一维周期介质中瞬态波的色散、界面和源点均质化模型

IF 1.9 3区 数学 Q2 Mathematics
Rémi Cornaggia, B. Lombard
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引用次数: 1

摘要

提出了一维微结构介质中线性波的均匀化模型。它结合了二阶渐近均匀化(以解释色散)和界面校正(用于从均匀介质传输或向均匀介质传输)。证明了二阶有效系数的新界,保证了均匀化模型在任何微观结构下的适定性。在类比已有的富连续体的基础上,将演化方程重新表述为一个色散双曲系统。通过时域数值模拟验证了该模型的有效性。对狄拉克源项进行了扩展。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A homogenized model accounting for dispersion, interfaces and source points for transient waves in 1D periodic media
A homogenized model is proposed for linear waves in 1D microstructured media. It combines second-order asymptotic homogenization (to account for dispersion) and interface correctors (for transmission from or towards homogeneous media). A new bound on a second-order effective coefficient is proven, ensuring well-posedness of the homogenized model whatever the microstructure. Based on an analogy with existing enriched continua, the evolution equations are reformulated as a dispersive hyperbolic system. The efficiency of the model is illustrated via time-domain numerical simulations. An extension to Dirac source terms is also proposed.
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来源期刊
CiteScore
2.70
自引率
5.30%
发文量
27
审稿时长
6-12 weeks
期刊介绍: M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.
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