Some thoughts on the relationship between finite elements, finite differences and TLM

Peter Silvester (see Finite Elements for Electrical Engineers, Cambridge University Press, Cambridge, Third Edition, 1996) has pioneered the application of finite element methods in electromagnetics. While this has been a strong focus of his work, he always placed considerable emphasis on the greater picture in order to avoid the inherent limitations of specialization and to preserve a clear view of the larger context of field modeling. This paper demonstrates in simple terms that finite element, finite difference and transmission line matrix (TLM) models, approaches so very different at first glance, can lead to identical discrete algorithms for field computation under certain conditions.