Come here to close this issue as it turned out to be an issue related to 
the reflective boundary condition in the weak form. When the boundary 
condition is turned off, solution will always be correct however number of 
processors is used.

But thanks for the discussions here.

在 2017年7月7日星期五 UTC-7下午2:47:46,Wolfgang Bangerth写道:
>
> On 07/06/2017 06:25 PM, Weixiong Zheng wrote: 
> > 
> > I suspect it would not be about the weak form directly. So, every time I 
> give 
> > an set of initial cells, I need to make sure total initial cell number 
> > N_cell_tot % n_process == 0. If this condition is fulfilled, solution 
> will 
> > always be correct. Say, I want to use 5 processors, then I have to give 
> N_cell 
> > = 5 or 10 or 5 * some integer. 
> > 
> > You see what's going wrong? 
>
> No :-) I only see from your description when something works correctly. So 
> try 
> a case where you have a 2x2 mesh and 3 processors. Or a 3x3 mesh and 2 
> processors. 
>
> I'm willing to believe that the problem is not in the weak form, but has 
> to do 
> with incorrectly setting up some vector, matrix, or other data structure. 
> The 
> question is where that happens. What I wanted to suggest is that if you 
> look 
> at the rhs vector, for example, and it is wrong, then the problem must 
> have 
> happened *during or before assembly*, not during the solution process. If, 
> however, system matrix and rhs are correct, then the problem must have 
> happened *after* assembly. 
>
> Debugging these sorts of problems always comes down to bisection the space 
> of 
> code where the problem could possibly be. For now, it is very large -- in 
> essence the entire time your program executes. The task then is to find a 
> convenient point in the middle to determine whether the problem happens in 
> the 
> first half or second half of the execution. And then to repeat. 
>
> Best 
>   W. 
>
> -- 
> ------------------------------------------------------------------------ 
> Wolfgang Bangerth          email:                 bang...@colostate.edu 
> <javascript:> 
>                             www: http://www.math.colostate.edu/~bangerth/ 
>
>

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