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arXiv · 2512.12414

A boundary integral equation method for wave scattering in periodic structures via the Floquet-Bloch transform

Wangtao Lu·Kuanrong Shen·Ruming Zhang
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Abstract

This paper is concerned with the problem of an acoustic wave scattering in a locally perturbed periodic structure. As the total wavefield is non-quasi-periodic, effective truncation techniques are pursued for high-accuracy numerical solvers. We adopt the Green's function for the background periodic structure to construct a boundary integral equation (BIE) on an artificial curve enclosing the perturbation. It serves as a transparent boundary condition (TBC) to truncate the unbounded domain. We develop efficient algorithms to compute such background Green's functions based on the Floquet-Bloch transform and its inverse. Spectrally accurate quadrature rules are developed to discretize the BIE-based TBC. Effective algorithms based on leap and pullback procedures are further developed to compute the total wavefield everywhere in the structure. A number of numerical experiments are carried out to illustrate the efficiency and accuracy of the new solver. They exhibit that our method for the non-quasi-periodic problem has a time complexity that is even comparable to that of a single quasi-periodic problem.

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Wangtao Lu, Kuanrong Shen, Ruming Zhang. 2025-12-13. A boundary integral equation method for wave scattering in periodic structures via the Floquet-Bloch transform. https://arxiv.org/abs/2512.12414

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