An Adaptive Finite Element PML Method for the Open Cavity Scattering Problems (Communications in Computational Physics, 2021)
Consider the electromagnetic scattering of a time-harmonic plane wave byan open cavity which is embedded in a perfectly electrically conducting infinite groundplane. This paper is concerned with the numerical solutions of the transverse electricand magnetic polarizations of the open cavity scattering problems. In each polarization, the scattering problem is reduced equivalently into a boundary value problem ofthe two-dimensional Helmholtz equation in a bounded domain by using the transparent boundary condition (TBC). An a posteriori estimate based adaptive finite elementmethod with the perfectly matched layer (PML) technique is developed to solve thereduced problem. The estimate takes account of both the finite element approximationerror and the PML truncation error, where the latter is shown to decay exponentiallywith respect to the PML medium parameter and the thickness of the PML layer. Numerical experiments are presented and compared with the adaptive finite element TBCmethod for both polarizations to illustrate the competitive behavior of the proposedmethod.
Keywords: Electromagnetic cavity scattering; TM and TE polarizations; perfectly matched layer; adaptive finite element method; a posteriori error estimates.