声学传输问题的自适应有限元DtN法

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-05-12 DOI:10.1016/j.cam.2025.116725

Lei Lin, Junliang Lv, Jiahui Gao

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引用次数: 0

摘要

本文研究时谐声入射波在有界可穿透障碍物上的散射问题。通过引入Dirichlet-to-Neumann （DtN）算子，将该模型表述为声学传输边值问题。导出了截断DtN算子的有限元法的后验误差估计，其中后验误差估计由有限元逼近误差和DtN算子的截断误差组成。基于后验误差，设计了一种自适应有限元算法来求解声传输问题。数值实验验证了该方法的有效性和鲁棒性。

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An adaptive finite element DtN method for the acoustic transmission problem

In the present paper, we consider the scattering of a time-harmonic acoustic incident wave by the bounded penetrable obstacle. By introducing the Dirichlet-to-Neumann (DtN) operator, the model is formulated as a transmission boundary value problem of acoustics. An a posteriori error estimate is derived for the finite element method with the truncated DtN operator, where the a posteriori error estimate consists of the finite element approximation error and the truncation error of the DtN operator. Based on the a posteriori error, an adaptive finite element algorithm is designed for solving the acoustic transmission problem. Numerical experiments are also presented to demonstrate the effectiveness and robustness of our adaptive method.

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.