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*/