A version of the Characteristic Basis Finite Element Method (CBFEM) by utilizing Physical Optics for large-scale electromagnetic problems

Abstract

During the last few years, the Characteristic Basis Function Method (CBFM) has been introduced to solve large-scale electromagnetic problems. The CBFM is a non-iterative domain decomposition approach that employs characteristic basis functions (CBFs), called the high-level physics-based basis functions, to represent the fields inside each sub-domain. This technique was first introduced to solve time-harmonic electromagnetic problems in the context of the Method of Moments (MoM) [1]. Quite recently, the CBFM procedure has been utilized for the first time in the Finite Element Method (FEM), and has been named the “Characteristic Basis Finite Element Method (CBFEM)” [2–4]. This method, which is different from the previous MoM-based CBFM, has been used in both the quasi-static [2] and the time-harmonic regimes [3–4], by generating the CBFs via point charges and dipole-type sources, respectively. Two major features of the CBFEM are: (i) it leads to a reduced-matrix that can be handled by using direct—as opposed to iterative—solvers; and (ii) its parallelizable nature can be taken advantage of to reduce the overall computation time. The basic steps of the CBFEM algorithm are summarized as follows: (i) Divide the computational domain into a number of subdomains; (ii) Generate the CBFs that are tailored to each individual subdomain; (iii) Express the unknowns as a weighted sum of CBFs; (iv) Transform the original matrix into a smaller one (called reduced-matrix) by using the Galerkin procedure, which uses the CBFs as both basis and testing functions; (v) Solve the reduced matrix for the weight coefficients, and substitute the coefficients into the series expressions to find the unknowns inside the entire computational domain.