Actual source code: ex13.c

petsc-3.9.3 2018-07-02
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  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 -snes_monitor -ksp_monitor
 11:     mpiexec -n 1 ./ex13 -snes_fd_color -ts_monitor_draw_solution
 12:     mpiexec -n 2 ./ex13 -ts_type sundials -ts_monitor 
 13: */

 15:  #include <petscdm.h>
 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,void*);
 28: extern PetscErrorCode FormInitialSolution(DM,Vec,void*);

 30: int main(int argc,char **argv)
 31: {
 32:   TS             ts;                   /* nonlinear solver */
 33:   Vec            u,r;                  /* solution, residual vector */
 34:   Mat            J;                    /* Jacobian matrix */
 35:   PetscInt       steps;                /* iterations for convergence */
 37:   DM             da;
 38:   PetscReal      ftime,dt;
 39:   AppCtx         user;              /* user-defined work context */

 41:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
 42:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 43:      Create distributed array (DMDA) to manage parallel grid and vectors
 44:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 45:   DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,8,8,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
 46:   DMSetFromOptions(da);
 47:   DMSetUp(da);

 49:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 50:      Extract global vectors from DMDA;
 51:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 52:   DMCreateGlobalVector(da,&u);
 53:   VecDuplicate(u,&r);

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

 58:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 59:      Create timestepping solver context
 60:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 61:   TSCreate(PETSC_COMM_WORLD,&ts);
 62:   TSSetDM(ts,da);
 63:   TSSetType(ts,TSBEULER);
 64:   TSSetRHSFunction(ts,r,RHSFunction,&user);

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

 71:   ftime = 1.0;
 72:   TSSetMaxTime(ts,ftime);
 73:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);

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

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

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

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

103:   PetscFinalize();
104:   return ierr;
105: }
106: /* ------------------------------------------------------------------- */
107: /*
108:    RHSFunction - Evaluates nonlinear function, F(u).

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

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

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

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

136:   /*
137:      Scatter ghost points to local vector,using the 2-step process
138:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
139:      By placing code between these two statements, computations can be
140:      done while messages are in transition.
141:   */
142:   DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU);
143:   DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU);

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

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

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

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

174: /* --------------------------------------------------------------------- */
175: /*
176:    RHSJacobian - User-provided routine to compute the Jacobian of
177:    the nonlinear right-hand-side function of the ODE.

179:    Input Parameters:
180:    ts - the TS context
181:    t - current time
182:    U - global input vector
183:    dummy - optional user-defined context, as set by TSetRHSJacobian()

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

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

230: /* ------------------------------------------------------------------- */
231: PetscErrorCode FormInitialSolution(DM da,Vec U,void* ptr)
232: {
233:   AppCtx         *user=(AppCtx*)ptr;
234:   PetscReal      c=user->c;
236:   PetscInt       i,j,xs,ys,xm,ym,Mx,My;
237:   PetscScalar    **u;
238:   PetscReal      hx,hy,x,y,r;

241:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

243:   hx = 1.0/(PetscReal)(Mx-1);
244:   hy = 1.0/(PetscReal)(My-1);

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

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

252:   /* Compute function over the locally owned part of the grid */
253:   for (j=ys; j<ys+ym; j++) {
254:     y = j*hy;
255:     for (i=xs; i<xs+xm; i++) {
256:       x = i*hx;
257:       r = PetscSqrtReal((x-.5)*(x-.5) + (y-.5)*(y-.5));
258:       if (r < .125) u[j][i] = PetscExpReal(c*r*r*r);
259:       else u[j][i] = 0.0;
260:     }
261:   }

263:   /* Restore vectors */
264:   DMDAVecRestoreArray(da,U,&u);
265:   return(0);
266: }

268: /*TEST

270:     test:
271:       args: -ts_max_steps 5 -ts_monitor 

273:     test:
274:       suffix: 2
275:       args: -ts_max_steps 5 -ts_monitor

277:     test:
278:       suffix: 3
279:       args: -ts_max_steps 5 -snes_fd_color -ts_monitor

281: TEST*/