Actual source code: ex4.c
2: static char help[] = "Chemo-taxis Problems from Mathematical Biology.\n";
4: /*
5: Page 18, Chemo-taxis Problems from Mathematical Biology
7: rho_t =
8: c_t =
10: Further discussion on Page 134 and in 2d on Page 409
11: */
13: /*
15: Include "petscdmda.h" so that we can use distributed arrays (DMDAs).
16: Include "petscts.h" so that we can use SNES solvers. Note that this
17: file automatically includes:
18: petscsys.h - base PETSc routines petscvec.h - vectors
19: petscmat.h - matrices
20: petscis.h - index sets petscksp.h - Krylov subspace methods
21: petscviewer.h - viewers petscpc.h - preconditioners
22: petscksp.h - linear solvers
23: */
25: #include <petscdm.h>
26: #include <petscdmda.h>
27: #include <petscts.h>
29: typedef struct {
30: PetscScalar rho, c;
31: } Field;
33: typedef struct {
34: PetscScalar epsilon, delta, alpha, beta, gamma, kappa, lambda, mu, cstar;
35: PetscBool upwind;
36: } AppCtx;
38: /*
39: User-defined routines
40: */
41: extern PetscErrorCode IFunction(TS, PetscReal, Vec, Vec, Vec, void *), InitialConditions(DM, Vec);
43: int main(int argc, char **argv)
44: {
45: TS ts; /* nonlinear solver */
46: Vec U; /* solution, residual vectors */
47: DM da;
48: AppCtx appctx;
50: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
51: Initialize program
52: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
54: PetscInitialize(&argc, &argv, (char *)0, help);
56: appctx.epsilon = 1.0e-3;
57: appctx.delta = 1.0;
58: appctx.alpha = 10.0;
59: appctx.beta = 4.0;
60: appctx.gamma = 1.0;
61: appctx.kappa = .75;
62: appctx.lambda = 1.0;
63: appctx.mu = 100.;
64: appctx.cstar = .2;
65: appctx.upwind = PETSC_TRUE;
67: PetscOptionsGetScalar(NULL, NULL, "-delta", &appctx.delta, NULL);
68: PetscOptionsGetBool(NULL, NULL, "-upwind", &appctx.upwind, NULL);
70: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
71: Create distributed array (DMDA) to manage parallel grid and vectors
72: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
73: DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, 8, 2, 1, NULL, &da);
74: DMSetFromOptions(da);
75: DMSetUp(da);
76: DMDASetFieldName(da, 0, "rho");
77: DMDASetFieldName(da, 1, "c");
79: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
80: Extract global vectors from DMDA; then duplicate for remaining
81: vectors that are the same types
82: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
83: DMCreateGlobalVector(da, &U);
85: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
86: Create timestepping solver context
87: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
88: TSCreate(PETSC_COMM_WORLD, &ts);
89: TSSetType(ts, TSROSW);
90: TSSetDM(ts, da);
91: TSSetProblemType(ts, TS_NONLINEAR);
92: TSSetIFunction(ts, NULL, IFunction, &appctx);
94: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
95: Set initial conditions
96: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
97: InitialConditions(da, U);
98: TSSetSolution(ts, U);
100: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
101: Set solver options
102: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
103: TSSetTimeStep(ts, .0001);
104: TSSetMaxTime(ts, 1.0);
105: TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER);
106: TSSetFromOptions(ts);
108: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
109: Solve nonlinear system
110: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
111: TSSolve(ts, U);
113: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
114: Free work space. All PETSc objects should be destroyed when they
115: are no longer needed.
116: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
117: VecDestroy(&U);
118: TSDestroy(&ts);
119: DMDestroy(&da);
121: PetscFinalize();
122: return 0;
123: }
124: /* ------------------------------------------------------------------- */
125: /*
126: IFunction - Evaluates nonlinear function, F(U).
128: Input Parameters:
129: . ts - the TS context
130: . U - input vector
131: . ptr - optional user-defined context, as set by SNESSetFunction()
133: Output Parameter:
134: . F - function vector
135: */
136: PetscErrorCode IFunction(TS ts, PetscReal ftime, Vec U, Vec Udot, Vec F, void *ptr)
137: {
138: AppCtx *appctx = (AppCtx *)ptr;
139: DM da;
140: PetscInt i, Mx, xs, xm;
141: PetscReal hx, sx;
142: PetscScalar rho, c, rhoxx, cxx, cx, rhox, kcxrhox;
143: Field *u, *f, *udot;
144: Vec localU;
146: TSGetDM(ts, &da);
147: DMGetLocalVector(da, &localU);
148: DMDAGetInfo(da, PETSC_IGNORE, &Mx, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE);
150: hx = 1.0 / (PetscReal)(Mx - 1);
151: sx = 1.0 / (hx * hx);
153: /*
154: Scatter ghost points to local vector,using the 2-step process
155: DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
156: By placing code between these two statements, computations can be
157: done while messages are in transition.
158: */
159: DMGlobalToLocalBegin(da, U, INSERT_VALUES, localU);
160: DMGlobalToLocalEnd(da, U, INSERT_VALUES, localU);
162: /*
163: Get pointers to vector data
164: */
165: DMDAVecGetArrayRead(da, localU, &u);
166: DMDAVecGetArrayRead(da, Udot, &udot);
167: DMDAVecGetArrayWrite(da, F, &f);
169: /*
170: Get local grid boundaries
171: */
172: DMDAGetCorners(da, &xs, NULL, NULL, &xm, NULL, NULL);
174: if (!xs) {
175: f[0].rho = udot[0].rho; /* u[0].rho - 0.0; */
176: f[0].c = udot[0].c; /* u[0].c - 1.0; */
177: xs++;
178: xm--;
179: }
180: if (xs + xm == Mx) {
181: f[Mx - 1].rho = udot[Mx - 1].rho; /* u[Mx-1].rho - 1.0; */
182: f[Mx - 1].c = udot[Mx - 1].c; /* u[Mx-1].c - 0.0; */
183: xm--;
184: }
186: /*
187: Compute function over the locally owned part of the grid
188: */
189: for (i = xs; i < xs + xm; i++) {
190: rho = u[i].rho;
191: rhoxx = (-2.0 * rho + u[i - 1].rho + u[i + 1].rho) * sx;
192: c = u[i].c;
193: cxx = (-2.0 * c + u[i - 1].c + u[i + 1].c) * sx;
195: if (!appctx->upwind) {
196: rhox = .5 * (u[i + 1].rho - u[i - 1].rho) / hx;
197: cx = .5 * (u[i + 1].c - u[i - 1].c) / hx;
198: kcxrhox = appctx->kappa * (cxx * rho + cx * rhox);
199: } else {
200: kcxrhox = appctx->kappa * ((u[i + 1].c - u[i].c) * u[i + 1].rho - (u[i].c - u[i - 1].c) * u[i].rho) * sx;
201: }
203: f[i].rho = udot[i].rho - appctx->epsilon * rhoxx + kcxrhox - appctx->mu * PetscAbsScalar(rho) * (1.0 - rho) * PetscMax(0, PetscRealPart(c - appctx->cstar)) + appctx->beta * rho;
204: f[i].c = udot[i].c - appctx->delta * cxx + appctx->lambda * c + appctx->alpha * rho * c / (appctx->gamma + c);
205: }
207: /*
208: Restore vectors
209: */
210: DMDAVecRestoreArrayRead(da, localU, &u);
211: DMDAVecRestoreArrayRead(da, Udot, &udot);
212: DMDAVecRestoreArrayWrite(da, F, &f);
213: DMRestoreLocalVector(da, &localU);
214: return 0;
215: }
217: /* ------------------------------------------------------------------- */
218: PetscErrorCode InitialConditions(DM da, Vec U)
219: {
220: PetscInt i, xs, xm, Mx;
221: Field *u;
222: PetscReal hx, x;
224: DMDAGetInfo(da, PETSC_IGNORE, &Mx, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE, PETSC_IGNORE);
226: hx = 1.0 / (PetscReal)(Mx - 1);
228: /*
229: Get pointers to vector data
230: */
231: DMDAVecGetArrayWrite(da, U, &u);
233: /*
234: Get local grid boundaries
235: */
236: DMDAGetCorners(da, &xs, NULL, NULL, &xm, NULL, NULL);
238: /*
239: Compute function over the locally owned part of the grid
240: */
241: for (i = xs; i < xs + xm; i++) {
242: x = i * hx;
243: if (i < Mx - 1) u[i].rho = 0.0;
244: else u[i].rho = 1.0;
245: u[i].c = PetscCosReal(.5 * PETSC_PI * x);
246: }
248: /*
249: Restore vectors
250: */
251: DMDAVecRestoreArrayWrite(da, U, &u);
252: return 0;
253: }
255: /*TEST
257: test:
258: args: -pc_type lu -da_refine 2 -ts_view -ts_monitor -ts_max_time 1
259: requires: double
261: test:
262: suffix: 2
263: args: -pc_type lu -da_refine 2 -ts_view -ts_monitor_draw_solution -ts_monitor -ts_max_time 1
264: requires: x double
265: output_file: output/ex4_1.out
267: TEST*/