xref: /petsc/src/ts/tutorials/extchemfield.c (revision ef1023bda9d7138933c4c6fa7b7cf4a26d60c86d)
1 static const char help[] = "Integrate chemistry using TChem.\n";
2 
3 #include <petscts.h>
4 #include <petscdmda.h>
5 
6 #if defined(PETSC_HAVE_TCHEM)
7 #if defined(MAX)
8 #undef MAX
9 #endif
10 #if defined(MIN)
11 #undef MIN
12 #endif
13 #  include <TC_params.h>
14 #  include <TC_interface.h>
15 #else
16 #  error TChem is required for this example.  Reconfigure PETSc using --download-tchem.
17 #endif
18 /*
19 
20     This is an extension of extchem.c to solve the reaction equations independently in each cell of a one dimensional field
21 
22     Obtain the three files into this directory
23 
24        curl http://combustion.berkeley.edu/gri_mech/version30/files30/grimech30.dat > chem.inp
25        curl http://combustion.berkeley.edu/gri_mech/version30/files30/thermo30.dat > therm.dat
26        cp $PETSC_DIR/$PETSC_ARCH/externalpackages/tchem/data/periodictable.dat .
27 
28     Run with
29      ./extchemfield  -ts_arkimex_fully_implicit -ts_max_snes_failures -1 -ts_adapt_monitor -ts_adapt_dt_max 1e-4 -ts_arkimex_type 4 -ts_max_time .005
30 
31      Options for visualizing the solution:
32         Watch certain variables in each cell evolve with time
33         -draw_solution 1 -ts_monitor_lg_solution_variables Temp,H2,O2,H2O,CH4,CO,CO2,C2H2,N2 -lg_use_markers false  -draw_pause -2
34 
35         Watch certain variables in all cells evolve with time
36         -da_refine 4 -ts_monitor_draw_solution -draw_fields_by_name Temp,H2 -draw_vec_mark_points  -draw_pause -2
37 
38         Keep the initial temperature distribution as one monitors the current temperature distribution
39         -ts_monitor_draw_solution_initial -draw_bounds .9,1.7 -draw_fields_by_name Temp
40 
41         Save the images in a .gif (movie) file
42         -draw_save -draw_save_single_file
43 
44         Compute the sensitivies of the solution of the first temperature on the initial conditions
45         -ts_adjoint_solve  -ts_dt 1.e-5 -ts_type cn -ts_adjoint_view_solution draw
46 
47         Turn off diffusion
48         -diffusion no
49 
50         Turn off reactions
51         -reactions no
52 
53     The solution for component i = 0 is the temperature.
54 
55     The solution, i > 0, is the mass fraction, massf[i], of species i, i.e. mass of species i/ total mass of all species
56 
57     The mole fraction molef[i], i > 0, is the number of moles of a species/ total number of moles of all species
58         Define M[i] = mass per mole of species i then
59         molef[i] = massf[i]/(M[i]*(sum_j massf[j]/M[j]))
60 
61     FormMoleFraction(User,massf,molef) converts the mass fraction solution of each species to the mole fraction of each species.
62 
63 */
64 typedef struct _User *User;
65 struct _User {
66   PetscReal pressure;
67   int       Nspec;
68   int       Nreac;
69   PetscReal Tini,dx;
70   PetscReal diffus;
71   DM        dm;
72   PetscBool diffusion,reactions;
73   double    *tchemwork;
74   double    *Jdense;        /* Dense array workspace where Tchem computes the Jacobian */
75   PetscInt  *rows;
76 };
77 
78 static PetscErrorCode MonitorCell(TS,User,PetscInt);
79 static PetscErrorCode FormRHSFunction(TS,PetscReal,Vec,Vec,void*);
80 static PetscErrorCode FormRHSJacobian(TS,PetscReal,Vec,Mat,Mat,void*);
81 static PetscErrorCode FormInitialSolution(TS,Vec,void*);
82 
83 #define PetscCallTC(ierr) do {PetscCheck(!ierr,PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in TChem library, return code %d",ierr);} while (0)
84 
85 int main(int argc,char **argv)
86 {
87   TS                ts;         /* time integrator */
88   TSAdapt           adapt;
89   Vec               X;          /* solution vector */
90   Mat               J;          /* Jacobian matrix */
91   PetscInt          steps,ncells,xs,xm,i;
92   PetscReal         ftime,dt;
93   char              chemfile[PETSC_MAX_PATH_LEN] = "chem.inp",thermofile[PETSC_MAX_PATH_LEN] = "therm.dat";
94   struct _User      user;
95   TSConvergedReason reason;
96   PetscBool         showsolutions = PETSC_FALSE;
97   char              **snames,*names;
98   Vec               lambda;     /* used with TSAdjoint for sensitivities */
99 
100   PetscCall(PetscInitialize(&argc,&argv,(char*)0,help));
101   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Chemistry solver options","");
102   PetscCall(PetscOptionsString("-chem","CHEMKIN input file","",chemfile,chemfile,sizeof(chemfile),NULL));
103   PetscCall(PetscOptionsString("-thermo","NASA thermo input file","",thermofile,thermofile,sizeof(thermofile),NULL));
104   user.pressure = 1.01325e5;    /* Pascal */
105   PetscCall(PetscOptionsReal("-pressure","Pressure of reaction [Pa]","",user.pressure,&user.pressure,NULL));
106   user.Tini   = 1550;
107   PetscCall(PetscOptionsReal("-Tini","Initial temperature [K]","",user.Tini,&user.Tini,NULL));
108   user.diffus = 100;
109   PetscCall(PetscOptionsReal("-diffus","Diffusion constant","",user.diffus,&user.diffus,NULL));
110   PetscCall(PetscOptionsBool("-draw_solution","Plot the solution for each cell","",showsolutions,&showsolutions,NULL));
111   user.diffusion = PETSC_TRUE;
112   PetscCall(PetscOptionsBool("-diffusion","Have diffusion","",user.diffusion,&user.diffusion,NULL));
113   user.reactions = PETSC_TRUE;
114   PetscCall(PetscOptionsBool("-reactions","Have reactions","",user.reactions,&user.reactions,NULL));
115   PetscOptionsEnd();
116 
117   PetscCallTC(TC_initChem(chemfile, thermofile, 0, 1.0));
118   user.Nspec = TC_getNspec();
119   user.Nreac = TC_getNreac();
120 
121   PetscCall(DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_PERIODIC,10,user.Nspec+1,1,NULL,&user.dm));
122   PetscCall(DMSetFromOptions(user.dm));
123   PetscCall(DMSetUp(user.dm));
124   PetscCall(DMDAGetInfo(user.dm,NULL,&ncells,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL));
125   user.dx = 1.0/ncells;  /* Set the coordinates of the cell centers; note final ghost cell is at x coordinate 1.0 */
126   PetscCall(DMDASetUniformCoordinates(user.dm,0.0,1.0,0.0,1.0,0.0,1.0));
127 
128   /* set the names of each field in the DMDA based on the species name */
129   PetscCall(PetscMalloc1((user.Nspec+1)*LENGTHOFSPECNAME,&names));
130   PetscCall(PetscStrcpy(names,"Temp"));
131   TC_getSnames(user.Nspec,names+LENGTHOFSPECNAME);
132   PetscCall(PetscMalloc1((user.Nspec+2),&snames));
133   for (i=0; i<user.Nspec+1; i++) snames[i] = names+i*LENGTHOFSPECNAME;
134   snames[user.Nspec+1] = NULL;
135   PetscCall(DMDASetFieldNames(user.dm,(const char * const *)snames));
136   PetscCall(PetscFree(snames));
137   PetscCall(PetscFree(names));
138 
139   PetscCall(DMCreateMatrix(user.dm,&J));
140   PetscCall(DMCreateGlobalVector(user.dm,&X));
141 
142   PetscCall(PetscMalloc3(user.Nspec+1,&user.tchemwork,PetscSqr(user.Nspec+1),&user.Jdense,user.Nspec+1,&user.rows));
143 
144   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
145      Create timestepping solver context
146      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
147   PetscCall(TSCreate(PETSC_COMM_WORLD,&ts));
148   PetscCall(TSSetDM(ts,user.dm));
149   PetscCall(TSSetType(ts,TSARKIMEX));
150   PetscCall(TSARKIMEXSetFullyImplicit(ts,PETSC_TRUE));
151   PetscCall(TSARKIMEXSetType(ts,TSARKIMEX4));
152   PetscCall(TSSetRHSFunction(ts,NULL,FormRHSFunction,&user));
153   PetscCall(TSSetRHSJacobian(ts,J,J,FormRHSJacobian,&user));
154 
155   ftime = 1.0;
156   PetscCall(TSSetMaxTime(ts,ftime));
157   PetscCall(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER));
158 
159   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
160      Set initial conditions
161    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
162   PetscCall(FormInitialSolution(ts,X,&user));
163   PetscCall(TSSetSolution(ts,X));
164   dt   = 1e-10;                 /* Initial time step */
165   PetscCall(TSSetTimeStep(ts,dt));
166   PetscCall(TSGetAdapt(ts,&adapt));
167   PetscCall(TSAdaptSetStepLimits(adapt,1e-12,1e-4)); /* Also available with -ts_adapt_dt_min/-ts_adapt_dt_max */
168   PetscCall(TSSetMaxSNESFailures(ts,-1));            /* Retry step an unlimited number of times */
169 
170   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
171      Pass information to graphical monitoring routine
172    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
173   if (showsolutions) {
174     PetscCall(DMDAGetCorners(user.dm,&xs,NULL,NULL,&xm,NULL,NULL));
175     for (i=xs;i<xs+xm;i++) {
176       PetscCall(MonitorCell(ts,&user,i));
177     }
178   }
179 
180   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
181      Set runtime options
182    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
183   PetscCall(TSSetFromOptions(ts));
184 
185   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
186      Set final conditions for sensitivities
187    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
188   PetscCall(DMCreateGlobalVector(user.dm,&lambda));
189   PetscCall(TSSetCostGradients(ts,1,&lambda,NULL));
190   PetscCall(VecSetValue(lambda,0,1.0,INSERT_VALUES));
191   PetscCall(VecAssemblyBegin(lambda));
192   PetscCall(VecAssemblyEnd(lambda));
193 
194   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
195      Solve ODE
196      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
197   PetscCall(TSSolve(ts,X));
198   PetscCall(TSGetSolveTime(ts,&ftime));
199   PetscCall(TSGetStepNumber(ts,&steps));
200   PetscCall(TSGetConvergedReason(ts,&reason));
201   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%s at time %g after %" PetscInt_FMT " steps\n",TSConvergedReasons[reason],(double)ftime,steps));
202 
203   {
204     Vec                max;
205     const char * const *names;
206     PetscInt           i;
207     const PetscReal    *bmax;
208 
209     PetscCall(TSMonitorEnvelopeGetBounds(ts,&max,NULL));
210     if (max) {
211       PetscCall(TSMonitorLGGetVariableNames(ts,&names));
212       if (names) {
213         PetscCall(VecGetArrayRead(max,&bmax));
214         PetscCall(PetscPrintf(PETSC_COMM_SELF,"Species - maximum mass fraction\n"));
215         for (i=1; i<user.Nspec; i++) {
216           if (bmax[i] > .01) PetscCall(PetscPrintf(PETSC_COMM_SELF,"%s %g\n",names[i],(double)bmax[i]));
217         }
218         PetscCall(VecRestoreArrayRead(max,&bmax));
219       }
220     }
221   }
222 
223   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
224      Free work space.
225    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
226   TC_reset();
227   PetscCall(DMDestroy(&user.dm));
228   PetscCall(MatDestroy(&J));
229   PetscCall(VecDestroy(&X));
230   PetscCall(VecDestroy(&lambda));
231   PetscCall(TSDestroy(&ts));
232   PetscCall(PetscFree3(user.tchemwork,user.Jdense,user.rows));
233   PetscCall(PetscFinalize());
234   return 0;
235 }
236 
237 /*
238    Applies the second order centered difference diffusion operator on a one dimensional periodic domain
239 */
240 static PetscErrorCode FormDiffusionFunction(TS ts,PetscReal t,Vec X,Vec F,void *ptr)
241 {
242   User              user = (User)ptr;
243   PetscScalar       **f;
244   const PetscScalar **x;
245   DM                dm;
246   PetscInt          i,xs,xm,j,dof;
247   Vec               Xlocal;
248   PetscReal         idx;
249 
250   PetscFunctionBeginUser;
251   PetscCall(TSGetDM(ts,&dm));
252   PetscCall(DMDAGetInfo(dm,NULL,NULL,NULL,NULL,NULL,NULL,NULL,&dof,NULL,NULL,NULL,NULL,NULL));
253   PetscCall(DMGetLocalVector(dm,&Xlocal));
254   PetscCall(DMGlobalToLocalBegin(dm,X,INSERT_VALUES,Xlocal));
255   PetscCall(DMGlobalToLocalEnd(dm,X,INSERT_VALUES,Xlocal));
256   PetscCall(DMDAVecGetArrayDOFRead(dm,Xlocal,&x));
257   PetscCall(DMDAVecGetArrayDOF(dm,F,&f));
258   PetscCall(DMDAGetCorners(dm,&xs,NULL,NULL,&xm,NULL,NULL));
259 
260   idx = 1.0*user->diffus/user->dx;
261   for (i=xs; i<xs+xm; i++) {
262     for (j=0; j<dof; j++) {
263       f[i][j] += idx*(x[i+1][j] - 2.0*x[i][j] + x[i-1][j]);
264     }
265   }
266   PetscCall(DMDAVecRestoreArrayDOFRead(dm,Xlocal,&x));
267   PetscCall(DMDAVecRestoreArrayDOF(dm,F,&f));
268   PetscCall(DMRestoreLocalVector(dm,&Xlocal));
269   PetscFunctionReturn(0);
270 }
271 
272 /*
273    Produces the second order centered difference diffusion operator on a one dimensional periodic domain
274 */
275 static PetscErrorCode FormDiffusionJacobian(TS ts,PetscReal t,Vec X,Mat Amat,Mat Pmat,void *ptr)
276 {
277   User              user = (User)ptr;
278   DM                dm;
279   PetscInt          i,xs,xm,j,dof;
280   PetscReal         idx,values[3];
281   MatStencil        row,col[3];
282 
283   PetscFunctionBeginUser;
284   PetscCall(TSGetDM(ts,&dm));
285   PetscCall(DMDAGetInfo(dm,NULL,NULL,NULL,NULL,NULL,NULL,NULL,&dof,NULL,NULL,NULL,NULL,NULL));
286   PetscCall(DMDAGetCorners(dm,&xs,NULL,NULL,&xm,NULL,NULL));
287 
288   idx = 1.0*user->diffus/user->dx;
289   values[0] = idx;
290   values[1] = -2.0*idx;
291   values[2] = idx;
292   for (i=xs; i<xs+xm; i++) {
293     for (j=0; j<dof; j++) {
294       row.i = i;      row.c = j;
295       col[0].i = i-1; col[0].c = j;
296       col[1].i = i;   col[1].c = j;
297       col[2].i = i+1; col[2].c = j;
298       PetscCall(MatSetValuesStencil(Pmat,1,&row,3,col,values,ADD_VALUES));
299     }
300   }
301   PetscCall(MatAssemblyBegin(Pmat,MAT_FINAL_ASSEMBLY));
302   PetscCall(MatAssemblyEnd(Pmat,MAT_FINAL_ASSEMBLY));
303   PetscFunctionReturn(0);
304 }
305 
306 static PetscErrorCode FormRHSFunction(TS ts,PetscReal t,Vec X,Vec F,void *ptr)
307 {
308   User              user = (User)ptr;
309   PetscScalar       **f;
310   const PetscScalar **x;
311   DM                dm;
312   PetscInt          i,xs,xm;
313 
314   PetscFunctionBeginUser;
315   if (user->reactions) {
316     PetscCall(TSGetDM(ts,&dm));
317     PetscCall(DMDAVecGetArrayDOFRead(dm,X,&x));
318     PetscCall(DMDAVecGetArrayDOF(dm,F,&f));
319     PetscCall(DMDAGetCorners(dm,&xs,NULL,NULL,&xm,NULL,NULL));
320 
321     for (i=xs; i<xs+xm; i++) {
322       PetscCall(PetscArraycpy(user->tchemwork,x[i],user->Nspec+1));
323       user->tchemwork[0] *= user->Tini; /* Dimensionalize */
324       PetscCallTC(TC_getSrc(user->tchemwork,user->Nspec+1,f[i]));
325       f[i][0] /= user->Tini;           /* Non-dimensionalize */
326     }
327 
328     PetscCall(DMDAVecRestoreArrayDOFRead(dm,X,&x));
329     PetscCall(DMDAVecRestoreArrayDOF(dm,F,&f));
330   } else {
331     PetscCall(VecZeroEntries(F));
332   }
333   if (user->diffusion) PetscCall(FormDiffusionFunction(ts,t,X,F,ptr));
334   PetscFunctionReturn(0);
335 }
336 
337 static PetscErrorCode FormRHSJacobian(TS ts,PetscReal t,Vec X,Mat Amat,Mat Pmat,void *ptr)
338 {
339   User              user = (User)ptr;
340   const PetscScalar **x;
341   PetscInt          M = user->Nspec+1,i,j,xs,xm;
342   DM                dm;
343 
344   PetscFunctionBeginUser;
345   if (user->reactions) {
346     PetscCall(TSGetDM(ts,&dm));
347     PetscCall(MatZeroEntries(Pmat));
348     PetscCall(MatSetOption(Pmat,MAT_ROW_ORIENTED,PETSC_FALSE));
349     PetscCall(MatSetOption(Pmat,MAT_IGNORE_ZERO_ENTRIES,PETSC_TRUE));
350     PetscCall(DMDAVecGetArrayDOFRead(dm,X,&x));
351     PetscCall(DMDAGetCorners(dm,&xs,NULL,NULL,&xm,NULL,NULL));
352 
353     for (i=xs; i<xs+xm; i++) {
354       PetscCall(PetscArraycpy(user->tchemwork,x[i],user->Nspec+1));
355       user->tchemwork[0] *= user->Tini;  /* Dimensionalize temperature (first row) because that is what Tchem wants */
356       PetscCall(TC_getJacTYN(user->tchemwork,user->Nspec,user->Jdense,1));
357 
358       for (j=0; j<M; j++) user->Jdense[j + 0*M] /= user->Tini; /* Non-dimensionalize first column */
359       for (j=0; j<M; j++) user->Jdense[0 + j*M] /= user->Tini; /* Non-dimensionalize first row */
360       for (j=0; j<M; j++) user->rows[j] = i*M+j;
361       PetscCall(MatSetValues(Pmat,M,user->rows,M,user->rows,user->Jdense,INSERT_VALUES));
362     }
363     PetscCall(DMDAVecRestoreArrayDOFRead(dm,X,&x));
364     PetscCall(MatAssemblyBegin(Pmat,MAT_FINAL_ASSEMBLY));
365     PetscCall(MatAssemblyEnd(Pmat,MAT_FINAL_ASSEMBLY));
366   } else {
367     PetscCall(MatZeroEntries(Pmat));
368   }
369   if (user->diffusion) PetscCall(FormDiffusionJacobian(ts,t,X,Amat,Pmat,ptr));
370   if (Amat != Pmat) {
371     PetscCall(MatAssemblyBegin(Amat,MAT_FINAL_ASSEMBLY));
372     PetscCall(MatAssemblyEnd(Amat,MAT_FINAL_ASSEMBLY));
373   }
374   PetscFunctionReturn(0);
375 }
376 
377 PetscErrorCode FormInitialSolution(TS ts,Vec X,void *ctx)
378 {
379   PetscScalar    **x,*xc;
380   struct {const char *name; PetscReal massfrac;} initial[] = {
381     {"CH4", 0.0948178320887},
382     {"O2", 0.189635664177},
383     {"N2", 0.706766236705},
384     {"AR", 0.00878026702874}
385   };
386   PetscInt       i,j,xs,xm;
387   DM             dm;
388 
389   PetscFunctionBeginUser;
390   PetscCall(VecZeroEntries(X));
391   PetscCall(TSGetDM(ts,&dm));
392   PetscCall(DMDAGetCorners(dm,&xs,NULL,NULL,&xm,NULL,NULL));
393 
394   PetscCall(DMDAGetCoordinateArray(dm,&xc));
395   PetscCall(DMDAVecGetArrayDOF(dm,X,&x));
396   for (i=xs; i<xs+xm; i++) {
397     x[i][0] = 1.0 + .05*PetscSinScalar(2.*PETSC_PI*xc[i]);  /* Non-dimensionalized by user->Tini */
398     for (j=0; j<PETSC_STATIC_ARRAY_LENGTH(initial); j++) {
399       int ispec = TC_getSpos(initial[j].name, strlen(initial[j].name));
400       PetscCheck(ispec >= 0,PETSC_COMM_SELF,PETSC_ERR_USER,"Could not find species %s",initial[j].name);
401       PetscCall(PetscPrintf(PETSC_COMM_SELF,"Species %d: %s %g\n",j,initial[j].name,(double)initial[j].massfrac));
402       x[i][1+ispec] = initial[j].massfrac;
403     }
404   }
405   PetscCall(DMDAVecRestoreArrayDOF(dm,X,&x));
406   PetscCall(DMDARestoreCoordinateArray(dm,&xc));
407   PetscFunctionReturn(0);
408 }
409 
410 /*
411     Routines for displaying the solutions
412 */
413 typedef struct {
414   PetscInt cell;
415   User     user;
416 } UserLGCtx;
417 
418 static PetscErrorCode FormMoleFraction(UserLGCtx *ctx,Vec massf,Vec *molef)
419 {
420   User              user = ctx->user;
421   PetscReal         *M,tM=0;
422   PetscInt          i,n = user->Nspec+1;
423   PetscScalar       *mof;
424   const PetscScalar **maf;
425 
426   PetscFunctionBegin;
427   PetscCall(VecCreateSeq(PETSC_COMM_SELF,n,molef));
428   PetscCall(PetscMalloc1(user->Nspec,&M));
429   TC_getSmass(user->Nspec, M);
430   PetscCall(DMDAVecGetArrayDOFRead(user->dm,massf,&maf));
431   PetscCall(VecGetArray(*molef,&mof));
432   mof[0] = maf[ctx->cell][0]; /* copy over temperature */
433   for (i=1; i<n; i++) tM += maf[ctx->cell][i]/M[i-1];
434   for (i=1; i<n; i++) {
435     mof[i] = maf[ctx->cell][i]/(M[i-1]*tM);
436   }
437   PetscCall(DMDAVecRestoreArrayDOFRead(user->dm,massf,&maf));
438   PetscCall(VecRestoreArray(*molef,&mof));
439   PetscCall(PetscFree(M));
440   PetscFunctionReturn(0);
441 }
442 
443 static PetscErrorCode MonitorCellDestroy(UserLGCtx *uctx)
444 {
445   PetscFunctionBegin;
446   PetscCall(PetscFree(uctx));
447   PetscFunctionReturn(0);
448 }
449 
450 /*
451    Use TSMonitorLG to monitor the reactions in a particular cell
452 */
453 static PetscErrorCode MonitorCell(TS ts,User user,PetscInt cell)
454 {
455   TSMonitorLGCtx ctx;
456   char           **snames;
457   UserLGCtx      *uctx;
458   char           label[128];
459   PetscReal      temp,*xc;
460   PetscMPIInt    rank;
461 
462   PetscFunctionBegin;
463   PetscCall(DMDAGetCoordinateArray(user->dm,&xc));
464   temp = 1.0 + .05*PetscSinScalar(2.*PETSC_PI*xc[cell]);  /* Non-dimensionalized by user->Tini */
465   PetscCall(DMDARestoreCoordinateArray(user->dm,&xc));
466   PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD,&rank));
467   PetscCall(PetscSNPrintf(label,sizeof(label),"Initial Temperature %g Cell %d Rank %d",(double)user->Tini*temp,(int)cell,rank));
468   PetscCall(TSMonitorLGCtxCreate(PETSC_COMM_SELF,NULL,label,PETSC_DECIDE,PETSC_DECIDE,600,400,1,&ctx));
469   PetscCall(DMDAGetFieldNames(user->dm,(const char * const **)&snames));
470   PetscCall(TSMonitorLGCtxSetVariableNames(ctx,(const char * const *)snames));
471   PetscCall(PetscNew(&uctx));
472   uctx->cell = cell;
473   uctx->user = user;
474   PetscCall(TSMonitorLGCtxSetTransform(ctx,(PetscErrorCode (*)(void*,Vec,Vec*))FormMoleFraction,(PetscErrorCode (*)(void*))MonitorCellDestroy,uctx));
475   PetscCall(TSMonitorSet(ts,TSMonitorLGSolution,ctx,(PetscErrorCode (*)(void**))TSMonitorLGCtxDestroy));
476   PetscFunctionReturn(0);
477 }
478