[Gmsh] Problem with GMSH's 2D meshing algorithm

[Al Sc]

Dear Sir or Madam,

I am a new user of gmsh, and I have stubled across some possible issue with
GMSH's algorithm. The version I used is the most recent binary (git). In my
application of gmsh, I feed it a .geo-file, which already contains a
partial triangulation of some of the model's surfaces. This seems to lead
to very degenerate tetrahedra, that even the optimization algorithm cannot
fix any more.

Having analyzed and simplified the issue, I found out that in my complex
example, already after the 2D meshing step the mesh seems to feature bad
angles. In the appended file "issue_gmsh_2018.geo" you find a very much
simplified example, demonstrating the said behavior: With any 2D algorithm
you support, I obtain very lengthy 2D triangles in the "border", as you
will see. However, what I would expect is that the algorithm would
subdivide the edges of the "border", resulting in a rather fine, and
well-shaped (e.g. no small angles), triangle mesh in the "border".
Moreover, I would expect that the inner quad is filled with fine triangles
on the outside, and more coarse triangles in the inside. (See also:
http://gmsh.info/gallery/gbr_small.png ).

Having done some research, I speculate that your 2D delaunay mesher
probably computes a "constrained Delaunay triangulation" (see also:
https://www.cs.cmu.edu/~quake/triangle.defs.html ), and therefore does not
dare to split any edge which I specify in the .geo file, unless the 1D
mesher splits it. To me this seems to be the root of the problem. I propose
the solution of my problem is to rather have computed the "conforming
Delaunay triangulation" (see also:
https://www.cs.cmu.edu/~quake/triangle.defs.html ).

Could you please verify if this line of thought is right? If so, can you
help me achieve what I want with gmsh? I already tried out several
combinations of algorithms and parameters, which was was unsuccessful.

Thanks and Best regards

A. S
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