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FEA vs BEM

Posted by EGeddes on January 28, 2006 at 07:12:59:
First let me ask you a question which will lead into the BEM description.
How do you terminate the FEA model? Obviously you don't take the mesh to infinity. So where does it end and what are the boundary conditions there?
Depending on how you terminated the FEA model there can be a lot of errors. You can look up a complete description of this problem, and its solution in a paper I did in the AES in about 1985.
BEM meshs only the exterior boundary of the problem. Using Green's theorem one can transcribe the wave equation in three dimensions into an integral at the bounding surface of that space, i.e. two dimensions. Now for radiation problems this is ideal since the integral of the boundary at infinity is zero - has to be. So this leaves an integral only over the actual radiating surfaces. Rayleighs equation is a special case of BEM where the radiating surface is flat and finite.
So for an axi-symmetric problem, like yours, one would only have to mesh a line representing the horn contour, but then some form of enclosure would have to be assumed and meshed. The order of the BEM is always one dimension lower than that of the same FEA problem so it should be faster, but, unlike FEA which has a banded matrix structure, BEM is full. So it has a smaller but full matrix to FEA's larger but banded matrix. In essence the run times are about the same.
There is one catch. The BEM equations go singular at any internal resonance and so the equations must be suplimented by an additional equation for each resonance. There are some very nice BEM programs available (let me know if you are interested) and for a time the Navy gave away their BEM source code - in FORTRAN. I still have a copy, just as I have a source code copy of an old FEA program.

Earl Geddes