I am beginning to work with 2D finite element analysis, and I am following Jin's book on FEM applied to electromagnetism. I already passed chapter 3, which deals with 1D problems and everything was OK. However, for 2D the author says that the mesh should have some characteristics, but fails to provide some kind of strategy/algorithm for creating the mesh (or at least, I have not been able to find it). Thus, I would like to hear your suggestions regarding the matter, and any pointers would be appreciated.
Ps: I was thinking about either creating an algorithm for a uniform mesh, or using some kind of optimization strategy (e.g. GA, PSO, etc.) for assigning the area to the elements.
I would use triangles for 2D and tetrahedrons for 3D. Of course you could use polygons with more vertices, but then you will get into computational problems when you do FEM analysis: those polygons can get torque in them, highly complicating matters.
Thin elongated triangles/tetrahedrons are to be avoided: they span more length and (if very elongated) could cause topological problems. Search the web for Delaunay triangulation.
Hi Lambert, thanks for the input. Yes, I forgot to mention that I am trying to implement triangles for discretizing the domain. I am going to check out Delaunay triangulation and see what I can find.
Most of the publicly available codes for mesh generation will give you some quality parameters that can be tuned to get the prescribed mesh quality. There is a vast number of packages that are freely available (just google "mesh generation tools"). The ultimate choice will depend of the programming language and compatibility with your existing software.
Thanks Milan, I am going to check that out and see if I can incorporate some of those into my code.
I used quadtree meshing then isolated the boundaries using a technique called delta zone. This was followed by constrained Delunay triangulation. You can find more information about the technique on my page /publications/modelling of semiconductor....
you might be interested by some packages in the open source CGAL library
http://doc.cgal.org/latest/Manual/packages.html#PartMeshing
Hi Monique,
Thx for your input. I skimmed throught the site and it seems as it is c-based. I am working on Matlab first, although I will eventually migrate to C, and I think it would be helpful then. As of now, it looks like a good alternative would be to use distmesh, since it is already on Matlab.
Thx again
I recommend you to take a look at the exact or constrained Delaunay triangulation. A very useful tool that implements this kind of discretization is "Triangle". You can find more information and download it from the following link.
http://www.cs.cmu.edu/~quake/triangle.html
https://www.researchgate.net/publication/297245624_Particle_Swarm_Optimization_Algorithm_and_its_Codes_in_MATLAB
Research Particle Swarm Optimization: Algorithm and its Codes in MATLAB
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