[Gmsh] Refine by splitting (tetrahedral meshes)

[Christophe Geuzaine]

> On 8 Apr 2019, at 11:37, Jose Paulo Moitinho de Almeida <moitinho at civil.ist.utl.pt> wrote:
> 
> Hello 
> 
> Trying to understand the quality of the meshes obtained when using the "Refine 
> by splitting" option I looked at the code in Mesh/meshRefine.cpp
> 
> After some digging I came to realise why the comment at line 198 is there,
>>> // FIXME: we should choose the template to maximize the quality
> at first thinking that the "right choice" would imply some geometry 
> calculations.
> 
> Then I found
>> Bey, Jürgen. "Simplicial grid refinement: on Freudenthal's algorithm and the
>> optimal number of congruence classes." Numerische Mathematik 85.1 (2000):
>> 1-29.
> and updated the template using the sequence in Algorithm RedRefinement3D 
> therein.
> 
> At first the result was not correct, but  a simple switch of indices made it 
> work. Starting with  a mesh where all elements are equal we obtain refined 
> meshes with elements of 3 shapes and for a non-regular mesh the properties of 
> the elements stabilise.
> 
> The code is attached, I hope it is useful.
> 

It is - I have merged it in the master branch so it can be tested "in the wild".

Thanks!

Christophe

> (I know that this could be done in  a more efficient way with git. Sorry I will 
> learn how to do that next week..). 
> 
> Regards
> 
> ZP
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— 
Prof. Christophe Geuzaine
University of Liege, Electrical Engineering and Computer Science 
http://www.montefiore.ulg.ac.be/~geuzaine