[Gmsh] Zero volume elements in Delaunay 2d triangulation

[Jean-François Remacle]

Jose Paulo Moitinho de Almeida a écrit :
> On Monday 31 March 2008, you wrote:
>   
>> Jose Paulo Moitinho de Almeida a écrit :
>>     
>>> Hello
>>>
>>> I know that the Delaunay triangulation is "experimental", but I was
>>> solving the problem of face orientation when post-processing the mesh.
>>>
>>> Now, when refining the mesh around a singularity I came to an example
>>> where I get
>>>
>>> $ gmsh ref.geo -algo del2d -2 -bgm ref.bgm
>>> ....
>>> Warning : Colinear points in circum circle computation
>>> ....
>>>
>>> and the resulting mesh has triangles with colinear nodes.
>>>       
>> gmsh ref.geo -algo del2d -2 -bgm ref.bgm -rand 1.e-11
>>
>> gives a better result. Indeed your mesh has sizes that varies a lot, so it
>> is better to perturbate less the points of the initial mesh. BTW, if you
>> use nightly snapshots, try the "very very experimental"
>>
>>
>> gmsh ref.geo -algo frontal -2 -bgm ref.bgm -rand 1.e-11
>>
>> that produce more regular meshes.
>>
>> JFR
>>
>>     
>
> Merci
>
> With the -rand 1e-11 parameter and del2d I got fewer, but still some zero 
> volume elements.
>   
This is strange, because I do not have that pb here with the files you gave us.

I tryed 

gmsh ref.geo -algo del2d -2 -bgm ref.bgm -rand 1.e-11 -statreport ref.stat

and the worst element has an aspect ratio of 0.61

I then tryed 

gmsh ref.geo -algo del2d -2 -bgm ref.bgm -rand 1.e-9 -append_statreport ref.stat

and the worst element has an aspect ratio of 0. (sliver)

> With the frontal algorithm it worked fine, but broke again on the next step, 
> with zero volume elements and the message
> Warning : Colinear points in circum circle computation
>
>   
No problem here, the stats look very much the same.

> I know that I am reaching the limit for the precision of my numbers (the 
> minimum characteristic length is 2.85e-9 in this case) and reducing the 
> perturbation parameter results in 
> Error   : 3 identical points in Qtest
>
>   
Yes, you cannot generate a mesh with gmsh with such a ratio of 
characteristic lengths.
In the files you gave us, the ratio was about 10-6.

> (Two details)
> While playing around I found that by doing the mesh from the command line
> gmsh ref.geo -algo frontal -2 -rand 1.e-11 -bgm ref.xxx2
> I get the warnings mentioned above, but if I use the gui
> gmsh ref.geo -algo frontal -rand 1.e-11 -bgm ref.xxx2
> I don't, though the zero volume elements are there.
>
>   
The warnings are ther, in the message console window of gmsh

> When zoooooooooming in for these small elements it seems that some edges 
> have "dissapeared" near the singular vertices. I could not understand if this 
> has to do with the failure of the mesher or some (understandable) tolerance 
> failure in the render process.
>
>   
I cannot observe that here.

JFR

> Regards
>
> ZP
>
>
>
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