Hi Dr. Bangerth,

Thanks a lot for your guidance! I compared the solution in the vtu files 
using the minimal example above, they are nearly identical. Looking back 
into the code, I am outputting the system matrix from processor 0, which 
probably only printed the part that it locally owns, hence there's a 
difference in the matrices when running in serial and parallel. I guess I 
rushed to conclusion too quickly.

Best,
Jimmy

On Wednesday, July 29, 2020 at 9:55:38 AM UTC-5, Wolfgang Bangerth wrote:
>
>
> Jimmy, 
>
> > A minimum example to reproduce this is attached. When the mesh is built 
> using 
> > GridGenerator::hyper_cube or GridGenerator::subdivided_hyper_rectangle 
> with 
> > subsequent refinement, the program works as expected. When the same mesh 
> is 
> > generated using GridGenerator::subdivided_hyper_rectangle without any 
> > subsequent refinement, some entries in the global stiffness matrix (the 
> nodes 
> > on the right hand side of the mesh, in this case, using 2 processors) do 
> not 
> > get updated. The example output of stiffness matrices when using one and 
> two 
> > processors are also attached for reference. 
> > 
> > So my question is, is this the expected behavior of the function? If so, 
> why 
> > is that the case? 
>
> There is still a lot of stuff in the program that could be remove, 
> including 
> all of the comments, to make it substantially smaller and easier to 
> understand. 
>
> I don't know whether there is a bug, but here is a suggestion: The finite 
> element solution u_h(x) that results from the linear system should be the 
> same 
> independent of the partitioning. But the order of degrees of freedom may 
> be 
> different, and consequently the matrix may not be the same -- it should 
> only 
> be the same up to some column and row permutation. Have you verified that 
> the 
> *solution function* (not the solution vector) that results is the same 
> independent of the number of processors? 
>
> Best 
>   W. 
>
> -- 
> ------------------------------------------------------------------------ 
> Wolfgang Bangerth          email:                 bang...@colostate.edu 
> <javascript:> 
>                             www: http://www.math.colostate.edu/~bangerth/ 
>
>

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