Actual source code: ex13.c

petsc-3.4.4 2014-03-13

  3: static char help[] = "Time-dependent PDE in 2d. Simplified from ex7.c for illustrating how to use TS on a structured domain. \n";
  4: /*
  5:    u_t = uxx + uyy
  6:    0 < x < 1, 0 < y < 1;
  7:    At t=0: u(x,y) = exp(c*r*r*r), if r=PetscSqrtReal((x-.5)*(x-.5) + (y-.5)*(y-.5)) < .125
  8:            u(x,y) = 0.0           if r >= .125

 10:     mpiexec -n 2 ./ex13 -da_grid_x 40 -da_grid_y 40 -ts_max_steps 2 -use_coloring -snes_monitor -ksp_monitor
 11:          ./ex13 -use_coloring
 12:          ./ex13 -use_coloring  -draw_pause -1
 13:          mpiexec -n 2 ./ex13 -ts_type sundials -ts_sundials_monitor_steps
 14: */

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

 19: /*
 20:    User-defined data structures and routines
 21: */
 22: typedef struct {
 23:   PetscReal c;
 24: } AppCtx;

 26: extern PetscErrorCode RHSFunction(TS,PetscReal,Vec,Vec,void*);
 27: extern PetscErrorCode RHSJacobian(TS,PetscReal,Vec,Mat*,Mat*,MatStructure*,void*);
 28: extern PetscErrorCode FormInitialSolution(DM,Vec,void*);

 32: int main(int argc,char **argv)
 33: {
 34:   TS             ts;                   /* nonlinear solver */
 35:   Vec            u,r;                  /* solution, residual vector */
 36:   Mat            J;                    /* Jacobian matrix */
 37:   PetscInt       steps,maxsteps = 1000;     /* iterations for convergence */
 39:   DM             da;
 40:   PetscReal      ftime,dt;
 41:   AppCtx         user;              /* user-defined work context */

 43:   PetscInitialize(&argc,&argv,(char*)0,help);
 44:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 45:      Create distributed array (DMDA) to manage parallel grid and vectors
 46:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 47:   DMDACreate2d(PETSC_COMM_WORLD, DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE,DMDA_STENCIL_STAR,-8,-8,PETSC_DECIDE,PETSC_DECIDE,
 48:                       1,1,NULL,NULL,&da);

 50:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 51:      Extract global vectors from DMDA;
 52:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 53:   DMCreateGlobalVector(da,&u);
 54:   VecDuplicate(u,&r);

 56:   /* Initialize user application context */
 57:   user.c = -30.0;

 59:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 60:      Create timestepping solver context
 61:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 62:   TSCreate(PETSC_COMM_WORLD,&ts);
 63:   TSSetDM(ts,da);
 64:   TSSetType(ts,TSBEULER);
 65:   TSSetRHSFunction(ts,r,RHSFunction,&user);

 67:   /* Set Jacobian */
 68:   DMCreateMatrix(da,MATAIJ,&J);
 69:   TSSetRHSJacobian(ts,J,J,RHSJacobian,NULL);

 71:   ftime = 1.0;
 72:   TSSetDuration(ts,maxsteps,ftime);

 74:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 75:      Set initial conditions
 76:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 77:   FormInitialSolution(da,u,&user);
 78:   dt   = .01;
 79:   TSSetInitialTimeStep(ts,0.0,dt);

 81:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 82:      Set runtime options
 83:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 84:   TSSetFromOptions(ts);

 86:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 87:      Solve nonlinear system
 88:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 89:   TSSolve(ts,u);
 90:   TSGetSolveTime(ts,&ftime);
 91:   TSGetTimeStepNumber(ts,&steps);

 93:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 94:      Free work space.
 95:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 96:   MatDestroy(&J);
 97:   VecDestroy(&u);
 98:   VecDestroy(&r);
 99:   TSDestroy(&ts);
100:   DMDestroy(&da);

102:   PetscFinalize();
103:   return(0);
104: }
105: /* ------------------------------------------------------------------- */
108: /*
109:    RHSFunction - Evaluates nonlinear function, F(u).

111:    Input Parameters:
112: .  ts - the TS context
113: .  U - input vector
114: .  ptr - optional user-defined context, as set by TSSetFunction()

116:    Output Parameter:
117: .  F - function vector
118:  */
119: PetscErrorCode RHSFunction(TS ts,PetscReal ftime,Vec U,Vec F,void *ptr)
120: {
121:   /* PETSC_UNUSED AppCtx *user=(AppCtx*)ptr; */
122:   DM             da;
124:   PetscInt       i,j,Mx,My,xs,ys,xm,ym;
125:   PetscReal      two = 2.0,hx,hy,sx,sy;
126:   PetscScalar    u,uxx,uyy,**uarray,**f;
127:   Vec            localU;

130:   TSGetDM(ts,&da);
131:   DMGetLocalVector(da,&localU);
132:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
133:                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

135:   hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
136:   hy = 1.0/(PetscReal)(My-1); sy = 1.0/(hy*hy);

138:   /*
139:      Scatter ghost points to local vector,using the 2-step process
140:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
141:      By placing code between these two statements, computations can be
142:      done while messages are in transition.
143:   */
144:   DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU);
145:   DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU);

147:   /* Get pointers to vector data */
148:   DMDAVecGetArray(da,localU,&uarray);
149:   DMDAVecGetArray(da,F,&f);

151:   /* Get local grid boundaries */
152:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

154:   /* Compute function over the locally owned part of the grid */
155:   for (j=ys; j<ys+ym; j++) {
156:     for (i=xs; i<xs+xm; i++) {
157:       if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
158:         f[j][i] = uarray[j][i];
159:         continue;
160:       }
161:       u       = uarray[j][i];
162:       uxx     = (-two*u + uarray[j][i-1] + uarray[j][i+1])*sx;
163:       uyy     = (-two*u + uarray[j-1][i] + uarray[j+1][i])*sy;
164:       f[j][i] = uxx + uyy;
165:     }
166:   }

168:   /* Restore vectors */
169:   DMDAVecRestoreArray(da,localU,&uarray);
170:   DMDAVecRestoreArray(da,F,&f);
171:   DMRestoreLocalVector(da,&localU);
172:   PetscLogFlops(11.0*ym*xm);
173:   return(0);
174: }

176: /* --------------------------------------------------------------------- */
179: /*
180:    RHSJacobian - User-provided routine to compute the Jacobian of
181:    the nonlinear right-hand-side function of the ODE.

183:    Input Parameters:
184:    ts - the TS context
185:    t - current time
186:    U - global input vector
187:    dummy - optional user-defined context, as set by TSetRHSJacobian()

189:    Output Parameters:
190:    J - Jacobian matrix
191:    Jpre - optionally different preconditioning matrix
192:    str - flag indicating matrix structure
193: */
194: PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec U,Mat *J,Mat *Jpre,MatStructure *str,void *ctx)
195: {
197:   DM             da;
198:   DMDALocalInfo  info;
199:   PetscInt       i,j;
200:   PetscReal      hx,hy,sx,sy;

203:   TSGetDM(ts,&da);
204:   DMDAGetLocalInfo(da,&info);
205:   hx   = 1.0/(PetscReal)(info.mx-1); sx = 1.0/(hx*hx);
206:   hy   = 1.0/(PetscReal)(info.my-1); sy = 1.0/(hy*hy);
207:   for (j=info.ys; j<info.ys+info.ym; j++) {
208:     for (i=info.xs; i<info.xs+info.xm; i++) {
209:       PetscInt    nc = 0;
210:       MatStencil  row,col[5];
211:       PetscScalar val[5];
212:       row.i = i; row.j = j;
213:       if (i == 0 || j == 0 || i == info.mx-1 || j == info.my-1) {
214:         col[nc].i = i; col[nc].j = j; val[nc++] = 1.0;
215:       } else {
216:         col[nc].i = i-1; col[nc].j = j;   val[nc++] = sx;
217:         col[nc].i = i+1; col[nc].j = j;   val[nc++] = sx;
218:         col[nc].i = i;   col[nc].j = j-1; val[nc++] = sy;
219:         col[nc].i = i;   col[nc].j = j+1; val[nc++] = sy;
220:         col[nc].i = i;   col[nc].j = j;   val[nc++] = -2*sx - 2*sy;
221:       }
222:       MatSetValuesStencil(*Jpre,1,&row,nc,col,val,INSERT_VALUES);
223:     }
224:   }
225:   MatAssemblyBegin(*Jpre,MAT_FINAL_ASSEMBLY);
226:   MatAssemblyEnd(*Jpre,MAT_FINAL_ASSEMBLY);
227:   if (*J != *Jpre) {
228:     MatAssemblyBegin(*J,MAT_FINAL_ASSEMBLY);
229:     MatAssemblyEnd(*J,MAT_FINAL_ASSEMBLY);
230:   }
231:   return(0);
232: }

234: /* ------------------------------------------------------------------- */
237: PetscErrorCode FormInitialSolution(DM da,Vec U,void* ptr)
238: {
239:   AppCtx         *user=(AppCtx*)ptr;
240:   PetscReal      c=user->c;
242:   PetscInt       i,j,xs,ys,xm,ym,Mx,My;
243:   PetscScalar    **u;
244:   PetscReal      hx,hy,x,y,r;

247:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
248:                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

250:   hx = 1.0/(PetscReal)(Mx-1);
251:   hy = 1.0/(PetscReal)(My-1);

253:   /* Get pointers to vector data */
254:   DMDAVecGetArray(da,U,&u);

256:   /* Get local grid boundaries */
257:   DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);

259:   /* Compute function over the locally owned part of the grid */
260:   for (j=ys; j<ys+ym; j++) {
261:     y = j*hy;
262:     for (i=xs; i<xs+xm; i++) {
263:       x = i*hx;
264:       r = PetscSqrtScalar((x-.5)*(x-.5) + (y-.5)*(y-.5));
265:       if (r < .125) u[j][i] = PetscExpScalar(c*r*r*r);
266:       else u[j][i] = 0.0;
267:     }
268:   }

270:   /* Restore vectors */
271:   DMDAVecRestoreArray(da,U,&u);
272:   return(0);
273: }