Characteristic Basis Function Method (CBFM)—An Iteration-free Domain Decomposition Approach in Computational Electromagnetics

Abstract

In this paper we review a novel Domain Decomposition (DD) approach, called the Characteristic Basis Function Method (CBFM), which tackles large-scale electromagnetic problems by generalizing the concept of principle of localization that forms the cornerstone of asymptotic methods. The paper shows that the problem of having to deal with large matrices that arise in the conventional formulation of large problems with the Method of Moments (MoM) can be obviated, by dividing the original large problem into a number of smaller sub-problems that are more manageable to handle. However, unlike the conventional DD approaches that typically rely upon iteration algorithms to account for the inter-coupling between the subdomains, the CBFM tackles the problem with direct solvers instead. It is possible to do this in the context of CBFM, because it reduces the original large system matrix into one whose size is orders of magnitude smaller, and is appropriately called the “reduced matrix.” Furthermore, an important salutary feature of CBFM is that the algorithm is naturally parallelizable, an attribute that distinguishes it from many other CEM solvers, and makes it well suited for parallel platforms that have become ubiquitous in recent years. This, in turn, enables us to take advantage of the power of these platforms and to solve, numerically efficiently, large problems that were well beyond our reach in the past. The paper also shows that the basic concepts of CBFM are quite general, and they not only apply to MoM, but can also be tailored for both FEM and FDTD. Index Terms─ Characteristic Basis Function Method (CBFM), Domain Decomposition, Method of Moments (MoM), Finite element Method (FEM), Finite Difference Time Domain (FDTD).