A fast direct solver for two dimensional quasi-periodic multilayered media scattering problems, Part II

TL;DR

This paper introduces an improved fast direct solver for 2D quasi-periodic multilayered media scattering problems, with linear scaling in discretization points and layers, enhancing efficiency for complex multilayer configurations.

Contribution

It presents a new solver with linear computational cost in both discretization points and layers, improving upon previous methods for multilayered media scattering problems.

Findings

Linear scaling with respect to discretization points

Enhanced efficiency for multiple incident angles

Numerical results confirm improved performance

Abstract

This manuscript is the second in a series presenting fast direct solution techniques for solving two-dimensional wave scattering problems from quasi-periodic multilayered structures. The fast direct solvers presented in the series are for the linear system that results from the discretization of a robust integral formulation. The fast direct solver presented in this manuscript has a computational cost that scales linearly with respect to the number of discretization points on the interfaces and the number of layers. The latter is an improvement over the previous solver and makes the new solver more efficient especially for problems involving multiple incident angles and changes to the layered media. Numerical results illustrate the improved performance of the new solver over the previous one.