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<div class="moz-cite-prefix">Here is some extra information and
clarification:<br>
<br>
- I am using the newest version of Gmsh (2.8.4) on Ubuntu 12.04. I
have also tested 2.8.3 but it does not work any better.<br>
<br>
- I can now confirm that changing the tolerance value of Tetgen is
crucial if I want to set the characteristic length at the tip to
0.2 nm.<br>
<br>
- The value of Mesh.RandomFactor definitely plays some role too.<br>
<br>
- The meshing process leads to an error depending on the generated
random number sequence. The seed of the random number generator
determines whether the meshing is successful or not.<br>
<br>
Juha<br>
<br>
On 2014-02-20 16:18, Juha Ritala wrote:<br>
</div>
<blockquote
cite="mid:13101_1392918278_53063F06_13101_3598_1_53060E9A.1000503@aalto.fi"
type="cite">Hi,
<br>
<br>
I have used the geometry module of Gmsh to model one quarter of a
cylinder symmetric system representing the cantilever and tip of
an atomic force microscope (AFM) on top of a sample (see the
attached .geo file). My goal is to compute the electric field
between the AFM probe and the back plate when a bias voltage is
applied between those. The distance between the tip and the sample
(h) can be as small as 1 nm, whereas the radius and height of the
container (Lc) is 20 mm to justify setting the electrostatic
potential to zero at the boundary.
<br>
<br>
If I set the distance between the AFM tip and the sample to 1 nm,
the characteristic length of the mesh around the tip (tip_ls) must
obviously be smaller than that. Using a characteristic length of
exactly 1 nm usually results in a successful mesh generation, but
if I set the characteristic length to be smaller than 1 nm, the 3D
meshing process gives me a self intersecting surface mesh error. I
suspect this is caused by the extremely small ratio of the
characteristic length at the tip to the size of the model. If I
set the characteristic length at the tip to 0.2 nm, this ratio is
10^-8.
<br>
<br>
<br>
I have no prior knowledge of mesh generation algorithms, but it
seems to me that this is either a tolerance or a numerical
precision problem. I have made the following attempts to solve the
problem:
<br>
<br>
The most notable attempt I made was to change the tolerance of the
Tetgen algorithm, which is the first part of the 3D meshing, and
where the self intersecting surface mesh error arises. Changing
the tolerance from the default value of 10^-8 to 10^-9 seems to
have a clear positive impact on the success of meshing. Without
this change, the meshing fails always if the characteristic length
at the tip is set to 0.2 nm. With this change, I have managed to
generate a good 3D mesh, although the meshing still randomly
fails. I have not yet tried to set the tolerance even smaller, as
changing the tolerance of the Tetgen requires recompilation of the
source.
<br>
<br>
I have tried to tune the options that are on the first lines of my
.geo file. The option Mesh.RandomFactor seems to have a clear
impact on the meshing process. It seems that a smaller value is
better, but the 2D meshing fails if the value is too small.
According to the documentation, too small value of
Mesh.RandomFactor leads to problems with numerical precision.
<br>
<br>
<br>
The questions I have are:
<br>
Has someone else had this kind of a problem? Am I on the right
with my solution attempts? Is there something else that can be
done? Where is the value of Mesh.RandomFactor actually used?
<br>
<br>
<br>
Best regards,
<br>
Juha
<br>
<br>
<br>
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<br>
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</pre>
</blockquote>
<br>
<br>
<pre class="moz-signature" cols="72">--
Juha Ritala
Department of Applied Physics
Aalto University, Finland
<a class="moz-txt-link-abbreviated" href="mailto:juha.ritala@aalto.fi">juha.ritala@aalto.fi</a></pre>
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