Actual source code: ex4.c
petsc-3.8.3 2017-12-09
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 discusson 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: */
24: #include <petscdm.h>
25: #include <petscdmda.h>
26: #include <petscts.h>
28: typedef struct {
29: PetscScalar rho,c;
30: } Field;
32: typedef struct {
33: PetscScalar epsilon,delta,alpha,beta,gamma,kappa,lambda,mu,cstar;
34: PetscBool upwind;
35: } AppCtx;
37: /*
38: User-defined routines
39: */
40: extern PetscErrorCode IFunction(TS,PetscReal,Vec,Vec,Vec,void*),InitialConditions(DM,Vec);
42: int main(int argc,char **argv)
43: {
44: TS ts; /* nonlinear solver */
45: Vec U; /* solution, residual vectors */
47: DM da;
48: AppCtx appctx;
50: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
51: Initialize program
52: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
53: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
55: appctx.epsilon = 1.0e-3;
56: appctx.delta = 1.0;
57: appctx.alpha = 10.0;
58: appctx.beta = 4.0;
59: appctx.gamma = 1.0;
60: appctx.kappa = .75;
61: appctx.lambda = 1.0;
62: appctx.mu = 100.;
63: appctx.cstar = .2;
64: appctx.upwind = PETSC_TRUE;
66: PetscOptionsGetScalar(NULL,NULL,"-delta",&appctx.delta,NULL);
67: PetscOptionsGetBool(NULL,NULL,"-upwind",&appctx.upwind,NULL);
69: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
70: Create distributed array (DMDA) to manage parallel grid and vectors
71: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
72: DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE,-8,2,1,NULL,&da);
73: DMSetFromOptions(da);
74: DMSetUp(da);
75: DMDASetFieldName(da,0,"rho");
76: DMDASetFieldName(da,1,"c");
78: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
79: Extract global vectors from DMDA; then duplicate for remaining
80: vectors that are the same types
81: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
82: DMCreateGlobalVector(da,&U);
84: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
85: Create timestepping solver context
86: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
87: TSCreate(PETSC_COMM_WORLD,&ts);
88: TSSetType(ts,TSROSW);
89: TSSetDM(ts,da);
90: TSSetProblemType(ts,TS_NONLINEAR);
91: 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 ierr;
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;
141: PetscInt i,Mx,xs,xm;
142: PetscReal hx,sx;
143: PetscScalar rho,c,rhoxx,cxx,cx,rhox,kcxrhox;
144: Field *u,*f,*udot;
145: Vec localU;
148: TSGetDM(ts,&da);
149: DMGetLocalVector(da,&localU);
150: 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);
152: hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
154: /*
155: Scatter ghost points to local vector,using the 2-step process
156: DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
157: By placing code between these two statements, computations can be
158: done while messages are in transition.
159: */
160: DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU);
161: DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU);
163: /*
164: Get pointers to vector data
165: */
166: DMDAVecGetArrayRead(da,localU,&u);
167: DMDAVecGetArrayRead(da,Udot,&udot);
168: DMDAVecGetArray(da,F,&f);
170: /*
171: Get local grid boundaries
172: */
173: DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);
175: if (!xs) {
176: f[0].rho = udot[0].rho; /* u[0].rho - 0.0; */
177: f[0].c = udot[0].c; /* u[0].c - 1.0; */
178: xs++;
179: xm--;
180: }
181: if (xs+xm == Mx) {
182: f[Mx-1].rho = udot[Mx-1].rho; /* u[Mx-1].rho - 1.0; */
183: f[Mx-1].c = udot[Mx-1].c; /* u[Mx-1].c - 0.0; */
184: xm--;
185: }
187: /*
188: Compute function over the locally owned part of the grid
189: */
190: for (i=xs; i<xs+xm; i++) {
191: rho = u[i].rho;
192: rhoxx = (-2.0*rho + u[i-1].rho + u[i+1].rho)*sx;
193: c = u[i].c;
194: cxx = (-2.0*c + u[i-1].c + u[i+1].c)*sx;
196: if (!appctx->upwind) {
197: rhox = .5*(u[i+1].rho - u[i-1].rho)/hx;
198: cx = .5*(u[i+1].c - u[i-1].c)/hx;
199: kcxrhox = appctx->kappa*(cxx*rho + cx*rhox);
200: } else {
201: 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;
202: }
204: 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;
205: f[i].c = udot[i].c - appctx->delta*cxx + appctx->lambda*c + appctx->alpha*rho*c/(appctx->gamma + c);
206: }
208: /*
209: Restore vectors
210: */
211: DMDAVecRestoreArrayRead(da,localU,&u);
212: DMDAVecRestoreArrayRead(da,Udot,&udot);
213: DMDAVecRestoreArray(da,F,&f);
214: DMRestoreLocalVector(da,&localU);
215: return(0);
216: }
218: /* ------------------------------------------------------------------- */
219: PetscErrorCode InitialConditions(DM da,Vec U)
220: {
222: PetscInt i,xs,xm,Mx;
223: Field *u;
224: PetscReal hx,x;
227: 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);
229: hx = 1.0/(PetscReal)(Mx-1);
231: /*
232: Get pointers to vector data
233: */
234: DMDAVecGetArray(da,U,&u);
236: /*
237: Get local grid boundaries
238: */
239: DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);
241: /*
242: Compute function over the locally owned part of the grid
243: */
244: for (i=xs; i<xs+xm; i++) {
245: x = i*hx;
246: if (x < 1.0) u[i].rho = 0.0;
247: else u[i].rho = 1.0;
248: u[i].c = PetscCosReal(.5*PETSC_PI*x);
249: }
251: /*
252: Restore vectors
253: */
254: DMDAVecRestoreArray(da,U,&u);
255: return(0);
256: }