An Adaptive Finite Element DtN Method for the Open Cavity Scattering Problems (CSIAM Transactions on Applied Mathematics, 2020)
Consider the scattering of a time-harmonic electromagnetic plane wave byan open cavity which is embedded in a perfectly electrically conducting infinite groundplane. This paper concerns the numerical solutions of the open cavity scattering problems in both transverse magnetic and transverse electric polarizations. Based on theDirichlet-to-Neumann (DtN) map for each polarization, a transparent boundary condition is imposed to reduce the scattering problem equivalently into a boundary valueproblem in a bounded domain. An a posteriori error estimate based adaptive finiteelement 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 decayexponentially with respect to the truncation parameter. Numerical experiments arepresented for both polarizations to illustrate the competitive behavior of the adaptivemethod.