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Meshing of Disproportionate Geometries
Posted Feb 9, 2012, 12:01 p.m. EST Mesh Version 4.2a 1 Reply
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Hi,
Small structures are often disproportionate Geometries with orders of magnitude difference in height to width. E.g. There is a thin film 10nm high (y) and 0.5cm(x) long.
There was a thread on a similar topic in 3D which suggested the use of sweep meshing.
www.comsol.de/community/forums/mesh/thread/19108/
However I am usually working in 2D since that simplifies the model and there this isn't possible.
In the upper example when creating a standard normal mesh I get very many meshpoints even when there are only 4 "layers" of mesh points. So perhaps longer a meshpoint could be longer in x direction and smaller in y direction. However how does this influence the accuracy of the simulation.
I also found some other approaches used.
(1) "scaling the problem": E.g. in an electric only problem: A diode which is only about 100nm thick is scaled to 1 or 10um with 10 or 100 times less resistance.
(2) "cutting the problem" Since sometimes most of the lenght of the "layer" is not important another geometry is created which just simulates the interesting part and the other part is taken with a boundary condition in account.
Especially I am looking for some literature about handling handling disproportionate kind of geometries in kind of meshing. Perhaps were such (simple) methods as the upper 2 are used and put on a scientific ground.
Cheers
Robert
edit:
I found a thin film paper which describes the problem and the solution (1) as follows:
de.arxiv.org/abs/1001.4447v2
To confirm the scenario discussed above, we calculated
the spatial distribution of the electrical potential and the
current in ring-shaped MTJs using finite element method
(FEM) simulations. The geometry of the ring-shaped junc-
tions is shown in Fig. 6. The in-plane conductivities used in
the simulations for the various layers of the junction stack
are summarized in Table 3. Since the simulation tool did
not allow to represent the real dimensions of the sample be-
cause of its large aspect ratio we scaled the geometry and
the conductivity in the out-of-plane direction by a factor of
100.
Small structures are often disproportionate Geometries with orders of magnitude difference in height to width. E.g. There is a thin film 10nm high (y) and 0.5cm(x) long.
There was a thread on a similar topic in 3D which suggested the use of sweep meshing.
www.comsol.de/community/forums/mesh/thread/19108/
However I am usually working in 2D since that simplifies the model and there this isn't possible.
In the upper example when creating a standard normal mesh I get very many meshpoints even when there are only 4 "layers" of mesh points. So perhaps longer a meshpoint could be longer in x direction and smaller in y direction. However how does this influence the accuracy of the simulation.
I also found some other approaches used.
(1) "scaling the problem": E.g. in an electric only problem: A diode which is only about 100nm thick is scaled to 1 or 10um with 10 or 100 times less resistance.
(2) "cutting the problem" Since sometimes most of the lenght of the "layer" is not important another geometry is created which just simulates the interesting part and the other part is taken with a boundary condition in account.
Especially I am looking for some literature about handling handling disproportionate kind of geometries in kind of meshing. Perhaps were such (simple) methods as the upper 2 are used and put on a scientific ground.
Cheers
Robert
edit:
I found a thin film paper which describes the problem and the solution (1) as follows:
de.arxiv.org/abs/1001.4447v2
To confirm the scenario discussed above, we calculated
the spatial distribution of the electrical potential and the
current in ring-shaped MTJs using finite element method
(FEM) simulations. The geometry of the ring-shaped junc-
tions is shown in Fig. 6. The in-plane conductivities used in
the simulations for the various layers of the junction stack
are summarized in Table 3. Since the simulation tool did
not allow to represent the real dimensions of the sample be-
cause of its large aspect ratio we scaled the geometry and
the conductivity in the out-of-plane direction by a factor of
100.
1 Reply Last Post Feb 9, 2012, 3:58 p.m. EST
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Posted:
1 decade ago
Hi
just to note: I believe you can sweep a mesh in 2D just as in 3D. But you must first mesh the edge (would have to check not by my COMSOL WS just now ;).
You can also use a mapped mesh but first mesh the short edges, this will make a rectangular mesh with long, thin elements, which are often compatible with thin layers like that, or use te scaling factor
--
Good luck
Ivar
just to note: I believe you can sweep a mesh in 2D just as in 3D. But you must first mesh the edge (would have to check not by my COMSOL WS just now ;).
You can also use a mapped mesh but first mesh the short edges, this will make a rectangular mesh with long, thin elements, which are often compatible with thin layers like that, or use te scaling factor
--
Good luck
Ivar