An Adaptive Finite Element DtN Method for the Open Cavity Scattering Problems

Abstract

Consider the scattering of a time-harmonic electromagnetic plane wave by an open cavity which is embedded in a perfectly electrically conducting infinite ground plane. This paper concerns the numerical solutions of the open cavity scattering problems in both transverse magnetic and transverse electric polarizations. Based on the Dirichlet-to-Neumann (DtN) map for each polarization, a transparent boundary condition is imposed to reduce the scattering problem equivalently into a boundary value problem in a bounded domain. An a posteriori error estimate based adaptive finite element DtN method is proposed. The estimate consists of the finite element approximation error and the truncation error of the DtN operator, which is shown to decay exponentially with respect to the truncation parameter. Numerical experiments are presented for both polarizations to illustrate the competitive behavior of the adaptive method.

An adaptive finite element PML method for the open cavity scattering problems

“…In this section, we present some numerical examples to demonstrate the performance of the adaptive finite element PML method. The method is validated and compared with the adaptive finite element method with the transparent boundary condition (TBC) which is proposed in [28]. In the following examples, the PML parameters are ρ = 3R, σ 0 = 20 and m = 2.…”

“…When the incident angle and the observation angle are the same, the RCS is called the backscatter RCS. The specific formulas can be found in [28] for the backscatter RCS on both polarized wave fields. 5.1.…”

“…We point out a closely related work [28], where an adaptive finite element method with transparent boundary condition (TBC) was developed for solving the open cavity scattering problems. Since the nonlocal TBC is directly used to truncate the open domain, it does not require a layer of artificially designed absorbing medium to enclose the domain of interest, which makes the TBC method different from the PML approach.…”

A fast algorithm for the electromagnetic scattering from a large rectangular cavity in three dimensions

“…0 is not an eigenvalue of the Helmholtz operator with Dirichlet boundary condition, the continuous Helmholtz problem admits a unique solution; for h small enough, as an approximate problem, the discrete Helmholtz problem can also be shown to have a unique solution [23], which implies that…”

An adaptive finite element DtN method for the three-dimensional acoustic scattering problem

“…Recently, an alternative adaptive finite element method was developed for solving the two-dimensional acoustic obstacle scattering problem [23] and the open cavity scattering problem [33], where the PML was replaced by the TBC to truncate the open domain. Since the TBC is exact, it can be imposed on the boundary which could be put as close as possible to the obstacle.…”