Introduction
Omega3P is a parallel finite-element electrogmagnetic code for high-fidelity modeling of cavities. It calculates the resonant frequencies and other rf parameters of a cavity, as well as damping effects due to external couplings. It uses Nedelec-type hierarchical vector basis up to 6th order with quadratic (10-points) tetrahedral elements for improved solution accuracy.
Mathematical Modeling
Maxwell's equations in the frequency domain for a perfectly conducting cavity can be written as the following PDE,
\begin
\nabla \times \left(\frac
\nabla \times \vec
\right) - k^2 \epsilon \vec
& = 0 & on \quad \Omega
\vec
\times \vec
& = 0 & on \quad \Gamma_
\vec
\times \left( \frac
\nabla \times \vec
\right) & = 0 & on \quad \Gamma_
\end
We use Neelec-type vector basis functions to descretize the electric field
[\vec
=\sum_i x_i \vec
_i]
and obtain the following generalized eigenvalue problem:
\begin
& = k^2
& where
_
& = \int_
\left( \nabla \times \vec
_i \right) \cdot \left( \nabla \times \vec
_j \right) \ d\Omega &
\end