A Local Coupling Multitrace Domain Decomposition Method for Electromagnetic Scattering From Multilayered Dielectric Objects

Abstract

In this paper, a local coupling multi-trace domain decomposition method (LCMT-DDM) based on surface integral equation (SIE) formulations is proposed to analyze electromagnetic scattering from multilayered dielectric objects. Different from the traditional SIE-DDM, where the interactions between sub-domains are accounted for using global radiation coupling, LCMT-DDM uses a local coupling scheme. The original multilayered object is decomposed into several independent domains, i.e. the exterior region (free space) and many homogeneous interior regions (dielectrics). The boundaries of sub-domains are all touching-faces, where only the Robin transmission conditions (RTCs) are enforced to ensure the field continuity. Hence, each sub-domain only couples with its neighboring regions, which makes the DDM system a highly sparse matrix especially when the number of sub-domains is large. In each sub-domain, the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE) for dielectrics are used as the governing equations. By imposing RTCs, well-conditioned equations are formed in each sub-domain without invoking the combined field integral equation (CFIE), which usually causes accuracy issues in dielectric modeling. Since the sub-domain matrices are diagonally dominant, the flexible generalized minimal residual (FGMRES) technique is used to accelerate the iterative solution of the whole DDM system. Moreover, an effective preconditioner that can be recursively constructed is proposed.

A Multitrace Surface Integral Equation Method for PEC/Dielectric Composite Objects

“…Let Γ ij , i, j ∈ {0, 1, 2} denote an interface between any two sub-domains Ω i and Ω j . On Γ 20 and Γ 02 , i.e., the interfaces between the sub-domains of free space and the dielectric body, RTCs described in [25] are used. On Γ 01 , Γ 10 , Γ 21 , and Γ 12 , i.e., the interfaces between the PEC sub-domain and the other two sub-domains, the following RTCs are enforced:…”

“…and K j [.] are the well-known SIE operators associated with the Stratton-Chu representation of the electromagnetic fields in Ω j (see for example [25]). Eqs.…”

“…is the inner product between and j m and m m represent the sets of RWG functions used to expand J m and M m , respectively. In (9), A 0 and A 2 are dense matrix blocks corresponding to the self-interactions in Ω 0 and Ω 2 , respectively, and their expressions can be found in [25]. Note that A 0 and A 2 are well-conditioned and diagonally-dominant just like the matrices arising from the discretization of CFIE.…”

“…In [25], a multi-trace domain-decomposition method (MT-DD-SIE) has been developed for analyzing scattering from composite objects consisting of multiple dielectric bodies (subdomains) (no PEC bodies are included). This method uses EFIE and MFIE as the governing equations (in unknown equivalent currents) in each sub-domain and these currents on the sub-domain surfaces are locally coupled via the Robin transmission conditions (RTC) [14], [21], [22].…”

“…In this work, these bottlenecks are eliminated by using a special form of RTCs as the only governing equations on the PEC bodies (sub-domains) within MT-DD-SIE [25]. Consequently, the matrix blocks pertinent to the PEC subdomains, which are similar to the sparse Gram matrix obtained from the discretization of the self-term in CFIE, are wellconditioned.…”