This paper introduces a novel boundary integral equation (BIE) method for the numerical solution of problems of planewave scattering by periodic line arrays of two-dimensional penetrable obstacles. Our approach is built upon a direct BIE formulation that leverages the simplicity of the free-space Green function but in turn entails evaluation of integrals over the unit-cell boundaries. Such integrals are here treated via the window Green function method. The windowing approximation together with a finite-rank operator correction-used to properly impose the Rayleigh radiation condition-yield a robust second-kind BIE that produces super-algebraically convergent solutions throughout the spectrum, including at the challenging Rayleigh-Wood anomalies. The corrected windowed BIE can be discretized by means of off-theshelf Nyström and boundary element methods, and it leads to linear systems suitable for iterative linear-algebra solvers as well as standard fast matrix-vector product algorithms. A variety of numerical examples demonstrate the accuracy and robustness of the proposed methodology.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.