Actual source code: biharmonic.c


  2: static char help[] = "Solves biharmonic equation in 1d.\n";

  4: /*
  5:   Solves the equation

  7:     u_t = - kappa  \Delta \Delta u
  8:     Periodic boundary conditions

 10: Evolve the biharmonic heat equation:
 11: ---------------
 12: ./biharmonic -ts_monitor -snes_monitor   -pc_type lu  -draw_pause .1 -snes_converged_reason  -draw_pause -2   -ts_type cn  -da_refine 5 -mymonitor

 14: Evolve with the restriction that -1 <= u <= 1; i.e. as a variational inequality
 15: ---------------
 16: ./biharmonic -ts_monitor -snes_monitor   -pc_type lu  -draw_pause .1 -snes_converged_reason  -draw_pause -2   -ts_type cn   -da_refine 5  -mymonitor

 18:    u_t =  kappa \Delta \Delta u +   6.*u*(u_x)^2 + (3*u^2 - 12) \Delta u
 19:     -1 <= u <= 1
 20:     Periodic boundary conditions

 22: Evolve the Cahn-Hillard equations: double well Initial hump shrinks then grows
 23: ---------------
 24: ./biharmonic -ts_monitor -snes_monitor   -pc_type lu  -draw_pause .1 -snes_converged_reason   -draw_pause -2   -ts_type cn    -da_refine 6   -kappa .00001 -ts_dt 5.96046e-06 -cahn-hillard -ts_monitor_draw_solution --mymonitor

 26: Initial hump neither shrinks nor grows when degenerate (otherwise similar solution)

 28: ./biharmonic -ts_monitor -snes_monitor   -pc_type lu  -draw_pause .1 -snes_converged_reason   -draw_pause -2   -ts_type cn    -da_refine 6   -kappa .00001 -ts_dt 5.96046e-06 -cahn-hillard -degenerate -ts_monitor_draw_solution --mymonitor

 30: ./biharmonic -ts_monitor -snes_monitor   -pc_type lu  -draw_pause .1 -snes_converged_reason   -draw_pause -2   -ts_type cn    -da_refine 6   -kappa .00001 -ts_dt 5.96046e-06 -cahn-hillard -snes_vi_ignore_function_sign -ts_monitor_draw_solution --mymonitor

 32: Evolve the Cahn-Hillard equations: double obstacle
 33: ---------------
 34: ./biharmonic -ts_monitor -snes_monitor  -pc_type lu  -draw_pause .1 -snes_converged_reason   -draw_pause -2   -ts_type cn    -da_refine 5   -kappa .00001 -ts_dt 5.96046e-06 -cahn-hillard -energy 2 -snes_linesearch_monitor    -ts_monitor_draw_solution --mymonitor

 36: Evolve the Cahn-Hillard equations: logarithmic + double well (never shrinks and then grows)
 37: ---------------
 38: ./biharmonic -ts_monitor -snes_monitor  -pc_type lu  --snes_converged_reason  -draw_pause -2   -ts_type cn    -da_refine 5   -kappa .0001 -ts_dt 5.96046e-06 -cahn-hillard -energy 3 -snes_linesearch_monitor -theta .00000001    -ts_monitor_draw_solution --ts_max_time 1. -mymonitor

 40: ./biharmonic -ts_monitor -snes_monitor  -pc_type lu  --snes_converged_reason  -draw_pause -2   -ts_type cn    -da_refine 5   -kappa .0001 -ts_dt 5.96046e-06 -cahn-hillard -energy 3 -snes_linesearch_monitor -theta .00000001    -ts_monitor_draw_solution --ts_max_time 1. -degenerate -mymonitor

 42: Evolve the Cahn-Hillard equations: logarithmic +  double obstacle (never shrinks, never grows)
 43: ---------------
 44: ./biharmonic -ts_monitor -snes_monitor  -pc_type lu  --snes_converged_reason  -draw_pause -2   -ts_type cn    -da_refine 5   -kappa .00001 -ts_dt 5.96046e-06 -cahn-hillard -energy 4 -snes_linesearch_monitor -theta .00000001   -ts_monitor_draw_solution --mymonitor

 46: */
 47: #include <petscdm.h>
 48: #include <petscdmda.h>
 49: #include <petscts.h>
 50: #include <petscdraw.h>

 52: extern PetscErrorCode FormFunction(TS,PetscReal,Vec,Vec,void*),FormInitialSolution(DM,Vec),MyMonitor(TS,PetscInt,PetscReal,Vec,void*),MyDestroy(void**),FormJacobian(TS,PetscReal,Vec,Mat,Mat,void*);
 53: typedef struct {PetscBool cahnhillard;PetscBool degenerate;PetscReal kappa;PetscInt energy;PetscReal tol;PetscReal theta,theta_c;PetscInt truncation;PetscBool netforce; PetscDrawViewPorts *ports;} UserCtx;

 55: int main(int argc,char **argv)
 56: {
 57:   TS             ts;                 /* nonlinear solver */
 58:   Vec            x,r;                  /* solution, residual vectors */
 59:   Mat            J;                    /* Jacobian matrix */
 60:   PetscInt       steps,Mx;
 62:   DM             da;
 63:   PetscReal      dt;
 64:   PetscBool      mymonitor;
 65:   UserCtx        ctx;

 67:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 68:      Initialize program
 69:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 70:   PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
 71:   ctx.kappa       = 1.0;
 72:   PetscOptionsGetReal(NULL,NULL,"-kappa",&ctx.kappa,NULL);
 73:   ctx.degenerate  = PETSC_FALSE;
 74:   PetscOptionsGetBool(NULL,NULL,"-degenerate",&ctx.degenerate,NULL);
 75:   ctx.cahnhillard = PETSC_FALSE;
 76:   PetscOptionsGetBool(NULL,NULL,"-cahn-hillard",&ctx.cahnhillard,NULL);
 77:   ctx.netforce    = PETSC_FALSE;
 78:   PetscOptionsGetBool(NULL,NULL,"-netforce",&ctx.netforce,NULL);
 79:   ctx.energy      = 1;
 80:   PetscOptionsGetInt(NULL,NULL,"-energy",&ctx.energy,NULL);
 81:   ctx.tol         = 1.0e-8;
 82:   PetscOptionsGetReal(NULL,NULL,"-tol",&ctx.tol,NULL);
 83:   ctx.theta       = .001;
 84:   ctx.theta_c     = 1.0;
 85:   PetscOptionsGetReal(NULL,NULL,"-theta",&ctx.theta,NULL);
 86:   PetscOptionsGetReal(NULL,NULL,"-theta_c",&ctx.theta_c,NULL);
 87:   ctx.truncation  = 1;
 88:   PetscOptionsGetInt(NULL,NULL,"-truncation",&ctx.truncation,NULL);
 89:   PetscOptionsHasName(NULL,NULL,"-mymonitor",&mymonitor);

 91:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 92:      Create distributed array (DMDA) to manage parallel grid and vectors
 93:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 94:   DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC, 10,1,2,NULL,&da);
 95:   DMSetFromOptions(da);
 96:   DMSetUp(da);
 97:   DMDASetFieldName(da,0,"Biharmonic heat equation: u");
 98:   DMDAGetInfo(da,0,&Mx,0,0,0,0,0,0,0,0,0,0,0);
 99:   dt   = 1.0/(10.*ctx.kappa*Mx*Mx*Mx*Mx);

101:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
102:      Extract global vectors from DMDA; then duplicate for remaining
103:      vectors that are the same types
104:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
105:   DMCreateGlobalVector(da,&x);
106:   VecDuplicate(x,&r);

108:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
109:      Create timestepping solver context
110:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
111:   TSCreate(PETSC_COMM_WORLD,&ts);
112:   TSSetDM(ts,da);
113:   TSSetProblemType(ts,TS_NONLINEAR);
114:   TSSetRHSFunction(ts,NULL,FormFunction,&ctx);
115:   DMSetMatType(da,MATAIJ);
116:   DMCreateMatrix(da,&J);
117:   TSSetRHSJacobian(ts,J,J,FormJacobian,&ctx);
118:   TSSetMaxTime(ts,.02);
119:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_INTERPOLATE);

121:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
122:      Create matrix data structure; set Jacobian evaluation routine

124:      Set Jacobian matrix data structure and default Jacobian evaluation
125:      routine. User can override with:
126:      -snes_mf : matrix-free Newton-Krylov method with no preconditioning
127:                 (unless user explicitly sets preconditioner)
128:      -snes_mf_operator : form preconditioning matrix as set by the user,
129:                          but use matrix-free approx for Jacobian-vector
130:                          products within Newton-Krylov method

132:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
133:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
134:      Customize nonlinear solver
135:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
136:   TSSetType(ts,TSCN);

138:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
139:      Set initial conditions
140:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
141:   FormInitialSolution(da,x);
142:   TSSetTimeStep(ts,dt);
143:   TSSetSolution(ts,x);

145:   if (mymonitor) {
146:     ctx.ports = NULL;
147:     TSMonitorSet(ts,MyMonitor,&ctx,MyDestroy);
148:   }

150:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
151:      Set runtime options
152:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
153:   TSSetFromOptions(ts);

155:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
156:      Solve nonlinear system
157:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
158:   TSSolve(ts,x);
159:   TSGetStepNumber(ts,&steps);
160:   VecView(x,PETSC_VIEWER_BINARY_WORLD);

162:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
163:      Free work space.  All PETSc objects should be destroyed when they
164:      are no longer needed.
165:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
166:   MatDestroy(&J);
167:   VecDestroy(&x);
168:   VecDestroy(&r);
169:   TSDestroy(&ts);
170:   DMDestroy(&da);

172:   PetscFinalize();
173:   return ierr;
174: }
175: /* ------------------------------------------------------------------- */
176: /*
177:    FormFunction - Evaluates nonlinear function, F(x).

179:    Input Parameters:
180: .  ts - the TS context
181: .  X - input vector
182: .  ptr - optional user-defined context, as set by SNESSetFunction()

184:    Output Parameter:
185: .  F - function vector
186:  */
187: PetscErrorCode FormFunction(TS ts,PetscReal ftime,Vec X,Vec F,void *ptr)
188: {
189:   DM             da;
191:   PetscInt       i,Mx,xs,xm;
192:   PetscReal      hx,sx;
193:   PetscScalar    *x,*f,c,r,l;
194:   Vec            localX;
195:   UserCtx        *ctx = (UserCtx*)ptr;
196:   PetscReal      tol  = ctx->tol, theta=ctx->theta,theta_c=ctx->theta_c,a,b; /* a and b are used in the cubic truncation of the log function */

199:   TSGetDM(ts,&da);
200:   DMGetLocalVector(da,&localX);
201:   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);

203:   hx = 1.0/(PetscReal)Mx; sx = 1.0/(hx*hx);

205:   /*
206:      Scatter ghost points to local vector,using the 2-step process
207:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
208:      By placing code between these two statements, computations can be
209:      done while messages are in transition.
210:   */
211:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
212:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);

214:   /*
215:      Get pointers to vector data
216:   */
217:   DMDAVecGetArrayRead(da,localX,&x);
218:   DMDAVecGetArray(da,F,&f);

220:   /*
221:      Get local grid boundaries
222:   */
223:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);

225:   /*
226:      Compute function over the locally owned part of the grid
227:   */
228:   for (i=xs; i<xs+xm; i++) {
229:     if (ctx->degenerate) {
230:       c = (1. - x[i]*x[i])*(x[i-1] + x[i+1] - 2.0*x[i])*sx;
231:       r = (1. - x[i+1]*x[i+1])*(x[i] + x[i+2] - 2.0*x[i+1])*sx;
232:       l = (1. - x[i-1]*x[i-1])*(x[i-2] + x[i] - 2.0*x[i-1])*sx;
233:     } else {
234:       c = (x[i-1] + x[i+1] - 2.0*x[i])*sx;
235:       r = (x[i] + x[i+2] - 2.0*x[i+1])*sx;
236:       l = (x[i-2] + x[i] - 2.0*x[i-1])*sx;
237:     }
238:     f[i] = -ctx->kappa*(l + r - 2.0*c)*sx;
239:     if (ctx->cahnhillard) {
240:       switch (ctx->energy) {
241:       case 1: /*  double well */
242:         f[i] += 6.*.25*x[i]*(x[i+1] - x[i-1])*(x[i+1] - x[i-1])*sx + (3.*x[i]*x[i] - 1.)*(x[i-1] + x[i+1] - 2.0*x[i])*sx;
243:         break;
244:       case 2: /* double obstacle */
245:         f[i] += -(x[i-1] + x[i+1] - 2.0*x[i])*sx;
246:         break;
247:       case 3: /* logarithmic + double well */
248:         f[i] +=  6.*.25*x[i]*(x[i+1] - x[i-1])*(x[i+1] - x[i-1])*sx + (3.*x[i]*x[i] - 1.)*(x[i-1] + x[i+1] - 2.0*x[i])*sx;
249:         if (ctx->truncation==2) { /* log function with approximated with a quadratic polynomial outside -1.0+2*tol, 1.0-2*tol */
250:           if (PetscRealPart(x[i]) < -1.0 + 2.0*tol)     f[i] += (.25*theta/(tol-tol*tol))*(x[i-1] + x[i+1] - 2.0*x[i])*sx;
251:           else if (PetscRealPart(x[i]) > 1.0 - 2.0*tol) f[i] += (.25*theta/(tol-tol*tol))*(x[i-1] + x[i+1] - 2.0*x[i])*sx;
252:           else                                          f[i] += 2.0*theta*x[i]/((1.0-x[i]*x[i])*(1.0-x[i]*x[i]))*.25*(x[i+1] - x[i-1])*(x[i+1] - x[i-1])*sx + (theta/(1.0-x[i]*x[i]))*(x[i-1] + x[i+1] - 2.0*x[i])*sx;
253:         } else { /* log function is approximated with a cubic polynomial outside -1.0+2*tol, 1.0-2*tol */
254:           a = 2.0*theta*(1.0-2.0*tol)/(16.0*tol*tol*(1.0-tol)*(1.0-tol));
255:           b = theta/(4.0*tol*(1.0-tol)) - a*(1.0-2.0*tol);
256:           if (PetscRealPart(x[i]) < -1.0 + 2.0*tol)     f[i] += -1.0*a*.25*(x[i+1] - x[i-1])*(x[i+1] - x[i-1])*sx + (-1.0*a*x[i] + b)*(x[i-1] + x[i+1] - 2.0*x[i])*sx;
257:           else if (PetscRealPart(x[i]) > 1.0 - 2.0*tol) f[i] +=  1.0*a*.25*(x[i+1] - x[i-1])*(x[i+1] - x[i-1])*sx + (     a*x[i] + b)*(x[i-1] + x[i+1] - 2.0*x[i])*sx;
258:           else                                          f[i] += 2.0*theta*x[i]/((1.0-x[i]*x[i])*(1.0-x[i]*x[i]))*.25*(x[i+1] - x[i-1])*(x[i+1] - x[i-1])*sx + (theta/(1.0-x[i]*x[i]))*(x[i-1] + x[i+1] - 2.0*x[i])*sx;
259:         }
260:         break;
261:       case 4: /* logarithmic + double obstacle */
262:         f[i] += -theta_c*(x[i-1] + x[i+1] - 2.0*x[i])*sx;
263:         if (ctx->truncation==2) { /* quadratic */
264:           if (PetscRealPart(x[i]) < -1.0 + 2.0*tol)     f[i] += (.25*theta/(tol-tol*tol))*(x[i-1] + x[i+1] - 2.0*x[i])*sx;
265:           else if (PetscRealPart(x[i]) > 1.0 - 2.0*tol) f[i] += (.25*theta/(tol-tol*tol))*(x[i-1] + x[i+1] - 2.0*x[i])*sx;
266:           else                                          f[i] += 2.0*theta*x[i]/((1.0-x[i]*x[i])*(1.0-x[i]*x[i]))*.25*(x[i+1] - x[i-1])*(x[i+1] - x[i-1])*sx + (theta/(1.0-x[i]*x[i]))*(x[i-1] + x[i+1] - 2.0*x[i])*sx;
267:         } else { /* cubic */
268:           a = 2.0*theta*(1.0-2.0*tol)/(16.0*tol*tol*(1.0-tol)*(1.0-tol));
269:           b = theta/(4.0*tol*(1.0-tol)) - a*(1.0-2.0*tol);
270:           if (PetscRealPart(x[i]) < -1.0 + 2.0*tol)     f[i] += -1.0*a*.25*(x[i+1] - x[i-1])*(x[i+1] - x[i-1])*sx + (-1.0*a*x[i] + b)*(x[i-1] + x[i+1] - 2.0*x[i])*sx;
271:           else if (PetscRealPart(x[i]) > 1.0 - 2.0*tol) f[i] +=  1.0*a*.25*(x[i+1] - x[i-1])*(x[i+1] - x[i-1])*sx + (     a*x[i] + b)*(x[i-1] + x[i+1] - 2.0*x[i])*sx;
272:           else                                          f[i] +=  2.0*theta*x[i]/((1.0-x[i]*x[i])*(1.0-x[i]*x[i]))*.25*(x[i+1] - x[i-1])*(x[i+1] - x[i-1])*sx + (theta/(1.0-x[i]*x[i]))*(x[i-1] + x[i+1] - 2.0*x[i])*sx;
273:         }
274:         break;
275:       }
276:     }

278:   }

280:   /*
281:      Restore vectors
282:   */
283:   DMDAVecRestoreArrayRead(da,localX,&x);
284:   DMDAVecRestoreArray(da,F,&f);
285:   DMRestoreLocalVector(da,&localX);
286:   return(0);
287: }

289: /* ------------------------------------------------------------------- */
290: /*
291:    FormJacobian - Evaluates nonlinear function's Jacobian

293: */
294: PetscErrorCode FormJacobian(TS ts,PetscReal ftime,Vec X,Mat A,Mat B,void *ptr)
295: {
296:   DM             da;
298:   PetscInt       i,Mx,xs,xm;
299:   MatStencil     row,cols[5];
300:   PetscReal      hx,sx;
301:   PetscScalar    *x,vals[5];
302:   Vec            localX;
303:   UserCtx        *ctx = (UserCtx*)ptr;

306:   TSGetDM(ts,&da);
307:   DMGetLocalVector(da,&localX);
308:   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);

310:   hx = 1.0/(PetscReal)Mx; sx = 1.0/(hx*hx);

312:   /*
313:      Scatter ghost points to local vector,using the 2-step process
314:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
315:      By placing code between these two statements, computations can be
316:      done while messages are in transition.
317:   */
318:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
319:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);

321:   /*
322:      Get pointers to vector data
323:   */
324:   DMDAVecGetArrayRead(da,localX,&x);

326:   /*
327:      Get local grid boundaries
328:   */
329:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);

331:   /*
332:      Compute function over the locally owned part of the grid
333:   */
334:   for (i=xs; i<xs+xm; i++) {
335:     row.i = i;
336:     if (ctx->degenerate) {
337:       /*PetscScalar c,r,l;
338:       c = (1. - x[i]*x[i])*(x[i-1] + x[i+1] - 2.0*x[i])*sx;
339:       r = (1. - x[i+1]*x[i+1])*(x[i] + x[i+2] - 2.0*x[i+1])*sx;
340:       l = (1. - x[i-1]*x[i-1])*(x[i-2] + x[i] - 2.0*x[i-1])*sx; */
341:     } else {
342:       cols[0].i = i - 2; vals[0] = -ctx->kappa*sx*sx;
343:       cols[1].i = i - 1; vals[1] =  4.0*ctx->kappa*sx*sx;
344:       cols[2].i = i    ; vals[2] = -6.0*ctx->kappa*sx*sx;
345:       cols[3].i = i + 1; vals[3] =  4.0*ctx->kappa*sx*sx;
346:       cols[4].i = i + 2; vals[4] = -ctx->kappa*sx*sx;
347:     }
348:     MatSetValuesStencil(B,1,&row,5,cols,vals,INSERT_VALUES);

350:     if (ctx->cahnhillard) {
351:       switch (ctx->energy) {
352:       case 1: /* double well */
353:         /*  f[i] += 6.*.25*x[i]*(x[i+1] - x[i-1])*(x[i+1] - x[i-1])*sx + (3.*x[i]*x[i] - 1.)*(x[i-1] + x[i+1] - 2.0*x[i])*sx; */
354:         break;
355:       case 2: /* double obstacle */
356:         /*        f[i] += -(x[i-1] + x[i+1] - 2.0*x[i])*sx; */
357:         break;
358:       case 3: /* logarithmic + double well */
359:         break;
360:       case 4: /* logarithmic + double obstacle */
361:         break;
362:       }
363:     }

365:   }

367:   /*
368:      Restore vectors
369:   */
370:   DMDAVecRestoreArrayRead(da,localX,&x);
371:   DMRestoreLocalVector(da,&localX);
372:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
373:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
374:   if (A != B) {
375:     MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
376:     MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
377:   }
378:   return(0);
379: }
380: /* ------------------------------------------------------------------- */
381: PetscErrorCode FormInitialSolution(DM da,Vec U)
382: {
383:   PetscErrorCode    ierr;
384:   PetscInt          i,xs,xm,Mx,N,scale;
385:   PetscScalar       *u;
386:   PetscReal         r,hx,x;
387:   const PetscScalar *f;
388:   Vec               finesolution;
389:   PetscViewer       viewer;

392:   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);

394:   hx = 1.0/(PetscReal)Mx;

396:   /*
397:      Get pointers to vector data
398:   */
399:   DMDAVecGetArray(da,U,&u);

401:   /*
402:      Get local grid boundaries
403:   */
404:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);

406:   /*
407:       Seee heat.c for how to generate InitialSolution.heat
408:   */
409:   PetscViewerBinaryOpen(PETSC_COMM_WORLD,"InitialSolution.heat",FILE_MODE_READ,&viewer);
410:   VecCreate(PETSC_COMM_WORLD,&finesolution);
411:   VecLoad(finesolution,viewer);
412:   PetscViewerDestroy(&viewer);
413:   VecGetSize(finesolution,&N);
414:   scale = N/Mx;
415:   VecGetArrayRead(finesolution,&f);

417:   /*
418:      Compute function over the locally owned part of the grid
419:   */
420:   for (i=xs; i<xs+xm; i++) {
421:     x = i*hx;
422:     r = PetscSqrtReal((x-.5)*(x-.5));
423:     if (r < .125) u[i] = 1.0;
424:     else u[i] = -.5;

426:     /* With the initial condition above the method is first order in space */
427:     /* this is a smooth initial condition so the method becomes second order in space */
428:     /*u[i] = PetscSinScalar(2*PETSC_PI*x); */
429:     u[i] = f[scale*i];
430:   }
431:   VecRestoreArrayRead(finesolution,&f);
432:   VecDestroy(&finesolution);

434:   /*
435:      Restore vectors
436:   */
437:   DMDAVecRestoreArray(da,U,&u);
438:   return(0);
439: }

441: /*
442:     This routine is not parallel
443: */
444: PetscErrorCode  MyMonitor(TS ts,PetscInt step,PetscReal time,Vec U,void *ptr)
445: {
446:   UserCtx        *ctx = (UserCtx*)ptr;
447:   PetscDrawLG    lg;
449:   PetscScalar    *u,l,r,c;
450:   PetscInt       Mx,i,xs,xm,cnt;
451:   PetscReal      x,y,hx,pause,sx,len,max,xx[4],yy[4],xx_netforce,yy_netforce,yup,ydown,y2,len2;
452:   PetscDraw      draw;
453:   Vec            localU;
454:   DM             da;
455:   int            colors[] = {PETSC_DRAW_YELLOW,PETSC_DRAW_RED,PETSC_DRAW_BLUE,PETSC_DRAW_PLUM,PETSC_DRAW_BLACK};
456:   /*
457:   const char *const  legend[3][3] = {{"-kappa (\\grad u,\\grad u)","(1 - u^2)^2"},{"-kappa (\\grad u,\\grad u)","(1 - u^2)"},{"-kappa (\\grad u,\\grad u)","logarithmic"}};
458:    */
459:   PetscDrawAxis      axis;
460:   PetscDrawViewPorts *ports;
461:   PetscReal          tol = ctx->tol, theta=ctx->theta,theta_c=ctx->theta_c,a,b; /* a and b are used in the cubic truncation of the log function */
462:   PetscReal          vbounds[] = {-1.1,1.1};

465:   PetscViewerDrawSetBounds(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),1,vbounds);
466:   PetscViewerDrawResize(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),800,600);
467:   TSGetDM(ts,&da);
468:   DMGetLocalVector(da,&localU);
469:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
470:                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
471:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);
472:   hx   = 1.0/(PetscReal)Mx; sx = 1.0/(hx*hx);
473:   DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU);
474:   DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU);
475:   DMDAVecGetArrayRead(da,localU,&u);

477:   PetscViewerDrawGetDrawLG(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),1,&lg);
478:   PetscDrawLGGetDraw(lg,&draw);
479:   PetscDrawCheckResizedWindow(draw);
480:   if (!ctx->ports) {
481:     PetscDrawViewPortsCreateRect(draw,1,3,&ctx->ports);
482:   }
483:   ports = ctx->ports;
484:   PetscDrawLGGetAxis(lg,&axis);
485:   PetscDrawLGReset(lg);

487:   xx[0] = 0.0; xx[1] = 1.0; cnt = 2;
488:   PetscOptionsGetRealArray(NULL,NULL,"-zoom",xx,&cnt,NULL);
489:   xs    = xx[0]/hx; xm = (xx[1] - xx[0])/hx;

491:   /*
492:       Plot the  energies
493:   */
494:   PetscDrawLGSetDimension(lg,1 + (ctx->cahnhillard ? 1 : 0) + (ctx->energy == 3));
495:   PetscDrawLGSetColors(lg,colors+1);
496:   PetscDrawViewPortsSet(ports,2);
497:   x    = hx*xs;
498:   for (i=xs; i<xs+xm; i++) {
499:     xx[0] = xx[1]  = xx[2] = x;
500:     if (ctx->degenerate) yy[0] = PetscRealPart(.25*(1. - u[i]*u[i])*ctx->kappa*(u[i-1] - u[i+1])*(u[i-1] - u[i+1])*sx);
501:     else                 yy[0] = PetscRealPart(.25*ctx->kappa*(u[i-1] - u[i+1])*(u[i-1] - u[i+1])*sx);

503:     if (ctx->cahnhillard) {
504:       switch (ctx->energy) {
505:       case 1: /* double well */
506:         yy[1] = .25*PetscRealPart((1. - u[i]*u[i])*(1. - u[i]*u[i]));
507:         break;
508:       case 2: /* double obstacle */
509:         yy[1] = .5*PetscRealPart(1. - u[i]*u[i]);
510:         break;
511:       case 3: /* logarithm + double well */
512:         yy[1] = .25*PetscRealPart((1. - u[i]*u[i])*(1. - u[i]*u[i]));
513:         if (PetscRealPart(u[i]) < -1.0 + 2.0*tol)     yy[2] = .5*theta*(2.0*tol*PetscLogReal(tol) + PetscRealPart(1.0-u[i])*PetscLogReal(PetscRealPart(1.-u[i])/2.0));
514:         else if (PetscRealPart(u[i]) > 1.0 - 2.0*tol) yy[2] = .5*theta*(PetscRealPart(1.0+u[i])*PetscLogReal(PetscRealPart(1.0+u[i])/2.0) + 2.0*tol*PetscLogReal(tol));
515:         else                                          yy[2] = .5*theta*(PetscRealPart(1.0+u[i])*PetscLogReal(PetscRealPart(1.0+u[i])/2.0) + PetscRealPart(1.0-u[i])*PetscLogReal(PetscRealPart(1.0-u[i])/2.0));
516:         break;
517:       case 4: /* logarithm + double obstacle */
518:         yy[1] = .5*theta_c*PetscRealPart(1.0-u[i]*u[i]);
519:         if (PetscRealPart(u[i]) < -1.0 + 2.0*tol)     yy[2] = .5*theta*(2.0*tol*PetscLogReal(tol) + PetscRealPart(1.0-u[i])*PetscLogReal(PetscRealPart(1.-u[i])/2.0));
520:         else if (PetscRealPart(u[i]) > 1.0 - 2.0*tol) yy[2] = .5*theta*(PetscRealPart(1.0+u[i])*PetscLogReal(PetscRealPart(1.0+u[i])/2.0) + 2.0*tol*PetscLogReal(tol));
521:         else                                          yy[2] = .5*theta*(PetscRealPart(1.0+u[i])*PetscLogReal(PetscRealPart(1.0+u[i])/2.0) + PetscRealPart(1.0-u[i])*PetscLogReal(PetscRealPart(1.0-u[i])/2.0));
522:         break;
523:       default:
524:         SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"It will always be one of the values");
525:       }
526:     }
527:     PetscDrawLGAddPoint(lg,xx,yy);
528:     x   += hx;
529:   }
530:   PetscDrawGetPause(draw,&pause);
531:   PetscDrawSetPause(draw,0.0);
532:   PetscDrawAxisSetLabels(axis,"Energy","","");
533:   /*  PetscDrawLGSetLegend(lg,legend[ctx->energy-1]); */
534:   PetscDrawLGDraw(lg);

536:   /*
537:       Plot the  forces
538:   */
539:   PetscDrawLGSetDimension(lg,0 + (ctx->cahnhillard ? 2 : 0) + (ctx->energy == 3));
540:   PetscDrawLGSetColors(lg,colors+1);
541:   PetscDrawViewPortsSet(ports,1);
542:   PetscDrawLGReset(lg);
543:   x    = xs*hx;
544:   max  = 0.;
545:   for (i=xs; i<xs+xm; i++) {
546:     xx[0] = xx[1] = xx[2] = xx[3] = x;
547:     xx_netforce = x;
548:     if (ctx->degenerate) {
549:       c = (1. - u[i]*u[i])*(u[i-1] + u[i+1] - 2.0*u[i])*sx;
550:       r = (1. - u[i+1]*u[i+1])*(u[i] + u[i+2] - 2.0*u[i+1])*sx;
551:       l = (1. - u[i-1]*u[i-1])*(u[i-2] + u[i] - 2.0*u[i-1])*sx;
552:     } else {
553:       c = (u[i-1] + u[i+1] - 2.0*u[i])*sx;
554:       r = (u[i] + u[i+2] - 2.0*u[i+1])*sx;
555:       l = (u[i-2] + u[i] - 2.0*u[i-1])*sx;
556:     }
557:     yy[0]       = PetscRealPart(-ctx->kappa*(l + r - 2.0*c)*sx);
558:     yy_netforce = yy[0];
559:     max         = PetscMax(max,PetscAbs(yy[0]));
560:     if (ctx->cahnhillard) {
561:       switch (ctx->energy) {
562:       case 1: /* double well */
563:         yy[1] = PetscRealPart(6.*.25*u[i]*(u[i+1] - u[i-1])*(u[i+1] - u[i-1])*sx + (3.*u[i]*u[i] - 1.)*(u[i-1] + u[i+1] - 2.0*u[i])*sx);
564:         break;
565:       case 2: /* double obstacle */
566:         yy[1] = -PetscRealPart(u[i-1] + u[i+1] - 2.0*u[i])*sx;
567:         break;
568:       case 3: /* logarithmic + double well */
569:         yy[1] =  PetscRealPart(6.*.25*u[i]*(u[i+1] - u[i-1])*(u[i+1] - u[i-1])*sx + (3.*u[i]*u[i] - 1.)*(u[i-1] + u[i+1] - 2.0*u[i])*sx);
570:         if (ctx->truncation==2) { /* quadratic */
571:           if (PetscRealPart(u[i]) < -1.0 + 2.0*tol)     yy[2] = (.25*theta/(tol-tol*tol))*PetscRealPart(u[i-1] + u[i+1] - 2.0*u[i])*sx;
572:           else if (PetscRealPart(u[i]) > 1.0 - 2.0*tol) yy[2] = (.25*theta/(tol-tol*tol))*PetscRealPart(u[i-1] + u[i+1] - 2.0*u[i])*sx;
573:           else                                          yy[2] = PetscRealPart(2.0*theta*u[i]/((1.0-u[i]*u[i])*(1.0-u[i]*u[i]))*.25*(u[i+1] - u[i-1])*(u[i+1] - u[i-1])*sx + (theta/(1.0-u[i]*u[i]))*(u[i-1] + u[i+1] - 2.0*u[i])*sx);
574:         } else { /* cubic */
575:           a = 2.0*theta*(1.0-2.0*tol)/(16.0*tol*tol*(1.0-tol)*(1.0-tol));
576:           b = theta/(4.0*tol*(1.0-tol)) - a*(1.0-2.0*tol);
577:           if (PetscRealPart(u[i]) < -1.0 + 2.0*tol)     yy[2] = PetscRealPart(-1.0*a*.25*(u[i+1] - u[i-1])*(u[i+1] - u[i-1])*sx + (-1.0*a*u[i] + b)*(u[i-1] + u[i+1] - 2.0*u[i])*sx);
578:           else if (PetscRealPart(u[i]) > 1.0 - 2.0*tol) yy[2] =  PetscRealPart(1.0*a*.25*(u[i+1] - u[i-1])*(u[i+1] - u[i-1])*sx + (     a*u[i] + b)*(u[i-1] + u[i+1] - 2.0*u[i])*sx);
579:           else                                          yy[2] = PetscRealPart(2.0*theta*u[i]/((1.0-u[i]*u[i])*(1.0-u[i]*u[i]))*.25*(u[i+1] - u[i-1])*(u[i+1] - u[i-1])*sx + (theta/(1.0-u[i]*u[i]))*(u[i-1] + u[i+1] - 2.0*u[i])*sx);
580:         }
581:         break;
582:       case 4: /* logarithmic + double obstacle */
583:         yy[1] = theta_c*PetscRealPart(-(u[i-1] + u[i+1] - 2.0*u[i]))*sx;
584:         if (ctx->truncation==2) {
585:           if (PetscRealPart(u[i]) < -1.0 + 2.0*tol)     yy[2] = (.25*theta/(tol-tol*tol))*PetscRealPart(u[i-1] + u[i+1] - 2.0*u[i])*sx;
586:           else if (PetscRealPart(u[i]) > 1.0 - 2.0*tol) yy[2] = (.25*theta/(tol-tol*tol))*PetscRealPart(u[i-1] + u[i+1] - 2.0*u[i])*sx;
587:           else                                          yy[2] = PetscRealPart(2.0*theta*u[i]/((1.0-u[i]*u[i])*(1.0-u[i]*u[i]))*.25*(u[i+1] - u[i-1])*(u[i+1] - u[i-1])*sx + (theta/(1.0-u[i]*u[i]))*(u[i-1] + u[i+1] - 2.0*u[i])*sx);
588:         }
589:         else {
590:           a = 2.0*theta*(1.0-2.0*tol)/(16.0*tol*tol*(1.0-tol)*(1.0-tol));
591:           b = theta/(4.0*tol*(1.0-tol)) - a*(1.0-2.0*tol);
592:           if (PetscRealPart(u[i]) < -1.0 + 2.0*tol)     yy[2] = PetscRealPart(-1.0*a*.25*(u[i+1] - u[i-1])*(u[i+1] - u[i-1])*sx + (-1.0*a*u[i] + b)*(u[i-1] + u[i+1] - 2.0*u[i])*sx);
593:           else if (PetscRealPart(u[i]) > 1.0 - 2.0*tol) yy[2] =  PetscRealPart(1.0*a*.25*(u[i+1] - u[i-1])*(u[i+1] - u[i-1])*sx + (     a*u[i] + b)*(u[i-1] + u[i+1] - 2.0*u[i])*sx);
594:           else                                          yy[2] =  PetscRealPart(2.0*theta*u[i]/((1.0-u[i]*u[i])*(1.0-u[i]*u[i]))*.25*(u[i+1] - u[i-1])*(u[i+1] - u[i-1])*sx + (theta/(1.0-u[i]*u[i]))*(u[i-1] + u[i+1] - 2.0*u[i])*sx);
595:         }
596:         break;
597:       default:
598:         SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"It will always be one of the values");
599:       }
600:       if (ctx->energy < 3) {
601:         max         = PetscMax(max,PetscAbs(yy[1]));
602:         yy[2]       = yy[0]+yy[1];
603:         yy_netforce = yy[2];
604:       } else {
605:         max         = PetscMax(max,PetscAbs(yy[1]+yy[2]));
606:         yy[3]       = yy[0]+yy[1]+yy[2];
607:         yy_netforce = yy[3];
608:       }
609:     }
610:     if (ctx->netforce) {
611:       PetscDrawLGAddPoint(lg,&xx_netforce,&yy_netforce);
612:     } else {
613:       PetscDrawLGAddPoint(lg,xx,yy);
614:     }
615:     x += hx;
616:     /*if (max > 7200150000.0) */
617:     /* printf("max very big when i = %d\n",i); */
618:   }
619:   PetscDrawAxisSetLabels(axis,"Right hand side","","");
620:   PetscDrawLGSetLegend(lg,NULL);
621:   PetscDrawLGDraw(lg);

623:   /*
624:         Plot the solution
625:   */
626:   PetscDrawLGSetDimension(lg,1);
627:   PetscDrawViewPortsSet(ports,0);
628:   PetscDrawLGReset(lg);
629:   x    = hx*xs;
630:   PetscDrawLGSetLimits(lg,x,x+(xm-1)*hx,-1.1,1.1);
631:   PetscDrawLGSetColors(lg,colors);
632:   for (i=xs; i<xs+xm; i++) {
633:     xx[0] = x;
634:     yy[0] = PetscRealPart(u[i]);
635:     PetscDrawLGAddPoint(lg,xx,yy);
636:     x    += hx;
637:   }
638:   PetscDrawAxisSetLabels(axis,"Solution","","");
639:   PetscDrawLGDraw(lg);

641:   /*
642:       Print the  forces as arrows on the solution
643:   */
644:   x   = hx*xs;
645:   cnt = xm/60;
646:   cnt = (!cnt) ? 1 : cnt;

648:   for (i=xs; i<xs+xm; i += cnt) {
649:     y    = yup = ydown = PetscRealPart(u[i]);
650:     c    = (u[i-1] + u[i+1] - 2.0*u[i])*sx;
651:     r    = (u[i] + u[i+2] - 2.0*u[i+1])*sx;
652:     l    = (u[i-2] + u[i] - 2.0*u[i-1])*sx;
653:     len  = -.5*PetscRealPart(ctx->kappa*(l + r - 2.0*c)*sx)/max;
654:     PetscDrawArrow(draw,x,y,x,y+len,PETSC_DRAW_RED);
655:     if (ctx->cahnhillard) {
656:       if (len < 0.) ydown += len;
657:       else yup += len;

659:       switch (ctx->energy) {
660:       case 1: /* double well */
661:         len = .5*PetscRealPart(6.*.25*u[i]*(u[i+1] - u[i-1])*(u[i+1] - u[i-1])*sx + (3.*u[i]*u[i] - 1.)*(u[i-1] + u[i+1] - 2.0*u[i])*sx)/max;
662:         break;
663:       case 2: /* double obstacle */
664:         len = -.5*PetscRealPart(u[i-1] + u[i+1] - 2.0*u[i])*sx/max;
665:         break;
666:       case 3: /* logarithmic + double well */
667:         len = .5*PetscRealPart(6.*.25*u[i]*(u[i+1] - u[i-1])*(u[i+1] - u[i-1])*sx + (3.*u[i]*u[i] - 1.)*(u[i-1] + u[i+1] - 2.0*u[i])*sx)/max;
668:         if (len < 0.) ydown += len;
669:         else yup += len;

671:         if (ctx->truncation==2) { /* quadratic */
672:           if (PetscRealPart(u[i]) < -1.0 + 2.0*tol)     len2 = .5*(.25*theta/(tol-tol*tol))*PetscRealPart(u[i-1] + u[i+1] - 2.0*u[i])*sx/max;
673:           else if (PetscRealPart(u[i]) > 1.0 - 2.0*tol) len2 = .5*(.25*theta/(tol-tol*tol))*PetscRealPart(u[i-1] + u[i+1] - 2.0*u[i])*sx/max;
674:           else                                          len2 = PetscRealPart(.5*(2.0*theta*u[i]/((1.0-u[i]*u[i])*(1.0-u[i]*u[i]))*.25*(u[i+1] - u[i-1])*(u[i+1] - u[i-1])*sx + (theta/(1.0-u[i]*u[i]))*(u[i-1] + u[i+1] - 2.0*u[i])*sx)/max);
675:         } else { /* cubic */
676:           a = 2.0*theta*(1.0-2.0*tol)/(16.0*tol*tol*(1.0-tol)*(1.0-tol));
677:           b = theta/(4.0*tol*(1.0-tol)) - a*(1.0-2.0*tol);
678:           if (PetscRealPart(u[i]) < -1.0 + 2.0*tol)     len2 = PetscRealPart(.5*(-1.0*a*.25*(u[i+1] - u[i-1])*(u[i+1] - u[i-1])*sx + (-1.0*a*u[i] + b)*(u[i-1] + u[i+1] - 2.0*u[i])*sx)/max);
679:           else if (PetscRealPart(u[i]) > 1.0 - 2.0*tol) len2 = PetscRealPart(.5*(a*.25*(u[i+1] - u[i-1])*(u[i+1] - u[i-1])*sx + (     a*u[i] + b)*(u[i-1] + u[i+1] - 2.0*u[i])*sx)/max);
680:           else                                          len2 = PetscRealPart(.5*(2.0*theta*u[i]/((1.0-u[i]*u[i])*(1.0-u[i]*u[i]))*.25*(u[i+1] - u[i-1])*(u[i+1] - u[i-1])*sx + (theta/(1.0-u[i]*u[i]))*(u[i-1] + u[i+1] - 2.0*u[i])*sx)/max);
681:         }
682:         y2   = len < 0 ? ydown : yup;
683:         PetscDrawArrow(draw,x,y2,x,y2+len2,PETSC_DRAW_PLUM);
684:         break;
685:       case 4: /* logarithmic + double obstacle */
686:         len = -.5*theta_c*PetscRealPart(-(u[i-1] + u[i+1] - 2.0*u[i])*sx/max);
687:         if (len < 0.) ydown += len;
688:         else yup += len;

690:         if (ctx->truncation==2) { /* quadratic */
691:           if (PetscRealPart(u[i]) < -1.0 + 2.0*tol)     len2 = .5*(.25*theta/(tol-tol*tol))*PetscRealPart(u[i-1] + u[i+1] - 2.0*u[i])*sx/max;
692:           else if (PetscRealPart(u[i]) > 1.0 - 2.0*tol) len2 = .5*(.25*theta/(tol-tol*tol))*PetscRealPart(u[i-1] + u[i+1] - 2.0*u[i])*sx/max;
693:           else                                          len2 = PetscRealPart(.5*(2.0*theta*u[i]/((1.0-u[i]*u[i])*(1.0-u[i]*u[i]))*.25*(u[i+1] - u[i-1])*(u[i+1] - u[i-1])*sx + (theta/(1.0-u[i]*u[i]))*(u[i-1] + u[i+1] - 2.0*u[i])*sx)/max);
694:         } else { /* cubic */
695:           a = 2.0*theta*(1.0-2.0*tol)/(16.0*tol*tol*(1.0-tol)*(1.0-tol));
696:           b = theta/(4.0*tol*(1.0-tol)) - a*(1.0-2.0*tol);
697:           if (PetscRealPart(u[i]) < -1.0 + 2.0*tol)     len2 = .5*PetscRealPart(-1.0*a*.25*(u[i+1] - u[i-1])*(u[i+1] - u[i-1])*sx + (-1.0*a*u[i] + b)*(u[i-1] + u[i+1] - 2.0*u[i])*sx)/max;
698:           else if (PetscRealPart(u[i]) > 1.0 - 2.0*tol) len2 =  .5*PetscRealPart(a*.25*(u[i+1] - u[i-1])*(u[i+1] - u[i-1])*sx + (     a*u[i] + b)*(u[i-1] + u[i+1] - 2.0*u[i])*sx)/max;
699:           else                                          len2 =  .5*PetscRealPart(2.0*theta*u[i]/((1.0-u[i]*u[i])*(1.0-u[i]*u[i]))*.25*(u[i+1] - u[i-1])*(u[i+1] - u[i-1])*sx + (theta/(1.0-u[i]*u[i]))*(u[i-1] + u[i+1] - 2.0*u[i])*sx)/max;
700:         }
701:         y2   = len < 0 ? ydown : yup;
702:         PetscDrawArrow(draw,x,y2,x,y2+len2,PETSC_DRAW_PLUM);
703:         break;
704:       }
705:       PetscDrawArrow(draw,x,y,x,y+len,PETSC_DRAW_BLUE);
706:     }
707:     x += cnt*hx;
708:   }
709:   DMDAVecRestoreArrayRead(da,localU,&x);
710:   DMRestoreLocalVector(da,&localU);
711:   PetscDrawStringSetSize(draw,.2,.2);
712:   PetscDrawFlush(draw);
713:   PetscDrawSetPause(draw,pause);
714:   PetscDrawPause(draw);
715:   return(0);
716: }

718: PetscErrorCode  MyDestroy(void **ptr)
719: {
720:   UserCtx        *ctx = *(UserCtx**)ptr;

724:   PetscDrawViewPortsDestroy(ctx->ports);
725:   return(0);
726: }

728: /*TEST

730:    test:
731:      TODO: currently requires initial condition file generated by heat

733: TEST*/