Huygens' surface excitation for the finite element method applied to Maxwell's equations – A construction based on Nitsche's method

Abstract

We present a Huygens' surface for the finite element method applied to Maxwell's equations, where the equivalent electric and magnetic surface currents are incorporated in the weak form by means of Nitsche's method. The proposed method preserves the reciprocity of Maxwell's equations and it allows for the computation of the total field inside the Huygens' surface, whereas on its outside only the scattered field is computed. The equivalent magnetic surface current at the Huygens' surface requires a double representation of the discontinuous tangential component of the electric field and we demonstrate that it can be efficiently combined with a previously presented higher-order brick-tetrahedron hybridization. Also, it is demonstrated that the near-to-far-field transformation can be evaluated in an accurate manner if collocated with the Huygens' surface, which allows for a compact computational domain and a reduction in the required computational resources. The proposed Huygens' surface is tested on two scattering problems with perfect electric conductor scatterers: (i) a sphere that demonstrates second-order convergence towards the analytical result for a piecewise linear approximation of the electric field; and (ii) a double ogive with two sharp tips which gives a computed monostatic radar cross section that compares well with measurements and computations in the open literature for both polarizations.