Finite element analysis of scattering using coupled basis functions for elliptical boundaries

The formulation of a hybrid finite element method is presented for electromagnetic scattering by inhomogeneous dielectric/magnetic cylinders of arbitrary cross-section. In this method, an artificial elliptical boundary is employed to enclose the scatterer and divide the solution region into interior and exterior regions. The field in the interior region is discretised using the finite element method, and the field in the exterior region is represented by an eigenfunction expansion involving Mathieu functions. These fields are coupled at the elliptical boundary by enforcing field continuity conditions. To improve the efficiency of the method, coupled basis functions are developed for elliptical boundaries, which represent both the field and its normal derivative at the boundary with a common set of expansion coefficients. Numerical examples are given to demonstrate the efficiency and accuracy of the method