Stable FEM-FDTD Hybrid Method for Maxwell's Equations
In this thesis edge elements are applied to solve several problems in computational electromagnetics. In particular, a hybrid scheme joining the Finite Element Method (FEM) and the Finite-Difference Time-Domain (FDTD) algorithm is developed, tested and exploited. The hybrid scheme combines the efficiency of FDTD with the ability of the FEM to model complex geometry. The hybrid scheme is rigorously proven to be stable up to the maximal FDTD time step without added dissipation and it is free from spurious solutions. The reflection from the FEM-FDTD interface is low. The hybrid scheme has been tested by computing the Radar Cross Section (RCS) for a Perfect Electric Conducting (PEC) sphere and the NASA almond. It has also been used for extensive parameter studies of patch antennas and transitions from a waveguide to a microstrip.
Finite Element Method
proof of stability