Introducing the Scattering Element Method

In this paper we introduce the scattering element method (SEM) as a new generic denomination for a special type of electromagnetic field simulation. The SEM is characterized by the fact that every spatial element of the simulation domain is defined by a scattering matrix. Classically, this type of simulation method is known as transmission line matrix (TLM) method, where the unit cell is modeled with transmission lines. In this paper, we consider the two-dimensional case and present an alternative approach for defining/modelling the two-dimensional unit cell. This approach samples plane waves directly in the spatial domain. This wave sampling concept leads to a new unit cell, which is referred as wave sampling matrix (WSM). It turns out, that a SEM grid with this type of unit cell has improved dispersion properties compared to the classical cell. A grid with the WSM can be about 1.5 times coarser to obtain the same 1% phase velocity error. We show how the WSM is embedded in the classical grid. This demonstrates that the WSM cannot be derived with the classical transmission line approach and thus justifies the term SEM as a new generic denomination. Finally, the performance of WSM and “classical” frequency-domain TLM cells are compared in a numerical example determining the cutoff frequencies of a dielectric-loaded rectangular waveguide.