Spectrally-accurate numerical method for acoustic scattering from doubly-periodic 3D multilayered media

TL;DR

This paper introduces a spectrally-accurate numerical method for simulating acoustic wave scattering in complex three-dimensional multilayered media with doubly-periodic structures, avoiding singular quadratures and Green's functions.

Contribution

It presents a novel periodizing scheme combined with the method of fundamental solutions that achieves high accuracy and robustness across all scattering parameters, including Wood anomalies.

Findings

Achieves 10-digit numerical accuracy in simulations.

Effectively computes reflection and transmission spectra.

Robustly handles all scattering parameters without singular quadratures.

Abstract

A periodizing scheme and the method of fundamental solutions are used to solve acoustic wave scattering from doubly-periodic three-dimensional multilayered media. A scattered wave in a unit cell is represented by the sum of the near and distant contribution. The near contribution uses the free-space Green's function and its eight immediate neighbors. The contribution from the distant sources is expressed using proxy source points over a sphere surrounding the unit cell and its neighbors. The Rayleigh-Bloch radiation condition is applied to the top and bottom layers. Extra unknowns produced by the periodizing scheme in the linear system are eliminated using a Schur complement. The proposed numerical method avoids using singular quadratures and the quasi-periodic Green's function or complicated lattice sum techniques. Therefore, the proposed scheme is robust at all scattering parameters including Wood anomalies. The algorithm is also applicable to electromagnetic problems by using the dyadic Green's function. Numerical examples with 10-digit accuracy are provided. Finally, reflection and transmission spectra are computed over a wide range of incident angles for device characterization.