Finite element analysis of two-dimensional EM scattering via Padé approximation for complex permittivity

We present a computationally efficient algorithm which combines the finite element method with Padé approximation. The combination is used to solve the problem of transverse magnetic and transverse electric scattering from homogeneous lossy dielectric cylinders over a continuous range of the complex permittivity variable by requiring the finite element solution only at a single complex permittivity value. The proposed method is based on (1) assuming a power series expansion for the unknown solution vector, the excitation vector, and the system matrix, (2) substituting this into the system matrix equation, and (3) finding the recursion relation for the solution vectors.