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:
http://slfcem.sourceforge.net/thanks.html
if there are no objections.
You can get the software at:
http://slfcem.sourceforge.net /
San Le
slffea.com

On Jan 26, 5:18 pm, spam snipped-for-privacy@yahoo.com wrote:

------------------------
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
http://www.newelectromagnetism.com /
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.
San Le
http://slfcem.sourceforge.net /
slffea.com

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