An isogeometric boundary element method for three-dimensional doubly-periodic layered structures in electromagnetics

TL;DR

This paper introduces an isogeometric boundary element method tailored for three-dimensional doubly-periodic layered structures in electromagnetics, enabling accurate simulation of complex plasmonic phenomena.

Contribution

It develops a novel IGBEM framework with B-spline based surface construction and vector basis functions adapted for periodic multilayered structures.

Findings

Successfully solved numerical examples demonstrating method effectiveness.

Proved applicability to plasmonic simulations.

Achieved accurate electromagnetic scattering analysis.

Abstract

This paper proposes an isogeometric boundary element method (IGBEM) to solve the electromagnetic scattering problems for three-dimensional doubly-periodic multi-layered structures. The main concerns are the constructions of (i) an open surface (between two layers) and (ii) a vector basis function with using the B-spline functions. Regarding (i), we considered an algorithm to generate a doubly-periodic open surface with the tensor product of the B-spline functions of any degree. Regarding (ii), we employed the vector basis function based on the B-spline functions, which was proposed by Buffa et al. (2010), and adapted it to the underlying periodic problems so that it can satisfy the quasi-periodic condition on the boundary of an open surface. The proposed IGBEM worked for solving some numerical examples satisfactorily and proved the applicability to plasmonic simulations.