h2. 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. 

h2. Mathematical Modeling
Maxwell's equations in the frequency domain for a perfectly conducting cavity can be written as the following PDE,
{latex}
\begin{eqnarray*}
\nabla \times \left( \frac{1}{\mu} \nabla \times \vec{\mathbf E} \right) - k^2 \epsilon \vec{\mathbf E} & = 0 & on & \Omega \\
\end{eqnarray*}
{latex}