Finite-element method--method of lines approach for the analysis of three-dimensional electromagnetic cavities

A hybrid approach incorporating the finite-element method (FEM) and the method of lines (MoL) that can efficiently solve three-dimensional (3-D) electromagnetic cavities containing complex geometrical/material features has been presented here. The proposed approach uses the FEM to model the regions with complex geometrical/material profiles, and adopts the MoL to efficiently analyse the homogeneous regions. Since the complex regions are modelled by the FEM, advantages associated with the FEM in simulating complex features are retained. Furthermore, due to the fact that 3-D discretisation of finite-element analysis is employed only in certain parts of the entire problem domain whereas other parts are handled by two-dimensional discretisation following the analysis of MoL, the number of unknowns to be computed in this method would be much fewer than that required by the conventional FEM (in which 3-D discretisation is adopted in the entire problem domain). Therefore it is efficient and appropriate for handling an electromagnetic problem with complex features. Several simple cavity problems are investigated to demonstrate the validity and efficiency of this 3-D FEM-MoL approach