A 2-D differential surface admittance operator for combined magnetic and dielectric contrast

Construction of the differential surface admittance operator with an extended Fokas method for electromagnetic scattering at polygonal objects with arbitrary material parameters

“…For a circular cylinder, the 2-D TM scattering of a plane wave can be modeled entirely analytically (see Appendix B of [11]). Therefore, this case serves as a reference to validate our novel method.…”

“…We wish to find a relationship between the known values of ϕ and the unknown values of ∂ϕ ∂n on ∂S. To this end, we introduce the Legendre polynomials as a set of basis functions and enforce (11) for a set of well-chosen λ-values, with a cardinality significantly higher than the number of unknown expansion coefficients P for ∂ϕ ∂n . In the end, this leads to an overdetermined system of equations.…”

“…with α = −ȷτ and where I p+ 1 /2 is the modified Bessel function of the first kind and order p + 1 /2. This enables us to write an approximate, discretized version of the global relation (11):…”

“…In this section, we provide some additional insight underlying the reasoning found in [22], to select an appropriate set of λ-values. We return to (11) and recognize the Fourier-like integrals, similar to those found when determining an angular Fourier series:…”

“…In its original formulation [5], the DSA method was only applicable to problems involving infinite circular and rectangular cylinders, without magnetic contrast. Since then, multiple extensions have been conceived: to determine the per-unit-of-length parameters of transmission lines including semiconducting materials [6], to triangular cross-sections [7], to threedimensional (3-D) cylinders and cuboids [8,9,10], and, very recently, to situations including combined dielectric and magnetic contrast [11]. The traditional approach to construct the DSA operator requires the Dirichlet eigenfunctions of the modeled structure, enforcing a restriction to canonical shapes, while the extension presented in [7] involves specific modifications to avoid a significant Gibbs effect, and requires a composition of multiple triangular parts to model arbitrary polygonal shapes.…”