An adaptive finite element DtN method for the acoustic-elastic interaction problem in periodic structures

IF 2.1 3区数学 Q2 MATHEMATICS, APPLIED

Advances in Computational Mathematics Pub Date : 2025-08-14 DOI:10.1007/s10444-025-10253-9

Lei Lin, Junliang Lv

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引用次数: 0

Abstract

Consider a time-harmonic acoustic plane wave incident onto an elastic body with an unbounded periodic surface. The medium above the surface is supposed to be filled with a homogeneous compressible inviscid air/fluid of constant mass density, while the elastic body is assumed to be isotropic and linear. By introducing the Dirichlet-to-Neumann (DtN) operators for acoustic and elastic waves simultaneously, the model is formulated as an acoustic-elastic interaction problem in periodic structures. Based on a duality argument, an a posteriori error estimate is derived for the associated truncated finite element approximation. The a posteriori error estimate consists of the finite element approximation error and the truncation error of two different DtN operators, where the latter decays exponentially with respect to the truncation parameter. Based on the a posteriori error, an adaptive finite element algorithm is proposed for solving the acoustic-elastic interaction problem in periodic structures. Numerical experiments are presented to demonstrate the effectiveness of the proposed algorithm.

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周期结构声弹相互作用问题的自适应有限元DtN法

考虑入射到具有无界周期表面的弹性体上的时谐声平面波。假设表面以上的介质是均匀的、可压缩的、恒定质量密度的无粘空气/流体，而弹性体是各向同性的、线性的。通过同时引入声波和弹性波的Dirichlet-to-Neumann （DtN）算子，将该模型表述为周期结构中的声弹相互作用问题。基于对偶论证，导出了截断有限元近似的后验误差估计。后验误差估计由两种不同DtN算子的有限元逼近误差和截断误差组成，其中截断误差相对于截断参数呈指数衰减。基于后验误差，提出了求解周期结构声弹相互作用问题的自适应有限元算法。通过数值实验验证了该算法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Computational Mathematics 数学-应用数学

CiteScore

3.00

自引率

5.90%

发文量

审稿时长

3 months

期刊介绍： Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. The journal emphasizes three core areas: approximation theory and computational geometry; numerical analysis, modelling and simulation; imaging, signal processing and data analysis. This journal welcomes papers that are accessible to a broad audience in the mathematical sciences and that show either an advance in computational methodology or a novel scientific application area, or both. Methods papers should rely on rigorous analysis and/or convincing numerical studies.