I spent the last half of 2009 writing FEA software to solve waveguide problems along with electrostatics. I have just completed it with help from these groups, specifically the people:
Dr. Paul Kinsler Informed me about Permittivity and Permeability
Benj Informed me about Permittivity and Permeability and the boundary conditions of a waveguide
So thanks to the above people. I am also thanking you on my "Acknowledgments" page for the site:
Thanks for the acknowledgment. It certainly wasn't necessary. I am surprised that as a mechanical engineer you should have such an interest in electrostatics and electromagnetics. Nevertheless your images appear quite impressive. Of course, I've downloaded your software for a closer examination and best of all it's under the GNU license. I myself have had some interest in finite element electromagnetic calculations. In the past I have had interests in magnetic field displays such as calculate the fields that exist about magnetic structures of magnets and magnetic materials of various specifications. One such question still to be answered would be "what form and type of magnetic material produces a "magnetic antenna" with the most sensitivity" or stated another way which shape gives the maximum magnetic field through a given piece of magnetic material when placed in a uniform ambient magnetic field.
The bad news is that somehow I never got around to seriously answering these questions nor developing the finite element software to answer them. The good news is that now there is a freely available piece of software with which to start the quest! In recent times I have been working on another similar, but different, problem which is the question of inductance distribution over an arbitrary conductor in space. Some very interesting work has been done in this regard by several people.
see for example MS thesis by Distini
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Electromagnetic theory while commonly thought to be pretty much all hashed out, is far from it. One such area of ignorance would be the inductance of arbitrary conductors in space. A precise mathematical formulation has not yet been presented for this problem (there is the gnawing question of mathematics that blow up as spacing between current elements go to zero) and Finite element analysis seems an excellent way to get practical answers in the absence of an analytic solution. These efforts on my part have also sort of stalled as well over the last couple of years so I now am looking forward to a close examination of your approaches even though they are in an area unrelated to this.
In any event, I am really impressed with your work even though I am quite surprised that it shows Eigenfunctions of waveguides rather than say stress and strain in cantilevers of arbitrary shape! Quite obviously, YOU RULE!
Getting help for the project was frustrating. You're only 1 of 2 EEs that gave any help so it was definitely appreciated.
A lot comes from the difficulty I have leaving things unfinished.
This is beyond me, but it may be possible to do the reverse problem where you start with the desired magnetic field and then calculate the design/placement of the magnetic antenna. For statics, FEA allows for this. You may then be able to extrapolate this to an antenna design that will produce that mode.
I hope it turns out to be useful, but your needs may be beyond what the code can do. I certainly welcome anyone expanding on SLFCEM, but the lack of interest my be due to my coding design choices (which work for me, but I'm not sure for anyone else.)
This will have to find its way into a textbook before I can deal with it. Cutting edge research and journal articles are a bit of a struggle for me, especially in EE.
When it comes to EE and FEA in general, I sometimes abstract it into a math problem rather than physics. Although there are limits to this approach, it makes the problem about solving differential equations which can be more conceptually manageable. Of course, it only works as a starting point.
There are many issues:
1) Quirks in the physics requiring special accommodations. In EE, an example would be the need for edge based interpolation to prevent spurious modes in waveguide analysis. In ME, the fact that there are so many different types of elements (beams, bricks, shells, etc.) are due to all the geometries encountered.
2) Inherent math issues like what types of linear system you are dealing with. Matrices may be positive definite, semi-definite, complex, singular, etc. And if the system is big enough, an iterative solver may be necessary to speed up calculations and save memory.
3) The legitimacy of the differential equations. FEA works in solving problems that have geometries that make analytical solutions almost impossible. But if there are singularities in the mathematics, then there may be issues in the quality of results. I discuss this in some README files in SLFCEM for the point charge problem:
The mesh "mono7" is a solid disk mesh that greatly increases the discretization near the center where the point charge is located. This isn't quite enough to capture the 1/r behavior of the voltage or the 1/(r*r) behavior of the electric field.
Thanks. The physics problems that appeal to me the most are ones that have esthetically appealing visual results. The modes of waveguides produce some very interesting shapes when the electric field is treated as a displacement field.
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