We present a computationally efficient algorithmwhich combines the finite element method with Pad¿ approximation. Thecombination is used to solve the problem of transverse magnetic and transverseelectric scattering from homogeneous lossy dielectric cylinders over a continuousrange of the complex permittivity variable by requiring the finite elementsolution only at a single complex permittivity value. The proposed methodis based on (1) assuming a power series expansion for the unknown solutionvector, the excitation vector, and the system matrix, (2) substituting thisinto the system matrix equation, and (3) finding the recursion relation forthe solution vectors.