[Gmsh] Zero volume elements in Delaunay 2d triangulation
jean-francois.remacle at uclouvain.be
Tue Apr 1 15:12:36 CEST 2008
Jose Paulo Moitinho de Almeida a écrit :
> On Monday 31 March 2008, you wrote:
>> Jose Paulo Moitinho de Almeida a écrit :
>>> 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.
> 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.
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
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.
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