The use of transfinite elements in the method of moments applied to electromagnetic scattering by dielectric cylinders

We developed a volume surface integral equation (VSIE) based method of moments (MoM) employing transfinite elements which are a generalisation of all the elements appearing in the literature. Thanks to the transfinite elements it has been possible to study separately the influences of geometrical description and of the interpolation scheme in the MoM. This study has made now it possible to define the best elements to be used to solve the problem of the scattering of an electromagnetic wave by a dielectric cylinder in the case of high relative permittivity and large dimensions compared to the free-space wavelength of the incident wave. For the interpolation scheme it is clear that for computer memory problems the only interpolation which can be used for large bodies is the quadratic interpolation. Even with this interpolation, the number of unknowns remains a prohibitive problem of the MoM. For the geometrical description, it is sufficient for the stability to use quadrilateral elements and it is never necessary to use the more complex parabolic elements. The optimal choice is thus to use quadrilateral elements in combination with a quadratic interpolation which is equivalent to the subparametric elements encountered in the finite elements method.