Xi-Min Xin

In this paper, we propose a finite element domain decomposition method with Robin-type transmission conditions at discontinuous subdomain interfaces. By definition, these discontinuous interfaces refer to impedance surfaces where electromagnetic fields exhibit discontinuities, which are common in applications of metamaterials/metasurfaces, frequency-selective surfaces, or thin dielectric layer approximation. Through a detailed convergence study, we propose an optimized set of parameters in the transmission condition (TC). The proposed TC provides convergence for both propagating and evanescent electromagnetic waves across subdomain interfaces and is valid for all resistivity values. Numerical experiments are supplied to validate our theoretical analysis, demonstrating the convergence and accuracy of our proposed work.

The discontinuous Galerkin (DG) based domain decomposition method has been proposed for analyzing complex electromagnetic scattering problems. For targets involving material regions, the electric and magnetic current combined field integral equation (JMCFIE) is often used. Since JMCFIE integrates first- and second-kind Fredholm integral equations, its accuracy is lower compared to the one using only first-kind integral equations. To address this issue, this letter studies a mixed discretization scheme (MDS) for the DG-JMCFIE, using Buffa-Christiansen (BC) functions and Rao-Wilton-Glisson (RWG) functions as testing functions. For the first time, we provide explicit formulations for BC functions on the boundaries of DG subdomains. We also introduce a novel interior penalty (IP) method to weakly enforce current continuity across subdomain boundaries within the BC-RWG mixed discretization scheme. Numerical experiments are conducted to evaluate the accuracy and convergence of our proposed method.

Nowadays, extensive research on electromagnetic metamaterials and metasurfaces has resulted in many innovative devices and systems. While the potentials of advanced materials and their applications are appealing, it is often difficult to model them accurately by computational methods due to the inherently multi-scale, complex structures involved. In this work, we propose a metamaterial Green’s function (MGF) approach combined with the geometry-aware domain decomposition method for modeling complex, heterogeneous materials. The MGF can be viewed as a first-principles multiscale modeling approach that rigorously encodes the information of the microscopic structures through the up-front offline calculation. The outcome results in quasi-sublinear algorithms in which the online computational complexity does not depend on the microscopic size of metamaterial structures. The results have the potential to make the full-wave analysis of metamaterials and metasurfaces orders of magnitude faster.

This paper proposes a new preconditioning technique based on a restricted additive Schwarz (RAS) approach to improve the efficiency of the discontinuous Galerkin surface integral equation method. The RAS preconditioning is implemented efficiently using an oct-tree structure derived from the multilevel fast multipole algorithm (MLFMA) and is constructed using near-field matrices associated with boxes at the finest level. Compared to existing domain decomposition preconditioning methods based on subdomain block matrices, the proposed RAS preconditioning significantly reduces computation time and memory requirements, while providing scalable convergence for iterative solutions. Numerical experiments are presented to demonstrate the performance of the proposed cost-effective preconditioning technique.