Ah, I was just busy writing what Wolfgang said. You can find more info on 
custom partitions for parallel::shared::Triangulation here:
https://dealii.org/current/doxygen/deal.II/classparallel_1_1shared_1_1Triangulation.html#a686a3453dfec098eb64d1510aa1716e1
 
<https://dealii.org/current/doxygen/deal.II/classparallel_1_1shared_1_1Triangulation.html#a686a3453dfec098eb64d1510aa1716e1>

You might also be able to “encourage” another partitioning using cell weights, 
but this was more aimed at load balancing in an hp-FEM context:
https://dealii.org/current/doxygen/deal.II/classparallel_1_1CellWeights.html 
<https://dealii.org/current/doxygen/deal.II/classparallel_1_1CellWeights.html>
https://dealii.org/current/doxygen/deal.II/structTriangulation_1_1Signals.html#af58294e40c64257c9de55e78b6443e36
 
<https://dealii.org/current/doxygen/deal.II/structTriangulation_1_1Signals.html#af58294e40c64257c9de55e78b6443e36>


I hope that this helps,
Jean-Paul

> On 15 Sep 2020, at 22:46, Wolfgang Bangerth <bange...@colostate.edu> wrote:
> 
> On 9/14/20 7:29 PM, shahab.g...@gmail.com wrote:
>> I am using load balancing and I noticed after load balancing, that the cells 
>> owned by each processor are sometimes separated from each other. In other 
>> words, some processors may own cell domains that are not connected to each 
>> other.
>> As this increases the computational cost in my case, I was wondering whether 
>> it would be possible to limit the load balancing to define only adjacent 
>> cells?
> 
> Not with parallel::distributed::Triangulation. That class uses a partitioning 
> algorithm that optimizes for the data structures used in storing 
> triangulations, sometimes at the expense of creating these kinds of 
> disconnected sub-domains. In practice, however, this has relatively little 
> effect on the performance of programs to the best of our knowledge: Yes, it 
> is not *optimal*, but it is good enough to not be a major problem in most 
> cases. You state that it increases the computational cost -- that's true, but 
> do you have evidence that that creates a bottleneck?
> 
> If you do need a different partitioning algorithm, you can use 
> parallel::shared::Triangulation or, since deal.II 9.2, the 
> parallel::fullydistributed::Triangulation class.
> 
> Best
> W.
> 
> -- 
> ------------------------------------------------------------------------
> Wolfgang Bangerth          email:                 bange...@colostate.edu
>                           www: http://www.math.colostate.edu/~bangerth/
> 
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