Actual source code: ex7.c
2: static char help[] = "Nonlinear, time-dependent PDE in 2d.\n";
4: /*
5: Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
6: Include "petscts.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: */
14: #include <petscdm.h>
15: #include <petscdmda.h>
16: #include <petscts.h>
18: /*
19: User-defined routines
20: */
21: extern PetscErrorCode FormFunction(TS, PetscReal, Vec, Vec, void *), FormInitialSolution(DM, Vec);
22: extern PetscErrorCode MyTSMonitor(TS, PetscInt, PetscReal, Vec, void *);
23: extern PetscErrorCode MySNESMonitor(SNES, PetscInt, PetscReal, PetscViewerAndFormat *);
25: int main(int argc, char **argv)
26: {
27: TS ts; /* time integrator */
28: SNES snes;
29: Vec x, r; /* solution, residual vectors */
30: DM da;
31: PetscViewerAndFormat *vf;
33: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
34: Initialize program
35: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
36: PetscFunctionBeginUser;
37: PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
38: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
39: Create distributed array (DMDA) to manage parallel grid and vectors
40: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
41: 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));
42: PetscCall(DMSetFromOptions(da));
43: PetscCall(DMSetUp(da));
45: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
46: Extract global vectors from DMDA; then duplicate for remaining
47: vectors that are the same types
48: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
49: PetscCall(DMCreateGlobalVector(da, &x));
50: PetscCall(VecDuplicate(x, &r));
52: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
53: Create timestepping solver context
54: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
55: PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
56: PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
57: PetscCall(TSSetRHSFunction(ts, NULL, FormFunction, da));
59: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
60: Create matrix data structure; set Jacobian evaluation routine
62: Set Jacobian matrix data structure and default Jacobian evaluation
63: routine. User can override with:
64: -snes_mf : matrix-free Newton-Krylov method with no preconditioning
65: (unless user explicitly sets preconditioner)
66: -snes_mf_operator : form preconditioning matrix as set by the user,
67: but use matrix-free approx for Jacobian-vector
68: products within Newton-Krylov method
70: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
72: PetscCall(TSSetMaxTime(ts, 1.0));
73: PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER));
74: PetscCall(TSMonitorSet(ts, MyTSMonitor, PETSC_VIEWER_STDOUT_WORLD, NULL));
75: PetscCall(TSSetDM(ts, da));
76: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
77: Customize nonlinear solver
78: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
79: PetscCall(TSSetType(ts, TSBEULER));
80: PetscCall(TSGetSNES(ts, &snes));
81: PetscCall(PetscViewerAndFormatCreate(PETSC_VIEWER_STDOUT_WORLD, PETSC_VIEWER_DEFAULT, &vf));
82: PetscCall(SNESMonitorSet(snes, (PetscErrorCode(*)(SNES, PetscInt, PetscReal, void *))MySNESMonitor, vf, (PetscErrorCode(*)(void **))PetscViewerAndFormatDestroy));
84: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
85: Set initial conditions
86: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
87: PetscCall(FormInitialSolution(da, x));
88: PetscCall(TSSetTimeStep(ts, .0001));
89: PetscCall(TSSetSolution(ts, x));
91: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
92: Set runtime options
93: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
94: PetscCall(TSSetFromOptions(ts));
96: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
97: Solve nonlinear system
98: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
99: PetscCall(TSSolve(ts, x));
101: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
102: Free work space. All PETSc objects should be destroyed when they
103: are no longer needed.
104: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
105: PetscCall(VecDestroy(&x));
106: PetscCall(VecDestroy(&r));
107: PetscCall(TSDestroy(&ts));
108: PetscCall(DMDestroy(&da));
110: PetscCall(PetscFinalize());
111: return 0;
112: }
113: /* ------------------------------------------------------------------- */
114: /*
115: FormFunction - Evaluates nonlinear function, F(x).
117: Input Parameters:
118: . ts - the TS context
119: . X - input vector
120: . ptr - optional user-defined context, as set by SNESSetFunction()
122: Output Parameter:
123: . F - function vector
124: */
125: PetscErrorCode FormFunction(TS ts, PetscReal ftime, Vec X, Vec F, void *ptr)
126: {
127: DM da;
128: PetscInt i, j, Mx, My, xs, ys, xm, ym;
129: PetscReal two = 2.0, hx, hy, sx, sy;
130: PetscScalar u, uxx, uyy, **x, **f;
131: Vec localX;
133: PetscFunctionBeginUser;
134: PetscCall(TSGetDM(ts, &da));
135: PetscCall(DMGetLocalVector(da, &localX));
136: 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));
138: hx = 1.0 / (PetscReal)(Mx - 1);
139: sx = 1.0 / (hx * hx);
140: hy = 1.0 / (PetscReal)(My - 1);
141: sy = 1.0 / (hy * hy);
143: /*
144: Scatter ghost points to local vector,using the 2-step process
145: DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
146: By placing code between these two statements, computations can be
147: done while messages are in transition.
148: */
149: PetscCall(DMGlobalToLocalBegin(da, X, INSERT_VALUES, localX));
150: PetscCall(DMGlobalToLocalEnd(da, X, INSERT_VALUES, localX));
152: /*
153: Get pointers to vector data
154: */
155: PetscCall(DMDAVecGetArrayRead(da, localX, &x));
156: PetscCall(DMDAVecGetArray(da, F, &f));
158: /*
159: Get local grid boundaries
160: */
161: PetscCall(DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL));
163: /*
164: Compute function over the locally owned part of the grid
165: */
166: for (j = ys; j < ys + ym; j++) {
167: for (i = xs; i < xs + xm; i++) {
168: if (i == 0 || j == 0 || i == Mx - 1 || j == My - 1) {
169: f[j][i] = x[j][i];
170: continue;
171: }
172: u = x[j][i];
173: uxx = (two * u - x[j][i - 1] - x[j][i + 1]) * sx;
174: uyy = (two * u - x[j - 1][i] - x[j + 1][i]) * sy;
175: /* f[j][i] = -(uxx + uyy); */
176: 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);
177: }
178: }
180: /*
181: Restore vectors
182: */
183: PetscCall(DMDAVecRestoreArrayRead(da, localX, &x));
184: PetscCall(DMDAVecRestoreArray(da, F, &f));
185: PetscCall(DMRestoreLocalVector(da, &localX));
186: PetscCall(PetscLogFlops(11.0 * ym * xm));
187: PetscFunctionReturn(PETSC_SUCCESS);
188: }
190: /* ------------------------------------------------------------------- */
191: PetscErrorCode FormInitialSolution(DM da, Vec U)
192: {
193: PetscInt i, j, xs, ys, xm, ym, Mx, My;
194: PetscScalar **u;
195: PetscReal hx, hy, x, y, r;
197: PetscFunctionBeginUser;
198: 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));
200: hx = 1.0 / (PetscReal)(Mx - 1);
201: hy = 1.0 / (PetscReal)(My - 1);
203: /*
204: Get pointers to vector data
205: */
206: PetscCall(DMDAVecGetArray(da, U, &u));
208: /*
209: Get local grid boundaries
210: */
211: PetscCall(DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL));
213: /*
214: Compute function over the locally owned part of the grid
215: */
216: for (j = ys; j < ys + ym; j++) {
217: y = j * hy;
218: for (i = xs; i < xs + xm; i++) {
219: x = i * hx;
220: r = PetscSqrtReal((x - .5) * (x - .5) + (y - .5) * (y - .5));
221: if (r < .125) u[j][i] = PetscExpReal(-30.0 * r * r * r);
222: else u[j][i] = 0.0;
223: }
224: }
226: /*
227: Restore vectors
228: */
229: PetscCall(DMDAVecRestoreArray(da, U, &u));
230: PetscFunctionReturn(PETSC_SUCCESS);
231: }
233: PetscErrorCode MyTSMonitor(TS ts, PetscInt step, PetscReal ptime, Vec v, void *ctx)
234: {
235: PetscReal norm;
236: MPI_Comm comm;
238: PetscFunctionBeginUser;
239: if (step < 0) PetscFunctionReturn(PETSC_SUCCESS); /* step of -1 indicates an interpolated solution */
240: PetscCall(VecNorm(v, NORM_2, &norm));
241: PetscCall(PetscObjectGetComm((PetscObject)ts, &comm));
242: PetscCall(PetscPrintf(comm, "timestep %" PetscInt_FMT " time %g norm %g\n", step, (double)ptime, (double)norm));
243: PetscFunctionReturn(PETSC_SUCCESS);
244: }
246: /*
247: MySNESMonitor - illustrate how to set user-defined monitoring routine for SNES.
248: Input Parameters:
249: snes - the SNES context
250: its - iteration number
251: fnorm - 2-norm function value (may be estimated)
252: ctx - optional user-defined context for private data for the
253: monitor routine, as set by SNESMonitorSet()
254: */
255: PetscErrorCode MySNESMonitor(SNES snes, PetscInt its, PetscReal fnorm, PetscViewerAndFormat *vf)
256: {
257: PetscFunctionBeginUser;
258: PetscCall(SNESMonitorDefaultShort(snes, its, fnorm, vf));
259: PetscFunctionReturn(PETSC_SUCCESS);
260: }
262: /*TEST
264: test:
265: args: -ts_max_steps 5
267: test:
268: suffix: 2
269: args: -ts_max_steps 5 -snes_mf_operator
271: test:
272: suffix: 3
273: args: -ts_max_steps 5 -snes_mf -pc_type none
275: TEST*/