Vector finite element formulation for scattering from two-dimensional heterogeneous bodies

Abstract

A formulation is proposed for electromagnetic scattering from two-dimensional heterogeneous structures that illustrates the combination of the curl-curl form of the vector Helmholtz equation with a local radiation boundary condition (RBC). To eliminate spurious nonzero eigenvalues in the spectrum of the matrix operator, vector basis functions incorporating the Nedelec constraints are employed. Basis functions of linear and quadratic order are presented, and approximations made necessary by the use of the local RBC are discussed. Results obtained with linear-tangential/quadratic normal vector basis functions exhibit excellent agreement with exact solutions for layered circular cylinder geometries, and demonstrate that abrupt jump discontinuities in the normal field components at material interfaces can be accurately modeled. The vector 2D formulation illustrates the features necessary for a general three-dimensional implementation. >