A boundary integral equation method for wave scattering in periodic structures via the Floquet-Bloch transform
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| Format: | Preprint |
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2025
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| _version_ | 1866909960192917504 |
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| author | Lu, Wangtao Shen, Kuanrong Zhang, Ruming |
| author_facet | Lu, Wangtao Shen, Kuanrong Zhang, Ruming |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_12414 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A boundary integral equation method for wave scattering in periodic structures via the Floquet-Bloch transform Lu, Wangtao Shen, Kuanrong Zhang, Ruming Numerical Analysis Mathematical Physics 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. |
| title | A boundary integral equation method for wave scattering in periodic structures via the Floquet-Bloch transform |
| topic | Numerical Analysis Mathematical Physics |
| url | https://arxiv.org/abs/2512.12414 |