Re: NEC-LIST: Boundary Element/Moment Method interaction matrix

On Feb 21, 1999 19:45:38 -0500, Alexandre Kampouris wrote:

> Do the Eigenvalues and Eigenvectors of the moment method interaction
> matrix have any physical meaning?

I assume you are referring to the eigenvectors of the interaction
matrix for a given frequency. These are current-distributions, with an
impedance as eigenvalue. They are closely related to the resonances:
if an eigenvalue is close to zero, then it can be shifted to exactly
zero by a small change in frequency, usually into the complex
plane. In that case it has become a true resonance, and the
eigenvector will not have changed a lot.

But strictly, the impedance-eigenvectors are NOT the resonances. Their
only meaning is: if you want to generate a surface current density
equal to an eigenvector, then the required driving force (E-field) is
also proportional to this eigenvector (times the eigenvalue, that is).

Do they have physical meaning? I think they do, but what is the
meaning of "physical meaning?" At least we know that these eigenvalues
must have a non-negative real part, so they are not completely
arbitrary. Also, there clearly are capacitive and inductive
eigenvectors. The latter ones usually have a closed current path.

They are also useful mathematically, for understanding the behavior of
numerical solvers. They can, for instance, be used for preconditioning
iterative solvers. If you combine that with a matrix-free approach,
you can solve problems with millions of elements.

Greetings,
Jos

  --
  Dr. Jozef R. Bergervoet Electromagnetism and EMC
  Philips Research Laboratories, Eindhoven, The Netherlands
  Building WS01 FAX: +31-40-2741114
  E-mail: bergervo_at_natlab.research.philips.com Phone: +31-40-2742403
Received on Tue Feb 23 1999 - 04:01:29 EST