Actual source code: heat.c

petsc-3.5.4 2015-05-23
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  2: static char help[] = "Solves heat equation in 1d.\n";

  4: /*
  5:   Solves the equation

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

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

 14: Evolve the  Allen-Cahn equation:
 15: ---------------
 16: ./heat -ts_monitor -snes_monitor  -pc_type lu  -draw_pause .1 -snes_converged_reason  -wait   -ts_type cn  -da_refine 5   -allen-cahn -kappa .001 -ts_final_time 5  -mymonitor

 18: Evolve the  Allen-Cahn equation: zoom in on part of the domain
 19: ---------------
 20: ./heat -ts_monitor -snes_monitor  -pc_type lu   -snes_converged_reason     -ts_type cn  -da_refine 5   -allen-cahn -kappa .001 -ts_final_time 5  -zoom .25,.45 -wait  -mymonitor


 23: The option -square_initial indicates it should use a square wave initial condition otherwise it loads the file InitialSolution.heat as the initial solution. You should run with
 24: ./heat -square_initial -ts_monitor -snes_monitor  -pc_type lu   -snes_converged_reason    -ts_type cn  -da_refine 9 -ts_final_time 1.e-4 -ts_dt .125e-6 -snes_atol 1.e-25 -snes_rtol 1.e-25  -ts_max_steps 15
 25: to generate binaryoutput then do mv binaryoutput InitialSolution.heat to obtain the initial solution file

 27: */
 28: #include <petscdm.h>
 29: #include <petscdmda.h>
 30: #include <petscts.h>
 31: #include <petscdraw.h>

 33: /*
 34:    User-defined routines
 35: */
 36: extern PetscErrorCode FormFunction(TS,PetscReal,Vec,Vec,void*),FormInitialSolution(DM,Vec),MyMonitor(TS,PetscInt,PetscReal,Vec,void*),MyDestroy(void**);
 37: typedef struct {PetscReal kappa;PetscBool allencahn;PetscDrawViewPorts *ports;} UserCtx;

 41: int main(int argc,char **argv)
 42: {
 43:   TS             ts;                           /* time integrator */
 44:   Vec            x,r;                          /* solution, residual vectors */
 45:   Mat            J;                            /* Jacobian matrix */
 46:   PetscInt       steps,Mx, maxsteps = 1000000;
 48:   DM             da;
 49:   PetscReal      dt;
 50:   PetscReal      vbounds[] = {-1.1,1.1};
 51:   PetscBool      wait;
 52:   UserCtx        ctx;
 53:   PetscBool      mymonitor;

 55:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 56:      Initialize program
 57:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 58:   PetscInitialize(&argc,&argv,(char*)0,help);
 59:   ctx.kappa     = 1.0;
 60:   PetscOptionsGetReal(NULL,"-kappa",&ctx.kappa,NULL);
 61:   ctx.allencahn = PETSC_FALSE;
 62:   PetscOptionsHasName(NULL,"-allen-cahn",&ctx.allencahn);
 63:   PetscOptionsHasName(NULL,"-mymonitor",&mymonitor);

 65:   PetscViewerDrawSetBounds(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),1,vbounds);
 66:   PetscViewerDrawResize(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),1200,800);

 68:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 69:      Create distributed array (DMDA) to manage parallel grid and vectors
 70:   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 71:   DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC, -10,1,2,NULL,&da);
 72:   DMDASetFieldName(da,0,"Heat equation: u");
 73:   DMDAGetInfo(da,0,&Mx,0,0,0,0,0,0,0,0,0,0,0);
 74:   dt   = 1.0/(ctx.kappa*Mx*Mx);

 76:   /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 77:      Extract global vectors from DMDA; then duplicate for remaining
 78:      vectors that are the same types
 79:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 80:   DMCreateGlobalVector(da,&x);
 81:   VecDuplicate(x,&r);

 83:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 84:      Create timestepping solver context
 85:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 86:   TSCreate(PETSC_COMM_WORLD,&ts);
 87:   TSSetDM(ts,da);
 88:   TSSetProblemType(ts,TS_NONLINEAR);
 89:   TSSetRHSFunction(ts,NULL,FormFunction,&ctx);

 91:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 92:      Customize nonlinear solver
 93:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 94:   TSSetType(ts,TSCN);

 96:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 97:      Set initial conditions
 98:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 99:   FormInitialSolution(da,x);
100:   TSSetInitialTimeStep(ts,0.0,dt);
101:   TSSetDuration(ts,maxsteps,.02);
102:   TSSetExactFinalTime(ts,TS_EXACTFINALTIME_INTERPOLATE);
103:   TSSetSolution(ts,x);


106:   if (mymonitor) {
107:     ctx.ports = NULL;
108:     TSMonitorSet(ts,MyMonitor,&ctx,MyDestroy);
109:   }

111:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
112:      Set runtime options
113:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
114:   TSSetFromOptions(ts);

116:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
117:      Solve nonlinear system
118:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
119:   TSSolve(ts,x);
120:   wait = PETSC_FALSE;
121:   PetscOptionsGetBool(NULL,"-wait",&wait,NULL);
122:   if (wait) {
123:     PetscSleep(-1);
124:   }
125:   TSGetTimeStepNumber(ts,&steps);
126:   VecView(x,PETSC_VIEWER_BINARY_WORLD);

128:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
129:      Free work space.  All PETSc objects should be destroyed when they
130:      are no longer needed.
131:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
132:   MatDestroy(&J);
133:   VecDestroy(&x);
134:   VecDestroy(&r);
135:   TSDestroy(&ts);
136:   DMDestroy(&da);

138:   PetscFinalize();
139:   return(0);
140: }
141: /* ------------------------------------------------------------------- */
144: /*
145:    FormFunction - Evaluates nonlinear function, F(x).

147:    Input Parameters:
148: .  ts - the TS context
149: .  X - input vector
150: .  ptr - optional user-defined context, as set by SNESSetFunction()

152:    Output Parameter:
153: .  F - function vector
154:  */
155: PetscErrorCode FormFunction(TS ts,PetscReal ftime,Vec X,Vec F,void *ptr)
156: {
157:   DM             da;
159:   PetscInt       i,Mx,xs,xm;
160:   PetscReal      hx,sx;
161:   PetscScalar    *x,*f;
162:   Vec            localX;
163:   UserCtx        *ctx = (UserCtx*)ptr;

166:   TSGetDM(ts,&da);
167:   DMGetLocalVector(da,&localX);
168:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
169:                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

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

173:   /*
174:      Scatter ghost points to local vector,using the 2-step process
175:         DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
176:      By placing code between these two statements, computations can be
177:      done while messages are in transition.
178:   */
179:   DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);
180:   DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);

182:   /*
183:      Get pointers to vector data
184:   */
185:   DMDAVecGetArray(da,localX,&x);
186:   DMDAVecGetArray(da,F,&f);

188:   /*
189:      Get local grid boundaries
190:   */
191:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);

193:   /*
194:      Compute function over the locally owned part of the grid
195:   */
196:   for (i=xs; i<xs+xm; i++) {
197:     f[i] = ctx->kappa*(x[i-1] + x[i+1] - 2.0*x[i])*sx;
198:     if (ctx->allencahn) f[i] += (x[i] - x[i]*x[i]*x[i]);
199:   }

201:   /*
202:      Restore vectors
203:   */
204:   DMDAVecRestoreArray(da,localX,&x);
205:   DMDAVecRestoreArray(da,F,&f);
206:   DMRestoreLocalVector(da,&localX);
207:   return(0);
208: }

210: /* ------------------------------------------------------------------- */
213: PetscErrorCode FormInitialSolution(DM da,Vec U)
214: {
215:   PetscErrorCode    ierr;
216:   PetscInt          i,xs,xm,Mx,scale,N;
217:   PetscScalar       *u;
218:   const PetscScalar *f;
219:   PetscReal         hx,x,r;
220:   Vec               finesolution;
221:   PetscViewer       viewer;
222:   PetscBool         flg;

225:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
226:                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);

228:   hx = 1.0/(PetscReal)Mx;

230:   /*
231:      Get pointers to vector data
232:   */
233:   DMDAVecGetArray(da,U,&u);

235:   /*
236:      Get local grid boundaries
237:   */
238:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);

240:   /*  InitialSolution is obtained with
241:       ./heat -ts_monitor -snes_monitor  -pc_type lu   -snes_converged_reason    -ts_type cn  -da_refine 9 -ts_final_time 1.e-4 -ts_dt .125e-6 -snes_atol 1.e-25 -snes_rtol 1.e-25  -ts_max_steps 15
242:    */

244:   /* PetscViewerBinaryOpen(PETSC_COMM_WORLD,"InitialSolution",FILE_MODE_READ,&viewer); */
245:   /* VecCreate(PETSC_COMM_WORLD,&finesolution); */
246:   /* VecLoad(finesolution,viewer); */
247:   /* PetscViewerDestroy(&viewer); */
248:   /* VecGetSize(finesolution,&N); */
249:   /* scale = N/Mx; */
250:   /* VecGetArrayRead(finesolution,&f); */

252:   PetscOptionsHasName(NULL,"-square_initial",&flg);
253:   if (!flg) {
254:     PetscViewerBinaryOpen(PETSC_COMM_WORLD,"InitialSolution.heat",FILE_MODE_READ,&viewer);
255:     VecCreate(PETSC_COMM_WORLD,&finesolution);
256:     VecLoad(finesolution,viewer);
257:     PetscViewerDestroy(&viewer);
258:     VecGetSize(finesolution,&N);
259:     scale = N/Mx;
260:     VecGetArrayRead(finesolution,&f);
261:   }

263:   /*
264:      Compute function over the locally owned part of the grid
265:   */
266:   for (i=xs; i<xs+xm; i++) {
267:     x = i*hx;
268:     r = PetscSqrtScalar((x-.5)*(x-.5));
269:     if (r < .125) u[i] = 1.0;
270:     else u[i] = -.5;

272:     /* With the initial condition above the method is first order in space */
273:     /* this is a smooth initial condition so the method becomes second order in space */
274:     /*u[i] = PetscSinScalar(2*PETSC_PI*x); */
275:     /*  u[i] = f[scale*i];*/
276:     if (!flg) u[i] = f[scale*i];
277:   }
278:   if (!flg) {
279:     VecRestoreArrayRead(finesolution,&f);
280:     VecDestroy(&finesolution);
281:   }
282:   /* VecRestoreArrayRead(finesolution,&f);
283:    VecDestroy(&finesolution);*/

285:   /*
286:      Restore vectors
287:   */
288:   DMDAVecRestoreArray(da,U,&u);
289:   return(0);
290: }

294: /*
295:     This routine is not parallel
296: */
297: PetscErrorCode  MyMonitor(TS ts,PetscInt step,PetscReal time,Vec U,void *ptr)
298: {
299:   UserCtx            *ctx = (UserCtx*)ptr;
300:   PetscDrawLG        lg;
301:   PetscErrorCode     ierr;
302:   PetscScalar        *u;
303:   PetscInt           Mx,i,xs,xm,cnt;
304:   PetscReal          x,y,hx,pause,sx,len,max,xx[2],yy[2];
305:   PetscDraw          draw;
306:   Vec                localU;
307:   DM                 da;
308:   int                colors[] = {PETSC_DRAW_YELLOW,PETSC_DRAW_RED,PETSC_DRAW_BLUE};
309:   const char*const   legend[] = {"-kappa (\\grad u,\\grad u)","(1 - u^2)^2"};
310:   PetscDrawAxis      axis;
311:   PetscDrawViewPorts *ports;


315:   TSGetDM(ts,&da);
316:   DMGetLocalVector(da,&localU);
317:   DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
318:                      PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
319:   DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);
320:   hx   = 1.0/(PetscReal)Mx; sx = 1.0/(hx*hx);
321:   DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU);
322:   DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU);
323:   DMDAVecGetArray(da,localU,&u);

325:   PetscViewerDrawGetDrawLG(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),1,&lg);
326:   PetscDrawLGGetDraw(lg,&draw);
327:   PetscDrawCheckResizedWindow(draw);
328:   if (!ctx->ports) {
329:     PetscDrawViewPortsCreateRect(draw,1,3,&ctx->ports);
330:   }
331:   ports = ctx->ports;
332:   PetscDrawLGGetAxis(lg,&axis);
333:   PetscDrawLGReset(lg);

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

339:   /*
340:       Plot the  energies
341:   */
342:   PetscDrawLGSetDimension(lg,1 + (ctx->allencahn ? 1 : 0));
343:   PetscDrawLGSetColors(lg,colors+1);
344:   PetscDrawViewPortsSet(ports,2);
345:   x    = hx*xs;
346:   for (i=xs; i<xs+xm; i++) {
347:     xx[0] = xx[1] = x;
348:     yy[0] = PetscRealPart(.25*ctx->kappa*(u[i-1] - u[i+1])*(u[i-1] - u[i+1])*sx);
349:     if (ctx->allencahn) yy[1] = .25*PetscRealPart((1. - u[i]*u[i])*(1. - u[i]*u[i]));
350:     PetscDrawLGAddPoint(lg,xx,yy);
351:     x   += hx;
352:   }
353:   PetscDrawGetPause(draw,&pause);
354:   PetscDrawSetPause(draw,0.0);
355:   PetscDrawAxisSetLabels(axis,"Energy","","");
356:   PetscDrawLGSetLegend(lg,legend);
357:   PetscDrawLGDraw(lg);

359:   /*
360:       Plot the  forces
361:   */
362:   PetscDrawViewPortsSet(ports,1);
363:   PetscDrawLGReset(lg);
364:   x    = xs*hx;;
365:   max  = 0.;
366:   for (i=xs; i<xs+xm; i++) {
367:     xx[0] = xx[1] = x;
368:     yy[0] = PetscRealPart(ctx->kappa*(u[i-1] + u[i+1] - 2.0*u[i])*sx);
369:     max   = PetscMax(max,PetscAbs(yy[0]));
370:     if (ctx->allencahn) {
371:       yy[1] = PetscRealPart(u[i] - u[i]*u[i]*u[i]);
372:       max   = PetscMax(max,PetscAbs(yy[1]));
373:     }
374:     PetscDrawLGAddPoint(lg,xx,yy);
375:     x   += hx;
376:   }
377:   PetscDrawAxisSetLabels(axis,"Right hand side","","");
378:   PetscDrawLGSetLegend(lg,NULL);
379:   PetscDrawLGDraw(lg);

381:   /*
382:         Plot the solution
383:   */
384:   PetscDrawLGSetDimension(lg,1);
385:   PetscDrawViewPortsSet(ports,0);
386:   PetscDrawLGReset(lg);
387:   x    = hx*xs;
388:   PetscDrawLGSetLimits(lg,x,x+(xm-1)*hx,-1.1,1.1);
389:   PetscDrawLGSetColors(lg,colors);
390:   for (i=xs; i<xs+xm; i++) {
391:     xx[0] = x;
392:     yy[0] = PetscRealPart(u[i]);
393:     PetscDrawLGAddPoint(lg,xx,yy);
394:     x    += hx;
395:   }
396:   PetscDrawAxisSetLabels(axis,"Solution","","");
397:   PetscDrawLGDraw(lg);

399:   /*
400:       Print the  forces as arrows on the solution
401:   */
402:   x   = hx*xs;
403:   cnt = xm/60;
404:   cnt = (!cnt) ? 1 : cnt;

406:   for (i=xs; i<xs+xm; i += cnt) {
407:     y    = PetscRealPart(u[i]);
408:     len  = .5*PetscRealPart(ctx->kappa*(u[i-1] + u[i+1] - 2.0*u[i])*sx)/max;
409:     PetscDrawArrow(draw,x,y,x,y+len,PETSC_DRAW_RED);
410:     if (ctx->allencahn) {
411:       len  = .5*PetscRealPart(u[i] - u[i]*u[i]*u[i])/max;
412:       PetscDrawArrow(draw,x,y,x,y+len,PETSC_DRAW_BLUE);
413:     }
414:     x += cnt*hx;
415:   }
416:   DMDAVecRestoreArray(da,localU,&x);
417:   DMRestoreLocalVector(da,&localU);
418:   PetscDrawStringSetSize(draw,.2,.2);
419:   PetscDrawFlush(draw);
420:   PetscDrawSetPause(draw,pause);
421:   PetscDrawPause(draw);
422:   return(0);
423: }

427: PetscErrorCode  MyDestroy(void **ptr)
428: {
429:   UserCtx        *ctx = *(UserCtx**)ptr;

433:   PetscDrawViewPortsDestroy(ctx->ports);
434:   return(0);
435: }