Analysis of electromagnetic scattering from an overfilled cavity in the ground plane

In this paper, we consider the scattering of the time-harmonic plane wave by a protruding cavity embedded in the PEC ground plane. An artificial boundary condition is introduced on a semicircle enclosing the cavity that couples the fields from the infinite exterior domain to those inside. Variational formulations for the TM and TE polarizations are derived and existence and uniqueness of weak solutions are established. Finite element error analysis is also performed. Numerical experiments demonstrate the efficiency and accuracy of the method.