Actual source code: biharmonic.c

petsc-3.12.2 2019-11-22
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  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


 43: Evolve the Cahn-Hillard equations: logarithmic +  double obstacle (never shrinks, never grows)
 44: ---------------
 45: ./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




 50: */
 51:  #include <petscdm.h>
 52:  #include <petscdmda.h>
 53:  #include <petscts.h>
 54:  #include <petscdraw.h>

 56: 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*);
 57: typedef struct {PetscBool cahnhillard;PetscBool degenerate;PetscReal kappa;PetscInt energy;PetscReal tol;PetscReal theta,theta_c;PetscInt truncation;PetscBool netforce; PetscDrawViewPorts *ports;} UserCtx;

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

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

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

105:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
106:      Extract global vectors from DMDA; then duplicate for remaining
107:      vectors that are the same types
108:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
109:   DMCreateGlobalVector(da,&x);
110:   VecDuplicate(x,&r);

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

125:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
126:      Create matrix data structure; set Jacobian evaluation routine

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

136:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
137:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
138:      Customize nonlinear solver
139:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
140:   TSSetType(ts,TSCN);

142:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
143:      Set initial conditions
144:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
145:   FormInitialSolution(da,x);
146:   TSSetTimeStep(ts,dt);
147:   TSSetSolution(ts,x);

149:   if (mymonitor) {
150:     ctx.ports = NULL;
151:     TSMonitorSet(ts,MyMonitor,&ctx,MyDestroy);
152:   }

154:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
155:      Set runtime options
156:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
157:   TSSetFromOptions(ts);

159:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
160:      Solve nonlinear system
161:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
162:   TSSolve(ts,x);
163:   TSGetStepNumber(ts,&steps);
164:   VecView(x,PETSC_VIEWER_BINARY_WORLD);

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

176:   PetscFinalize();
177:   return ierr;
178: }
179: /* ------------------------------------------------------------------- */
180: /*
181:    FormFunction - Evaluates nonlinear function, F(x).

183:    Input Parameters:
184: .  ts - the TS context
185: .  X - input vector
186: .  ptr - optional user-defined context, as set by SNESSetFunction()

188:    Output Parameter:
189: .  F - function vector
190:  */
191: PetscErrorCode FormFunction(TS ts,PetscReal ftime,Vec X,Vec F,void *ptr)
192: {
193:   DM             da;
195:   PetscInt       i,Mx,xs,xm;
196:   PetscReal      hx,sx;
197:   PetscScalar    *x,*f,c,r,l;
198:   Vec            localX;
199:   UserCtx        *ctx = (UserCtx*)ptr;
200:   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 */

203:   TSGetDM(ts,&da);
204:   DMGetLocalVector(da,&localX);
205:   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);

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

209:   /*
210:      Scatter ghost points to local vector,using the 2-step process
211:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
212:      By placing code between these two statements, computations can be
213:      done while messages are in transition.
214:   */
215:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
216:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);

218:   /*
219:      Get pointers to vector data
220:   */
221:   DMDAVecGetArrayRead(da,localX,&x);
222:   DMDAVecGetArray(da,F,&f);

224:   /*
225:      Get local grid boundaries
226:   */
227:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);

229:   /*
230:      Compute function over the locally owned part of the grid
231:   */
232:   for (i=xs; i<xs+xm; i++) {
233:     if (ctx->degenerate) {
234:       c = (1. - x[i]*x[i])*(x[i-1] + x[i+1] - 2.0*x[i])*sx;
235:       r = (1. - x[i+1]*x[i+1])*(x[i] + x[i+2] - 2.0*x[i+1])*sx;
236:       l = (1. - x[i-1]*x[i-1])*(x[i-2] + x[i] - 2.0*x[i-1])*sx;
237:     } else {
238:       c = (x[i-1] + x[i+1] - 2.0*x[i])*sx;
239:       r = (x[i] + x[i+2] - 2.0*x[i+1])*sx;
240:       l = (x[i-2] + x[i] - 2.0*x[i-1])*sx;
241:     }
242:     f[i] = -ctx->kappa*(l + r - 2.0*c)*sx;
243:     if (ctx->cahnhillard) {
244:       switch (ctx->energy) {
245:       case 1: /*  double well */
246:         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;
247:         break;
248:       case 2: /* double obstacle */
249:         f[i] += -(x[i-1] + x[i+1] - 2.0*x[i])*sx;
250:         break;
251:       case 3: /* logarithmic + double well */
252:         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;
253:         if (ctx->truncation==2) { /* log function with approximated with a quadratic polynomial outside -1.0+2*tol, 1.0-2*tol */
254:           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;
255:           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;
256:           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;
257:         } else { /* log function is approximated with a cubic polynomial outside -1.0+2*tol, 1.0-2*tol */
258:           a = 2.0*theta*(1.0-2.0*tol)/(16.0*tol*tol*(1.0-tol)*(1.0-tol));
259:           b = theta/(4.0*tol*(1.0-tol)) - a*(1.0-2.0*tol);
260:           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;
261:           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;
262:           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;
263:         }
264:         break;
265:       case 4: /* logarithmic + double obstacle */
266:         f[i] += -theta_c*(x[i-1] + x[i+1] - 2.0*x[i])*sx;
267:         if (ctx->truncation==2) { /* quadratic */
268:           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;
269:           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;
270:           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;
271:         } else { /* cubic */
272:           a = 2.0*theta*(1.0-2.0*tol)/(16.0*tol*tol*(1.0-tol)*(1.0-tol));
273:           b = theta/(4.0*tol*(1.0-tol)) - a*(1.0-2.0*tol);
274:           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;
275:           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;
276:           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;
277:         }
278:         break;
279:       }
280:     }

282:   }

284:   /*
285:      Restore vectors
286:   */
287:   DMDAVecRestoreArrayRead(da,localX,&x);
288:   DMDAVecRestoreArray(da,F,&f);
289:   DMRestoreLocalVector(da,&localX);
290:   return(0);
291: }

293: /* ------------------------------------------------------------------- */
294: /*
295:    FormJacobian - Evaluates nonlinear function's Jacobian

297: */
298: PetscErrorCode FormJacobian(TS ts,PetscReal ftime,Vec X,Mat A,Mat B,void *ptr)
299: {
300:   DM             da;
302:   PetscInt       i,Mx,xs,xm;
303:   MatStencil     row,cols[5];
304:   PetscReal      hx,sx;
305:   PetscScalar    *x,vals[5];
306:   Vec            localX;
307:   UserCtx        *ctx = (UserCtx*)ptr;

310:   TSGetDM(ts,&da);
311:   DMGetLocalVector(da,&localX);
312:   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);

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

316:   /*
317:      Scatter ghost points to local vector,using the 2-step process
318:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
319:      By placing code between these two statements, computations can be
320:      done while messages are in transition.
321:   */
322:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
323:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);

325:   /*
326:      Get pointers to vector data
327:   */
328:   DMDAVecGetArrayRead(da,localX,&x);

330:   /*
331:      Get local grid boundaries
332:   */
333:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);

335:   /*
336:      Compute function over the locally owned part of the grid
337:   */
338:   for (i=xs; i<xs+xm; i++) {
339:     row.i = i;
340:     if (ctx->degenerate) {
341:       /*PetscScalar c,r,l;
342:       c = (1. - x[i]*x[i])*(x[i-1] + x[i+1] - 2.0*x[i])*sx;
343:       r = (1. - x[i+1]*x[i+1])*(x[i] + x[i+2] - 2.0*x[i+1])*sx;
344:       l = (1. - x[i-1]*x[i-1])*(x[i-2] + x[i] - 2.0*x[i-1])*sx; */
345:     } else {
346:       cols[0].i = i - 2; vals[0] = -ctx->kappa*sx*sx;
347:       cols[1].i = i - 1; vals[1] =  4.0*ctx->kappa*sx*sx;
348:       cols[2].i = i    ; vals[2] = -6.0*ctx->kappa*sx*sx;
349:       cols[3].i = i + 1; vals[3] =  4.0*ctx->kappa*sx*sx;
350:       cols[4].i = i + 2; vals[4] = -ctx->kappa*sx*sx;
351:     }
352:     MatSetValuesStencil(B,1,&row,5,cols,vals,INSERT_VALUES);

354:     if (ctx->cahnhillard) {
355:       switch (ctx->energy) {
356:       case 1: /* double well */
357:         /*  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; */
358:         break;
359:       case 2: /* double obstacle */
360:         /*        f[i] += -(x[i-1] + x[i+1] - 2.0*x[i])*sx; */
361:         break;
362:       case 3: /* logarithmic + double well */
363:         break;
364:       case 4: /* logarithmic + double obstacle */
365:         break;
366:       }
367:     }

369:   }

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

396:   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);

398:   hx = 1.0/(PetscReal)Mx;

400:   /*
401:      Get pointers to vector data
402:   */
403:   DMDAVecGetArray(da,U,&u);

405:   /*
406:      Get local grid boundaries
407:   */
408:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);

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

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

430:     /* With the initial condition above the method is first order in space */
431:     /* this is a smooth initial condition so the method becomes second order in space */
432:     /*u[i] = PetscSinScalar(2*PETSC_PI*x); */
433:     u[i] = f[scale*i];
434:   }
435:   VecRestoreArrayRead(finesolution,&f);
436:   VecDestroy(&finesolution);

438:   /*
439:      Restore vectors
440:   */
441:   DMDAVecRestoreArray(da,U,&u);
442:   return(0);
443: }

445: /*
446:     This routine is not parallel
447: */
448: PetscErrorCode  MyMonitor(TS ts,PetscInt step,PetscReal time,Vec U,void *ptr)
449: {
450:   UserCtx        *ctx = (UserCtx*)ptr;
451:   PetscDrawLG    lg;
453:   PetscScalar    *u,l,r,c;
454:   PetscInt       Mx,i,xs,xm,cnt;
455:   PetscReal      x,y,hx,pause,sx,len,max,xx[4],yy[4],xx_netforce,yy_netforce,yup,ydown,y2,len2;
456:   PetscDraw      draw;
457:   Vec            localU;
458:   DM             da;
459:   int            colors[] = {PETSC_DRAW_YELLOW,PETSC_DRAW_RED,PETSC_DRAW_BLUE,PETSC_DRAW_PLUM,PETSC_DRAW_BLACK};
460:   /*
461:   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"}};
462:    */
463:   PetscDrawAxis      axis;
464:   PetscDrawViewPorts *ports;
465:   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 */
466:   PetscReal          vbounds[] = {-1.1,1.1};


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

482:   PetscViewerDrawGetDrawLG(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),1,&lg);
483:   PetscDrawLGGetDraw(lg,&draw);
484:   PetscDrawCheckResizedWindow(draw);
485:   if (!ctx->ports) {
486:     PetscDrawViewPortsCreateRect(draw,1,3,&ctx->ports);
487:   }
488:   ports = ctx->ports;
489:   PetscDrawLGGetAxis(lg,&axis);
490:   PetscDrawLGReset(lg);

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

496:   /*
497:       Plot the  energies
498:   */
499:   PetscDrawLGSetDimension(lg,1 + (ctx->cahnhillard ? 1 : 0) + (ctx->energy == 3));
500:   PetscDrawLGSetColors(lg,colors+1);
501:   PetscDrawViewPortsSet(ports,2);
502:   x    = hx*xs;
503:   for (i=xs; i<xs+xm; i++) {
504:     xx[0] = xx[1]  = xx[2] = x;
505:     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);
506:     else                 yy[0] = PetscRealPart(.25*ctx->kappa*(u[i-1] - u[i+1])*(u[i-1] - u[i+1])*sx);

508:     if (ctx->cahnhillard) {
509:       switch (ctx->energy) {
510:       case 1: /* double well */
511:         yy[1] = .25*PetscRealPart((1. - u[i]*u[i])*(1. - u[i]*u[i]));
512:         break;
513:       case 2: /* double obstacle */
514:         yy[1] = .5*PetscRealPart(1. - u[i]*u[i]);
515:         break;
516:       case 3: /* logarithm + double well */
517:         yy[1] = .25*PetscRealPart((1. - u[i]*u[i])*(1. - u[i]*u[i]));
518:         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));
519:         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));
520:         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));
521:         break;
522:       case 4: /* logarithm + double obstacle */
523:         yy[1] = .5*theta_c*PetscRealPart(1.0-u[i]*u[i]);
524:         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));
525:         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));
526:         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));
527:         break;
528:       default:
529:         SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"It will always be one of the values");
530:         break;
531:       }
532:     }
533:     PetscDrawLGAddPoint(lg,xx,yy);
534:     x   += hx;
535:   }
536:   PetscDrawGetPause(draw,&pause);
537:   PetscDrawSetPause(draw,0.0);
538:   PetscDrawAxisSetLabels(axis,"Energy","","");
539:   /*  PetscDrawLGSetLegend(lg,legend[ctx->energy-1]); */
540:   PetscDrawLGDraw(lg);

542:   /*
543:       Plot the  forces
544:   */
545:   PetscDrawLGSetDimension(lg,0 + (ctx->cahnhillard ? 2 : 0) + (ctx->energy == 3));
546:   PetscDrawLGSetColors(lg,colors+1);
547:   PetscDrawViewPortsSet(ports,1);
548:   PetscDrawLGReset(lg);
549:   x    = xs*hx;
550:   max  = 0.;
551:   for (i=xs; i<xs+xm; i++) {
552:     xx[0] = xx[1] = xx[2] = xx[3] = x;
553:     xx_netforce = x;
554:     if (ctx->degenerate) {
555:       c = (1. - u[i]*u[i])*(u[i-1] + u[i+1] - 2.0*u[i])*sx;
556:       r = (1. - u[i+1]*u[i+1])*(u[i] + u[i+2] - 2.0*u[i+1])*sx;
557:       l = (1. - u[i-1]*u[i-1])*(u[i-2] + u[i] - 2.0*u[i-1])*sx;
558:     } else {
559:       c = (u[i-1] + u[i+1] - 2.0*u[i])*sx;
560:       r = (u[i] + u[i+2] - 2.0*u[i+1])*sx;
561:       l = (u[i-2] + u[i] - 2.0*u[i-1])*sx;
562:     }
563:     yy[0]       = PetscRealPart(-ctx->kappa*(l + r - 2.0*c)*sx);
564:     yy_netforce = yy[0];
565:     max         = PetscMax(max,PetscAbs(yy[0]));
566:     if (ctx->cahnhillard) {
567:       switch (ctx->energy) {
568:       case 1: /* 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:         break;
571:       case 2: /* double obstacle */
572:         yy[1] = -PetscRealPart(u[i-1] + u[i+1] - 2.0*u[i])*sx;
573:         break;
574:       case 3: /* logarithmic + double well */
575:         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);
576:         if (ctx->truncation==2) { /* quadratic */
577:           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;
578:           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;
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:         } else { /* cubic */
581:           a = 2.0*theta*(1.0-2.0*tol)/(16.0*tol*tol*(1.0-tol)*(1.0-tol));
582:           b = theta/(4.0*tol*(1.0-tol)) - a*(1.0-2.0*tol);
583:           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);
584:           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);
585:           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);
586:         }
587:         break;
588:       case 4: /* logarithmic + double obstacle */
589:         yy[1] = theta_c*PetscRealPart(-(u[i-1] + u[i+1] - 2.0*u[i]))*sx;
590:         if (ctx->truncation==2) {
591:           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;
592:           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;
593:           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);
594:         }
595:         else {
596:           a = 2.0*theta*(1.0-2.0*tol)/(16.0*tol*tol*(1.0-tol)*(1.0-tol));
597:           b = theta/(4.0*tol*(1.0-tol)) - a*(1.0-2.0*tol);
598:           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);
599:           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);
600:           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);
601:         }
602:         break;
603:       default:
604:         SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"It will always be one of the values");
605:       break;
606:       }
607:       if (ctx->energy < 3) {
608:         max         = PetscMax(max,PetscAbs(yy[1]));
609:         yy[2]       = yy[0]+yy[1];
610:         yy_netforce = yy[2];
611:       } else {
612:         max         = PetscMax(max,PetscAbs(yy[1]+yy[2]));
613:         yy[3]       = yy[0]+yy[1]+yy[2];
614:         yy_netforce = yy[3];
615:       }
616:     }
617:     if (ctx->netforce) {
618:       PetscDrawLGAddPoint(lg,&xx_netforce,&yy_netforce);
619:     } else {
620:       PetscDrawLGAddPoint(lg,xx,yy);
621:     }
622:     x += hx;
623:     /*if (max > 7200150000.0) */
624:     /* printf("max very big when i = %d\n",i); */
625:   }
626:   PetscDrawAxisSetLabels(axis,"Right hand side","","");
627:   PetscDrawLGSetLegend(lg,NULL);
628:   PetscDrawLGDraw(lg);

630:   /*
631:         Plot the solution
632:   */
633:   PetscDrawLGSetDimension(lg,1);
634:   PetscDrawViewPortsSet(ports,0);
635:   PetscDrawLGReset(lg);
636:   x    = hx*xs;
637:   PetscDrawLGSetLimits(lg,x,x+(xm-1)*hx,-1.1,1.1);
638:   PetscDrawLGSetColors(lg,colors);
639:   for (i=xs; i<xs+xm; i++) {
640:     xx[0] = x;
641:     yy[0] = PetscRealPart(u[i]);
642:     PetscDrawLGAddPoint(lg,xx,yy);
643:     x    += hx;
644:   }
645:   PetscDrawAxisSetLabels(axis,"Solution","","");
646:   PetscDrawLGDraw(lg);

648:   /*
649:       Print the  forces as arrows on the solution
650:   */
651:   x   = hx*xs;
652:   cnt = xm/60;
653:   cnt = (!cnt) ? 1 : cnt;

655:   for (i=xs; i<xs+xm; i += cnt) {
656:     y    = yup = ydown = PetscRealPart(u[i]);
657:     c    = (u[i-1] + u[i+1] - 2.0*u[i])*sx;
658:     r    = (u[i] + u[i+2] - 2.0*u[i+1])*sx;
659:     l    = (u[i-2] + u[i] - 2.0*u[i-1])*sx;
660:     len  = -.5*PetscRealPart(ctx->kappa*(l + r - 2.0*c)*sx)/max;
661:     PetscDrawArrow(draw,x,y,x,y+len,PETSC_DRAW_RED);
662:     if (ctx->cahnhillard) {
663:       if (len < 0.) ydown += len;
664:       else yup += len;

666:       switch (ctx->energy) {
667:       case 1: /* double well */
668:         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;
669:         break;
670:       case 2: /* double obstacle */
671:         len = -.5*PetscRealPart(u[i-1] + u[i+1] - 2.0*u[i])*sx/max;
672:         break;
673:       case 3: /* logarithmic + double well */
674:         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;
675:         if (len < 0.) ydown += len;
676:         else yup += len;

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

697:         if (ctx->truncation==2) { /* quadratic */
698:           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;
699:           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;
700:           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);
701:         } else { /* cubic */
702:           a = 2.0*theta*(1.0-2.0*tol)/(16.0*tol*tol*(1.0-tol)*(1.0-tol));
703:           b = theta/(4.0*tol*(1.0-tol)) - a*(1.0-2.0*tol);
704:           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;
705:           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;
706:           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;
707:         }
708:         y2   = len < 0 ? ydown : yup;
709:         PetscDrawArrow(draw,x,y2,x,y2+len2,PETSC_DRAW_PLUM);
710:         break;
711:       }
712:       PetscDrawArrow(draw,x,y,x,y+len,PETSC_DRAW_BLUE);
713:     }
714:     x += cnt*hx;
715:   }
716:   DMDAVecRestoreArrayRead(da,localU,&x);
717:   DMRestoreLocalVector(da,&localU);
718:   PetscDrawStringSetSize(draw,.2,.2);
719:   PetscDrawFlush(draw);
720:   PetscDrawSetPause(draw,pause);
721:   PetscDrawPause(draw);
722:   return(0);
723: }

725: PetscErrorCode  MyDestroy(void **ptr)
726: {
727:   UserCtx        *ctx = *(UserCtx**)ptr;

731:   PetscDrawViewPortsDestroy(ctx->ports);
732:   return(0);
733: }



737: /*TEST

739:    test:
740:      TODO: currently requires initial condition file generated by heat

742: TEST*/