Solution of large scattering problems using a multilevel scheme in the context of Characteristic Basis Finite Element Method

Abstract

The Characteristic Basis Finite Element Method (CBFEM) [1–3] is a new descendant of the Characteristic Basis Function Method (CBFM), which is a non-iterative domain decomposition approach for solving large-scale electromagnetic problems by using characteristic basis functions (CBFs). The CBFM was originally introduced in the context of Method of Moments [4], but has rapidly evolved, with appropriate modifications, into a general-purpose approach that is also applicable to Finite Element Method (FEM). Some of the features that are common to all of the CBFM-based approaches are: (i) utilization of high-level physics-based basis functions — called CBFs — to represent the fields inside each sub-domain; (ii) reduced-matrix that can be handled by using direct solvers; (iii) parallelization to reduce the overall CPU time and memory. The basic steps of the CBFEM algorithm are as follows: (i) computational domain is divided into a number of sub-domains; (ii) CBFs are generated for each sub-domain; (iii) unknowns are expressed as a weighted sum of CBFs; (iv) original matrix is transformed into a reduced-matrix by using the Galerkin procedure, which uses the CBFs as both basis and testing functions; (v) reduced matrix is solved for the weight coefficients, which are substituted into the series expressions to solve for the unknowns in the entire computational domain.