On the Convergence of Finite Element Domain Decomposition Methods for Discontinuous Subdomain Interfaces

In this communication, we propose a finite element domain decomposition method (FE-DDM) with Robin-type transmission conditions (TCs) at discontinuous subdomain interfaces. By definition, these discontinuous interfaces refer to impedance surfaces where electromagnetic (EM) 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 TC. The proposed TC provides convergence for both propagating and evanescent EM 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.