_STDOUT_WORLD, NULL));
74: PetscCall(TSSetDM(ts, da));
75: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
76: Customize nonlinear solver
77: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
78: PetscCall(TSSetType(ts, TSBEULER));
79: PetscCall(TSGetSNES(ts, &snes));
80: PetscCall(PetscViewerAndFormatCreate(PETSC_VIEWER_STDOUT_WORLD, PETSC_VIEWER_DEFAULT, &vf));
81: PetscCall(SNESMonitorSet(snes, (PetscErrorCode (*)(SNES, PetscInt, PetscReal, void *))MySNESMonitor, vf, (PetscErrorCode (*)(void **))PetscViewerAndFormatDestroy));
83: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
84: Set initial conditions
85: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
86: PetscCall(FormInitialSolution(da, x));
87: PetscCall(TSSetTimeStep(ts, .0001));
88: PetscCall(TSSetSolution(ts, x));
90: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
91: Set runtime options
92: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
93: PetscCall(TSSetFromOptions(ts));
95: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
96: Solve nonlinear system
97: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
98: PetscCall(TSSolve(ts, x));
100: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
101: Free work space. All PETSc objects should be destroyed when they
102: are no longer needed.
103: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
104: PetscCall(VecDestroy(&x));
105: PetscCall(VecDestroy(&r));
106: PetscCall(TSDestroy(&ts));
107: PetscCall(DMDestroy(&da));
109: PetscCall(PetscFinalize());
110: return 0;
111: }
112: /* ------------------------------------------------------------------- */
113: /*
114: FormFunction - Evaluates nonlinear function, F(x).
116: Input Parameters:
117: . ts - the TS context
118: . X - input vector
119: . ptr - optional user-defined context, as set by SNESSetFunction()
121: Output Parameter:
122: . F - function vector
123: */
124: PetscErrorCode FormFunction(TS ts, PetscReal ftime, Vec X, Vec F, void *ptr)
125: {
126: DM da;
127: PetscInt i, j, Mx, My, xs, ys, xm, ym;
128: PetscReal two = 2.0, hx, hy, sx, sy;
129: PetscScalar u, uxx, uyy, **x, **f;
130: Vec localX;
132: PetscFunctionBeginUser;
133: PetscCall(TSGetDM(ts, &da));
134: PetscCall(DMGetLocalVector(da, &localX));
135: PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &Mx, &My, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE));
137: hx = 1.0 / (PetscReal)(Mx - 1);
138: sx = 1.0 / (hx * hx);
139: hy = 1.0 / (PetscReal)(My - 1);
140: sy = 1.0 / (hy * hy);
142: /*
143: Scatter ghost points to local vector,using the 2-step process
144: DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
145: By placing code between these two statements, computations can be
146: done while messages are in transition.
147: */
148: PetscCall(DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX));
149: PetscCall(DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX));
151: /*
152: Get pointers to vector data
153: */
154: PetscCall(DMDAVecGetArrayRead(da, localX, &x));
155: PetscCall(DMDAVecGetArray(da, F, &f));
157: /*
158: Get local grid boundaries
159: */
160: PetscCall(DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL));
162: /*
163: Compute function over the locally owned part of the grid
164: */
165: for (j = ys; j < ys + ym; j++) {
166: for (i = xs; i < xs + xm; i++) {
167: if (i == 0 || j == 0 || i == Mx - 1 || j == My - 1) {
168: f[j][i] = x[j][i];
169: continue;
170: }
171: u = x[j][i];
172: uxx = (two * u - x[j][i - 1] - x[j][i + 1]) * sx;
173: uyy = (two * u - x[j - 1][i] - x[j + 1][i]) * sy;
174: /* f[j][i] = -(uxx + uyy); */
175: f[j][i] = -u * (uxx + uyy) - (4.0 - 1.0) * ((x[j][i + 1] - x[j][i - 1]) * (x[j][i + 1] - x[j][i - 1]) * .25 * sx + (x[j + 1][i] - x[j - 1][i]) * (x[j + 1][i] - x[j - 1][i]) * .25 * sy);
176: }
177: }
179: /*
180: Restore vectors
181: */
182: PetscCall(DMDAVecRestoreArrayRead(da, localX, &x));
183: PetscCall(DMDAVecRestoreArray(da, F, &f));
184: PetscCall(DMRestoreLocalVector(da, &localX));
185: PetscCall(PetscLogFlops(11.0 * ym * xm));
186: PetscFunctionReturn(PETSC_SUCCESS);
187: }
189: /* ------------------------------------------------------------------- */
190: PetscErrorCode FormInitialSolution(DM da, Vec U)
191: {
192: PetscInt i, j, xs, ys, xm, ym, Mx, My;
193: PetscScalar **u;
194: PetscReal hx, hy, x, y, r;
196: PetscFunctionBeginUser;
197: PetscCall(DMDAGetInfo(da, PETSC_IGNORE, &Mx, &My, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE));
199: hx = 1.0 / (PetscReal)(Mx - 1);
200: hy = 1.0 / (PetscReal)(My - 1);
202: /*
203: Get pointers to vector data
204: */
205: PetscCall(DMDAVecGetArray(da, U, &u));
207: /*
208: Get local grid boundaries
209: */
210: PetscCall(DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL));
212: /*
213: Compute function over the locally owned part of the grid
214: */
215: for (j = ys; j < ys + ym; j++) {
216: y = j * hy;
217: for (i = xs; i < xs + xm; i++) {
218: x = i * hx;
219: r = PetscSqrtReal((x - .5) * (x - .5) + (y - .5) * (y - .5));
220: if (r < .125) u[j][i] = PetscExpReal(-30.0 * r * r * r);
221: else u[j][i] = 0.0;
222: }
223: }
225: /*
226: Restore vectors
227: */
228: PetscCall(DMDAVecRestoreArray(da, U, &u));
229: PetscFunctionReturn(PETSC_SUCCESS);
230: }
232: PetscErrorCode MyTSMonitor(TS ts, PetscInt step, PetscReal ptime, Vec v, void *ctx)
233: {
234: PetscReal norm;
235: MPI_Comm comm;
237: PetscFunctionBeginUser;
238: if (step < 0) PetscFunctionReturn(PETSC_SUCCESS); /* step of -1 indicates an interpolated solution */
239: PetscCall(VecNorm(v, NORM_2, &norm));
240: PetscCall(PetscObjectGetComm((PetscObject)ts, &comm));
241: PetscCall(PetscPrintf(comm, "timestep %" PetscInt_FMT " time %g norm %g\n", step, (double)ptime, (double)norm));
242: PetscFunctionReturn(PETSC_SUCCESS);
243: }
245: /*
246: MySNESMonitor - illustrate how to set user-defined monitoring routine for SNES.
247: Input Parameters:
248: snes - the SNES context
249: its - iteration number
250: fnorm - 2-norm function value (may be estimated)
251: ctx - optional user-defined context for private data for the
252: monitor routine, as set by SNESMonitorSet()
253: */
254: PetscErrorCode MySNESMonitor(SNES snes, PetscInt its, PetscReal fnorm, PetscViewerAndFormat *vf)
255: {
256: PetscFunctionBeginUser;
257: PetscCall(SNESMonitorDefaultShort(snes, its, fnorm, vf));
258: PetscFunctionReturn(PETSC_SUCCESS);
259: }
261: /*TEST
263: test:
264: args: -ts_max_steps 5
266: test:
267: suffix: 2
268: args: -ts_max_steps 5 -snes_mf_operator
270: test:
271: suffix: 3
272: args: -ts_max_steps 5 -snes_mf -pc_type none
274: TEST*/