Actual source code: ex25.c

petsc-3.4.4 2014-03-13
  1: static const char help[] = "Time-dependent Brusselator reaction-diffusion PDE in 1d. Demonstrates IMEX methods.\n";
  2: /*
  3:    u_t - alpha u_xx = A + u^2 v - (B+1) u
  4:    v_t - alpha v_xx = B u - u^2 v
  5:    0 < x < 1;
  6:    A = 1, B = 3, alpha = 1/50

  8:    Initial conditions:
  9:    u(x,0) = 1 + sin(2 pi x)
 10:    v(x,0) = 3

 12:    Boundary conditions:
 13:    u(0,t) = u(1,t) = 1
 14:    v(0,t) = v(1,t) = 3
 15: */

 17: #include <petscdmda.h>
 18: #include <petscts.h>

 20: typedef struct {
 21:   PetscScalar u,v;
 22: } Field;

 24: typedef struct _User *User;
 25: struct _User {
 26:   PetscReal A,B;                /* Reaction coefficients */
 27:   PetscReal alpha;              /* Diffusion coefficient */
 28:   PetscReal uleft,uright;       /* Dirichlet boundary conditions */
 29:   PetscReal vleft,vright;       /* Dirichlet boundary conditions */
 30: };

 32: static PetscErrorCode FormRHSFunction(TS,PetscReal,Vec,Vec,void*);
 33: static PetscErrorCode FormIFunction(TS,PetscReal,Vec,Vec,Vec,void*);
 34: static PetscErrorCode FormIJacobian(TS,PetscReal,Vec,Vec,PetscReal,Mat*,Mat*,MatStructure*,void*);
 35: static PetscErrorCode FormInitialSolution(TS,Vec,void*);

 39: int main(int argc,char **argv)
 40: {
 41:   TS                ts;         /* nonlinear solver */
 42:   Vec               X;          /* solution, residual vectors */
 43:   Mat               J;          /* Jacobian matrix */
 44:   PetscInt          steps,maxsteps,mx;
 45:   PetscErrorCode    ierr;
 46:   DM                da;
 47:   PetscReal         ftime,hx,dt;
 48:   struct _User      user;       /* user-defined work context */
 49:   TSConvergedReason reason;

 51:   PetscInitialize(&argc,&argv,(char*)0,help);

 53:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 54:      Create distributed array (DMDA) to manage parallel grid and vectors
 55:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 56:   DMDACreate1d(PETSC_COMM_WORLD,DMDA_BOUNDARY_NONE,-11,2,2,NULL,&da);

 58:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 59:      Extract global vectors from DMDA;
 60:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 61:   DMCreateGlobalVector(da,&X);

 63:   /* Initialize user application context */
 64:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Advection-reaction options","");
 65:   {
 66:     user.A      = 1;
 67:     user.B      = 3;
 68:     user.alpha  = 0.02;
 69:     user.uleft  = 1;
 70:     user.uright = 1;
 71:     user.vleft  = 3;
 72:     user.vright = 3;
 73:     PetscOptionsReal("-A","Reaction rate","",user.A,&user.A,NULL);
 74:     PetscOptionsReal("-B","Reaction rate","",user.B,&user.B,NULL);
 75:     PetscOptionsReal("-alpha","Diffusion coefficient","",user.alpha,&user.alpha,NULL);
 76:     PetscOptionsReal("-uleft","Dirichlet boundary condition","",user.uleft,&user.uleft,NULL);
 77:     PetscOptionsReal("-uright","Dirichlet boundary condition","",user.uright,&user.uright,NULL);
 78:     PetscOptionsReal("-vleft","Dirichlet boundary condition","",user.vleft,&user.vleft,NULL);
 79:     PetscOptionsReal("-vright","Dirichlet boundary condition","",user.vright,&user.vright,NULL);
 80:   }
 81:   PetscOptionsEnd();

 83:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 84:      Create timestepping solver context
 85:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 86:   TSCreate(PETSC_COMM_WORLD,&ts);
 87:   TSSetDM(ts,da);
 88:   TSSetType(ts,TSARKIMEX);
 89:   TSSetRHSFunction(ts,NULL,FormRHSFunction,&user);
 90:   TSSetIFunction(ts,NULL,FormIFunction,&user);
 91:   DMCreateMatrix(da,MATAIJ,&J);
 92:   TSSetIJacobian(ts,J,J,FormIJacobian,&user);

 94:   ftime    = 10.0;
 95:   maxsteps = 10000;
 96:   TSSetDuration(ts,maxsteps,ftime);

 98:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 99:      Set initial conditions
100:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
101:   FormInitialSolution(ts,X,&user);
102:   TSSetSolution(ts,X);
103:   VecGetSize(X,&mx);
104:   hx = 1.0/(PetscReal)(mx/2-1);
105:   dt = 0.4 * PetscSqr(hx) / user.alpha; /* Diffusive stability limit */
106:   TSSetInitialTimeStep(ts,0.0,dt);

108:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
109:      Set runtime options
110:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
111:   TSSetFromOptions(ts);

113:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
114:      Solve nonlinear system
115:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
116:   TSSolve(ts,X);
117:   TSGetSolveTime(ts,&ftime);
118:   TSGetTimeStepNumber(ts,&steps);
119:   TSGetConvergedReason(ts,&reason);
120:   PetscPrintf(PETSC_COMM_WORLD,"%s at time %G after %D steps\n",TSConvergedReasons[reason],ftime,steps);

122:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
123:      Free work space.
124:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
125:   MatDestroy(&J);
126:   VecDestroy(&X);
127:   TSDestroy(&ts);
128:   DMDestroy(&da);
129:   PetscFinalize();
130:   return 0;
131: }

135: static PetscErrorCode FormIFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ptr)
136: {
137:   User           user = (User)ptr;
138:   DM             da;
139:   DMDALocalInfo  info;
140:   PetscInt       i;
141:   Field          *x,*xdot,*f;
142:   PetscReal      hx;
143:   Vec            Xloc;

147:   TSGetDM(ts,&da);
148:   DMDAGetLocalInfo(da,&info);
149:   hx   = 1.0/(PetscReal)(info.mx-1);

151:   /*
152:      Scatter ghost points to local vector,using the 2-step process
153:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
154:      By placing code between these two statements, computations can be
155:      done while messages are in transition.
156:   */
157:   DMGetLocalVector(da,&Xloc);
158:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,Xloc);
159:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,Xloc);

161:   /* Get pointers to vector data */
162:   DMDAVecGetArray(da,Xloc,&x);
163:   DMDAVecGetArray(da,Xdot,&xdot);
164:   DMDAVecGetArray(da,F,&f);

166:   /* Compute function over the locally owned part of the grid */
167:   for (i=info.xs; i<info.xs+info.xm; i++) {
168:     if (i == 0) {
169:       f[i].u = hx * (x[i].u - user->uleft);
170:       f[i].v = hx * (x[i].v - user->vleft);
171:     } else if (i == info.mx-1) {
172:       f[i].u = hx * (x[i].u - user->uright);
173:       f[i].v = hx * (x[i].v - user->vright);
174:     } else {
175:       f[i].u = hx * xdot[i].u - user->alpha * (x[i-1].u - 2.*x[i].u + x[i+1].u) / hx;
176:       f[i].v = hx * xdot[i].v - user->alpha * (x[i-1].v - 2.*x[i].v + x[i+1].v) / hx;
177:     }
178:   }

180:   /* Restore vectors */
181:   DMDAVecRestoreArray(da,Xloc,&x);
182:   DMDAVecRestoreArray(da,Xdot,&xdot);
183:   DMDAVecRestoreArray(da,F,&f);
184:   DMRestoreLocalVector(da,&Xloc);
185:   return(0);
186: }

190: static PetscErrorCode FormRHSFunction(TS ts,PetscReal t,Vec X,Vec F,void *ptr)
191: {
192:   User           user = (User)ptr;
193:   DM             da;
194:   DMDALocalInfo  info;
195:   PetscInt       i;
196:   PetscReal      hx;
197:   Field          *x,*f;

201:   TSGetDM(ts,&da);
202:   DMDAGetLocalInfo(da,&info);
203:   hx   = 1.0/(PetscReal)(info.mx-1);

205:   /* Get pointers to vector data */
206:   DMDAVecGetArray(da,X,&x);
207:   DMDAVecGetArray(da,F,&f);

209:   /* Compute function over the locally owned part of the grid */
210:   for (i=info.xs; i<info.xs+info.xm; i++) {
211:     PetscScalar u = x[i].u,v = x[i].v;
212:     f[i].u = hx*(user->A + u*u*v - (user->B+1)*u);
213:     f[i].v = hx*(user->B*u - u*u*v);
214:   }

216:   /* Restore vectors */
217:   DMDAVecRestoreArray(da,X,&x);
218:   DMDAVecRestoreArray(da,F,&f);
219:   return(0);
220: }

222: /* --------------------------------------------------------------------- */
223: /*
224:   IJacobian - Compute IJacobian = dF/dU + a dF/dUdot
225: */
228: PetscErrorCode FormIJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat *J,Mat *Jpre,MatStructure *str,void *ptr)
229: {
230:   User           user = (User)ptr;
232:   DMDALocalInfo  info;
233:   PetscInt       i;
234:   PetscReal      hx;
235:   DM             da;
236:   Field          *x,*xdot;

239:   TSGetDM(ts,&da);
240:   DMDAGetLocalInfo(da,&info);
241:   hx   = 1.0/(PetscReal)(info.mx-1);

243:   /* Get pointers to vector data */
244:   DMDAVecGetArray(da,X,&x);
245:   DMDAVecGetArray(da,Xdot,&xdot);

247:   /* Compute function over the locally owned part of the grid */
248:   for (i=info.xs; i<info.xs+info.xm; i++) {
249:     if (i == 0 || i == info.mx-1) {
250:       const PetscInt    row        = i,col = i;
251:       const PetscScalar vals[2][2] = {{hx,0},{0,hx}};
252:       MatSetValuesBlocked(*Jpre,1,&row,1,&col,&vals[0][0],INSERT_VALUES);
253:     } else {
254:       const PetscInt    row           = i,col[] = {i-1,i,i+1};
255:       const PetscScalar dxxL          = -user->alpha/hx,dxx0 = 2.*user->alpha/hx,dxxR = -user->alpha/hx;
256:       const PetscScalar vals[2][3][2] = {{{dxxL,0},{a *hx+dxx0,0},{dxxR,0}},
257:                                          {{0,dxxL},{0,a*hx+dxx0},{0,dxxR}}};
258:       MatSetValuesBlocked(*Jpre,1,&row,3,col,&vals[0][0][0],INSERT_VALUES);
259:     }
260:   }

262:   /* Restore vectors */
263:   DMDAVecRestoreArray(da,X,&x);
264:   DMDAVecRestoreArray(da,Xdot,&xdot);

266:   MatAssemblyBegin(*Jpre,MAT_FINAL_ASSEMBLY);
267:   MatAssemblyEnd(*Jpre,MAT_FINAL_ASSEMBLY);
268:   if (*J != *Jpre) {
269:     MatAssemblyBegin(*J,MAT_FINAL_ASSEMBLY);
270:     MatAssemblyEnd(*J,MAT_FINAL_ASSEMBLY);
271:   }
272:   return(0);
273: }

277: PetscErrorCode FormInitialSolution(TS ts,Vec X,void *ctx)
278: {
279:   User           user = (User)ctx;
280:   DM             da;
281:   PetscInt       i;
282:   DMDALocalInfo  info;
283:   Field          *x;
284:   PetscReal      hx;

288:   TSGetDM(ts,&da);
289:   DMDAGetLocalInfo(da,&info);
290:   hx   = 1.0/(PetscReal)(info.mx-1);

292:   /* Get pointers to vector data */
293:   DMDAVecGetArray(da,X,&x);

295:   /* Compute function over the locally owned part of the grid */
296:   for (i=info.xs; i<info.xs+info.xm; i++) {
297:     PetscReal xi = i*hx;
298:     x[i].u = user->uleft*(1.-xi) + user->uright*xi + sin(2.*PETSC_PI*xi);
299:     x[i].v = user->vleft*(1.-xi) + user->vright*xi;
300:   }
301:   DMDAVecRestoreArray(da,X,&x);
302:   return(0);
303: }