Actual source code: ex5.c
1: static char help[] = "Demonstrates Pattern Formation with Reaction-Diffusion Equations.\n";
3: /*F
4: This example is taken from the book, Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations by
5: W. Hundsdorf and J.G. Verwer, Page 21, Pattern Formation with Reaction-Diffusion Equations
6: \begin{eqnarray*}
7: u_t = D_1 (u_{xx} + u_{yy}) - u*v^2 + \gamma(1 -u) \\
8: v_t = D_2 (v_{xx} + v_{yy}) + u*v^2 - (\gamma + \kappa)v
9: \end{eqnarray*}
10: Unlike in the book this uses periodic boundary conditions instead of Neumann
11: (since they are easier for finite differences).
12: F*/
14: /*
15: Helpful runtime monitor options:
16: -ts_monitor_draw_solution
17: -draw_save -draw_save_movie
19: Helpful runtime linear solver options:
20: -pc_type mg -pc_mg_galerkin pmat -da_refine 1 -snes_monitor -ksp_monitor -ts_view (note that these Jacobians are so well-conditioned multigrid may not be the best solver)
22: Point your browser to localhost:8080 to monitor the simulation
23: ./ex5 -ts_view_pre saws -stack_view saws -draw_save -draw_save_single_file -x_virtual -ts_monitor_draw_solution -saws_root .
25: */
27: /*
29: Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
30: Include "petscts.h" so that we can use SNES numerical (ODE) integrators. Note that this
31: file automatically includes:
32: petscsys.h - base PETSc routines petscvec.h - vectors
33: petscmat.h - matrices petscis.h - index sets
34: petscksp.h - Krylov subspace methods petscpc.h - preconditioners
35: petscviewer.h - viewers petscsnes.h - nonlinear solvers
36: */
37: #include "reaction_diffusion.h"
38: #include <petscdm.h>
39: #include <petscdmda.h>
41: /* ------------------------------------------------------------------- */
42: PetscErrorCode InitialConditions(DM da, Vec U)
43: {
44: PetscInt i, j, xs, ys, xm, ym, Mx, My;
45: Field **u;
46: PetscReal hx, hy, x, y;
48: PetscFunctionBegin;
49: 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));
51: hx = 2.5 / (PetscReal)Mx;
52: hy = 2.5 / (PetscReal)My;
54: /*
55: Get pointers to actual vector data
56: */
57: PetscCall(DMDAVecGetArray(da, U, &u));
59: /*
60: Get local grid boundaries
61: */
62: PetscCall(DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL));
64: /*
65: Compute function over the locally owned part of the grid
66: */
67: for (j = ys; j < ys + ym; j++) {
68: y = j * hy;
69: for (i = xs; i < xs + xm; i++) {
70: x = i * hx;
71: if (PetscApproximateGTE(x, 1.0) && PetscApproximateLTE(x, 1.5) && PetscApproximateGTE(y, 1.0) && PetscApproximateLTE(y, 1.5))
72: u[j][i].v = PetscPowReal(PetscSinReal(4.0 * PETSC_PI * x), 2.0) * PetscPowReal(PetscSinReal(4.0 * PETSC_PI * y), 2.0) / 4.0;
73: else u[j][i].v = 0.0;
75: u[j][i].u = 1.0 - 2.0 * u[j][i].v;
76: }
77: }
79: /*
80: Restore access to vector
81: */
82: PetscCall(DMDAVecRestoreArray(da, U, &u));
83: PetscFunctionReturn(PETSC_SUCCESS);
84: }
86: int main(int argc, char **argv)
87: {
88: TS ts; /* ODE integrator */
89: Vec x; /* solution */
90: DM da;
91: AppCtx appctx;
93: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
94: Initialize program
95: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
96: PetscFunctionBeginUser;
97: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
98: appctx.D1 = 8.0e-5;
99: appctx.D2 = 4.0e-5;
100: appctx.gamma = .024;
101: appctx.kappa = .06;
102: appctx.aijpc = PETSC_FALSE;
104: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
105: Create distributed array (DMDA) to manage parallel grid and vectors
106: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
107: PetscCall(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC, DM_BOUNDARY_PERIODIC, DMDA_STENCIL_STAR, 65, 65, PETSC_DECIDE, PETSC_DECIDE, 2, 1, NULL, NULL, &da));
108: PetscCall(DMSetFromOptions(da));
109: PetscCall(DMSetUp(da));
110: PetscCall(DMDASetFieldName(da, 0, "u"));
111: PetscCall(DMDASetFieldName(da, 1, "v"));
113: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
114: Create global vector from DMDA; this will be used to store the solution
115: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
116: PetscCall(DMCreateGlobalVector(da, &x));
118: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
119: Create timestepping solver context
120: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
121: PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
122: PetscCall(TSSetType(ts, TSARKIMEX));
123: PetscCall(TSARKIMEXSetFullyImplicit(ts, PETSC_TRUE));
124: PetscCall(TSSetDM(ts, da));
125: PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
126: PetscCall(TSSetRHSFunction(ts, NULL, RHSFunction, &appctx));
127: PetscCall(TSSetRHSJacobian(ts, NULL, NULL, RHSJacobian, &appctx));
129: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
130: Set initial conditions
131: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
132: PetscCall(InitialConditions(da, x));
133: PetscCall(TSSetSolution(ts, x));
135: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
136: Set solver options
137: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
138: PetscCall(TSSetMaxTime(ts, 2000.0));
139: PetscCall(TSSetTimeStep(ts, .0001));
140: PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER));
141: PetscCall(TSSetFromOptions(ts));
143: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
144: Solve ODE system
145: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
146: PetscCall(TSSolve(ts, x));
148: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
149: Free work space.
150: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
151: PetscCall(VecDestroy(&x));
152: PetscCall(TSDestroy(&ts));
153: PetscCall(DMDestroy(&da));
155: PetscCall(PetscFinalize());
156: return 0;
157: }
159: /*TEST
161: build:
162: depends: reaction_diffusion.c
164: test:
165: args: -ts_view -ts_monitor -ts_max_time 500
166: requires: double
167: timeoutfactor: 3
169: test:
170: suffix: 2
171: args: -ts_view -ts_monitor -ts_max_time 500 -ts_monitor_draw_solution
172: requires: x double
173: output_file: output/ex5_1.out
174: timeoutfactor: 3
176: TEST*/