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

Abstract

The multi-trace domain-decomposition surface integral equation (MT-DD-SIE) originally developed to analyze electromagnetic scattering from dielectric composite objects is extended to efficiently account for perfect electrically conducting (PEC) bodies. This is achieved by adopting Robin transmission conditions (RTCs) to PEC surfaces. These PEC-RTCs, which are the only governing equations for a PEC body, are used to "couple" it to the dielectric bodies. Upon discretization, PEC-RTCs produce a well-conditioned matrix block and therefore does not negatively affect the convergence of the iterative solution of the MT-DD-SIE matrix equation. The resulting method is significantly faster and has a smaller memory footprint than the traditional globally-coupled contact-region-modeling method that uses the coupled electric field and Poggio-Miller-Chang-Harrington-Wu-Tsai SIEs in analyzing electromagnetic scattering from composite PEC/dielectric objects. This is demonstrated by numerical examples involving electrically large scatterers.

A Multi-trace Surface Integral Equation Solver to Analyze Electromagnetic Field Interactions on Graphene-based Devices

“…Then, RTCs in (2) are modified to account for RBCs in (1). This modification yields RRTCs that are expressed as In the each subdomain, RTCs (2) and RRTCs (3) are used to "connect" the electric and magnetic field SIEs that are used as the subdomain's governing equations [7], [8]. Using Rao-Wilton-Glisson (RWG) functions [11] to discretize the resulting coupled system of equations yields…”

“…In this work, a multi-trace (MT) SIE solver is proposed to efficiently simulate electromagnetic field interactions on graphene-based devices. The computation domain is decomposed into two subdomains: an exterior subdomain that represents the background medium where the device resides in and an interior domain that represents the device's dielectric substrate [7], [8]. RBCs are enforced on the graphene sheet that is located on the interface between these two subdomains.…”

A Multiresolution Domain Decomposition Preconditioner for the MoM Solution of Multiscale Complex Structures

“…Alternatively, algebraic preconditioners such as incomplete lower unitriangular upper triangular (ILU), sparse approximate inverse (SPAI), or block-Jacobi [14]- [18] also improve convergence considerably. In the case of large-scale problems including multi-scale features, Schwarz preconditioners based on the domain decomposition method (DDM) [4], [19]- [22] stand out for their significant improvement in convergence, also bringing additional advantages in handling such complex problems. These preconditioners can be categorized as algebraic preconditioners, since they estimate an inverse of the matrix system, and also as physic-based preconditioners, since they allow to separate the physics of the different subsystems that make up the whole problem to adequately solve each one using the method best tailored to their particular features.…”

A Multitrace Surface Integral Equation Solver to Simulate Graphene-Based Devices

“…In recent years, integral-equation domain-decomposition methods that make use of multitrace SIEs (MT-SIEs) and Robin transmission conditions (RTCs) have found widespread use in the electromagnetic simulation of a wide range of structures changing from penetrable objects to large cavities, composite objects, and so on [30]- [34].…”

“…Compared to the SIE solvers developed to simulate only graphene sheets [18], [19], [21], [22], [24], [25], the proposed MT-SIE solver accounts for the dielectric substrate. Furthermore, it inherits all advantages of the MT-SIE solvers developed to simulate composite objects [32]- [34]. It yields a matrix system that can be efficiently solved using an iterative solver even for electrically large devices and allows for higher flexibility in mesh generation for multilayered substrates.…”