Actual source code: ex22.c

petsc-3.4.4 2014-03-13
  1: static const char help[] = "Time-dependent advection-reaction PDE in 1d, demonstrates IMEX methods.\n";
  2: /*
  3:    u_t + a1*u_x = -k1*u + k2*v + s1
  4:    v_t + a2*v_x = k1*u - k2*v + s2
  5:    0 < x < 1;
  6:    a1 = 1, k1 = 10^6, s1 = 0,
  7:    a2 = 0, k2 = 2*k1, s2 = 1

  9:    Initial conditions:
 10:    u(x,0) = 1 + s2*x
 11:    v(x,0) = k0/k1*u(x,0) + s1/k1

 13:    Upstream boundary conditions:
 14:    u(0,t) = 1-sin(12*t)^4

 16:    Useful command-line parameters:
 17:    -ts_arkimex_fully_implicit - treats advection implicitly, only relevant with -ts_type arkimex (default)
 18:    -ts_type rosw - use Rosenbrock-W method (linearly implicit IMEX, amortizes assembly and preconditioner setup)
 19: */

 21: #include <petscdmda.h>
 22: #include <petscts.h>

 24: typedef PetscScalar Field[2];

 26: typedef struct _User *User;
 27: struct _User {
 28:   PetscReal a[2];              /* Advection speeds */
 29:   PetscReal k[2];              /* Reaction coefficients */
 30:   PetscReal s[2];              /* Source terms */
 31: };

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

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

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

 56:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 57:      Create distributed array (DMDA) to manage parallel grid and vectors
 58:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 59:   DMDACreate1d(PETSC_COMM_WORLD,DMDA_BOUNDARY_NONE,-11,2,2,NULL,&da);

 61:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 62:      Extract global vectors from DMDA;
 63:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 64:   DMCreateGlobalVector(da,&X);

 66:   /* Initialize user application context */
 67:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Advection-reaction options","");
 68:   {
 69:     user.a[0] = 1;           PetscOptionsReal("-a0","Advection rate 0","",user.a[0],&user.a[0],NULL);
 70:     user.a[1] = 0;           PetscOptionsReal("-a1","Advection rate 1","",user.a[1],&user.a[1],NULL);
 71:     user.k[0] = 1e6;         PetscOptionsReal("-k0","Reaction rate 0","",user.k[0],&user.k[0],NULL);
 72:     user.k[1] = 2*user.k[0]; PetscOptionsReal("-k1","Reaction rate 1","",user.k[1],&user.k[1],NULL);
 73:     user.s[0] = 0;           PetscOptionsReal("-s0","Source 0","",user.s[0],&user.s[0],NULL);
 74:     user.s[1] = 1;           PetscOptionsReal("-s1","Source 1","",user.s[1],&user.s[1],NULL);
 75:   }
 76:   PetscOptionsEnd();

 78:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 79:      Create timestepping solver context
 80:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 81:   TSCreate(PETSC_COMM_WORLD,&ts);
 82:   TSSetDM(ts,da);
 83:   TSSetType(ts,TSARKIMEX);
 84:   TSSetRHSFunction(ts,NULL,FormRHSFunction,&user);
 85:   TSSetIFunction(ts,NULL,FormIFunction,&user);
 86:   DMCreateMatrix(da,MATAIJ,&J);
 87:   TSSetIJacobian(ts,J,J,FormIJacobian,&user);

 89:   /* A line search in the nonlinear solve can fail due to ill-conditioning unless an absolute tolerance is set. Since
 90:    * this problem is linear, we deactivate the line search. For a linear problem, it is usually recommended to also use
 91:    * SNESSetType(snes,SNESKSPONLY). */
 92:   TSGetSNES(ts,&snes);
 93:   SNESGetLineSearch(snes,&linesearch);
 94:   SNESLineSearchSetType(linesearch,SNESLINESEARCHBASIC);

 96:   ftime    = 1.0;
 97:   maxsteps = 10000;
 98:   TSSetDuration(ts,maxsteps,ftime);

100:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
101:      Set initial conditions
102:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
103:   FormInitialSolution(ts,X,&user);
104:   TSSetSolution(ts,X);
105:   VecGetSize(X,&mx);
106:   dt   = .1 * PetscMax(user.a[0],user.a[1]) / mx; /* Advective CFL, I don't know why it needs so much safety factor. */
107:   TSSetInitialTimeStep(ts,0.0,dt);

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

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

123:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
124:      Free work space.
125:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
126:   MatDestroy(&J);
127:   VecDestroy(&X);
128:   TSDestroy(&ts);
129:   DMDestroy(&da);
130:   PetscFinalize();
131:   return 0;
132: }

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

146:   TSGetDM(ts,&da);
147:   DMDAGetLocalInfo(da,&info);

149:   /* Get pointers to vector data */
150:   DMDAVecGetArray(da,X,&x);
151:   DMDAVecGetArray(da,Xdot,&xdot);
152:   DMDAVecGetArray(da,F,&f);

154:   /* Compute function over the locally owned part of the grid */
155:   for (i=info.xs; i<info.xs+info.xm; i++) {
156:     f[i][0] = xdot[i][0] + user->k[0]*x[i][0] - user->k[1]*x[i][1] - user->s[0];
157:     f[i][1] = xdot[i][1] - user->k[0]*x[i][0] + user->k[1]*x[i][1] - user->s[1];
158:   }

160:   /* Restore vectors */
161:   DMDAVecRestoreArray(da,X,&x);
162:   DMDAVecRestoreArray(da,Xdot,&xdot);
163:   DMDAVecRestoreArray(da,F,&f);
164:   return(0);
165: }

169: static PetscErrorCode FormRHSFunction(TS ts,PetscReal t,Vec X,Vec F,void *ptr)
170: {
171:   User           user = (User)ptr;
172:   DM             da;
173:   Vec            Xloc;
174:   DMDALocalInfo  info;
175:   PetscInt       i,j;
176:   PetscReal      hx;
177:   Field          *x,*f;

181:   TSGetDM(ts,&da);
182:   DMDAGetLocalInfo(da,&info);
183:   hx   = 1.0/(PetscReal)info.mx;

185:   /*
186:      Scatter ghost points to local vector,using the 2-step process
187:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
188:      By placing code between these two statements, computations can be
189:      done while messages are in transition.
190:   */
191:   DMGetLocalVector(da,&Xloc);
192:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,Xloc);
193:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,Xloc);

195:   /* Get pointers to vector data */
196:   DMDAVecGetArray(da,Xloc,&x);
197:   DMDAVecGetArray(da,F,&f);

199:   /* Compute function over the locally owned part of the grid */
200:   for (i=info.xs; i<info.xs+info.xm; i++) {
201:     const PetscReal *a     = user->a;
202:     PetscReal       u0t[2] = {1. - PetscPowScalar(sin(12*t),4.),0};
203:     for (j=0; j<2; j++) {
204:       if (i == 0)              f[i][j] = a[j]/hx*(1./3*u0t[j] + 0.5*x[i][j] - x[i+1][j] + 1./6*x[i+2][j]);
205:       else if (i == 1)         f[i][j] = a[j]/hx*(-1./12*u0t[j] + 2./3*x[i-1][j] - 2./3*x[i+1][j] + 1./12*x[i+2][j]);
206:       else if (i == info.mx-2) f[i][j] = a[j]/hx*(-1./6*x[i-2][j] + x[i-1][j] - 0.5*x[i][j] - 1./3*x[i+1][j]);
207:       else if (i == info.mx-1) f[i][j] = a[j]/hx*(-x[i][j] + x[i-1][j]);
208:       else                     f[i][j] = a[j]/hx*(-1./12*x[i-2][j] + 2./3*x[i-1][j] - 2./3*x[i+1][j] + 1./12*x[i+2][j]);
209:     }
210:   }

212:   /* Restore vectors */
213:   DMDAVecRestoreArray(da,Xloc,&x);
214:   DMDAVecRestoreArray(da,F,&f);
215:   DMRestoreLocalVector(da,&Xloc);
216:   return(0);
217: }

219: /* --------------------------------------------------------------------- */
220: /*
221:   IJacobian - Compute IJacobian = dF/dU + a dF/dUdot
222: */
225: PetscErrorCode FormIJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat *J,Mat *Jpre,MatStructure *str,void *ptr)
226: {
227:   User           user = (User)ptr;
229:   DMDALocalInfo  info;
230:   PetscInt       i;
231:   DM             da;
232:   Field          *x,*xdot;

235:   TSGetDM(ts,&da);
236:   DMDAGetLocalInfo(da,&info);

238:   /* Get pointers to vector data */
239:   DMDAVecGetArray(da,X,&x);
240:   DMDAVecGetArray(da,Xdot,&xdot);

242:   /* Compute function over the locally owned part of the grid */
243:   for (i=info.xs; i<info.xs+info.xm; i++) {
244:     const PetscReal *k = user->k;
245:     PetscScalar     v[2][2];

247:     v[0][0] = a + k[0]; v[0][1] =  -k[1];
248:     v[1][0] =    -k[0]; v[1][1] = a+k[1];
249:     MatSetValuesBlocked(*Jpre,1,&i,1,&i,&v[0][0],INSERT_VALUES);
250:   }

252:   /* Restore vectors */
253:   DMDAVecRestoreArray(da,X,&x);
254:   DMDAVecRestoreArray(da,Xdot,&xdot);

256:   MatAssemblyBegin(*Jpre,MAT_FINAL_ASSEMBLY);
257:   MatAssemblyEnd(*Jpre,MAT_FINAL_ASSEMBLY);
258:   if (*J != *Jpre) {
259:     MatAssemblyBegin(*J,MAT_FINAL_ASSEMBLY);
260:     MatAssemblyEnd(*J,MAT_FINAL_ASSEMBLY);
261:   }
262:   return(0);
263: }

267: PetscErrorCode FormInitialSolution(TS ts,Vec X,void *ctx)
268: {
269:   User           user = (User)ctx;
270:   DM             da;
271:   PetscInt       i;
272:   DMDALocalInfo  info;
273:   Field          *x;
274:   PetscReal      hx;

278:   TSGetDM(ts,&da);
279:   DMDAGetLocalInfo(da,&info);
280:   hx   = 1.0/(PetscReal)info.mx;

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

285:   /* Compute function over the locally owned part of the grid */
286:   for (i=info.xs; i<info.xs+info.xm; i++) {
287:     PetscReal r = (i+1)*hx,ik = user->k[1] != 0.0 ? 1.0/user->k[1] : 1.0;
288:     x[i][0] = 1 + user->s[1]*r;
289:     x[i][1] = user->k[0]*ik*x[i][0] + user->s[1]*ik;
290:   }
291:   DMDAVecRestoreArray(da,X,&x);
292:   return(0);
293: }