Robust and high‐order effective boundary conditions for perfectly conducting scatterers coated by a thin dielectric layer

A new approach is considered to construct effective boundary conditions for the solution of problems related to the scattering of electromagnetic waves by perfectly conducting cylinders coated by a thin dielectric shell. These boundary conditions aim to be both robust and of high order while remaining set in terms of surface differential operators involving at most second-order derivatives. Error estimates yield a theoretical basis for the use of these boundary conditions in practical computations. Some numerical experiments at frequencies beyond the range of validity of the usual impedance boundary conditions validate the efficiency of the approach.