The transfinite element method for computing electromagnetic scattering from arbitrary lossy cylinders

A new numerical procedure called the transfinite element method is used to solve two-dimensional electromagnetic scattering problems involving lossy dielectric cylinders. In this procedure, the problem region is divided into two parts: A circular region
R_{i}
of finite extent that must enclose all scatterers and an exterior region
R_{e}
surrounding
R_{j}
that is homogeneous and unbounded. Within
R_{i}
finite element basis functions are used to approximate the electromagnetic field; in
R_{e}
the separation of variables technique is used to find a complete set of basis functions for the field. Requiring continuity along the circular boundary in a variational procedure then provides a matrix equation that is solved to compute the scattered field.