Here is some extra information and clarification:
- 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.
- 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.
- The value of Mesh.RandomFactor definitely plays some role too.
- 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.
Juha
On 2014-02-20 16:18, Juha Ritala wrote:
Hi,
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.
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.
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:
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.
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.
The questions I have are:
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?
Best regards,
Juha
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--
Juha Ritala
Department of Applied Physics
Aalto University, Finland
[email protected]
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