双曲超材料有限元方法及其在超透镜中的应用

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2024-06-17 DOI:10.1137/23m1591207

Fuhao Liu, Wei Yang, Jichun Li

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引用次数: 0

摘要

SIAM 数值分析期刊》第 62 卷第 3 期第 1420-1442 页，2024 年 6 月。摘要本文首先推导了一个时变麦克斯韦方程模型，用于模拟各向异性色散介质和双曲超材料中的波传播。模型方程是通过使用 Drude-Lorentz 模型来近似计算介电常数和磁导率得到的。然后，我们开发了一种时域有限元方法，并证明了其离散稳定性和最佳误差估计。该数学模型和所提出的数值方法可用于设计不同频率范围内介质-金属多层超材料的有效双曲超透镜。本文给出了大量二维和三维数值结果，证明了许多二维和三维双曲超透镜在不同频率范围内的良好性能。这是第一篇在时域中求解双曲超材料的有限元论文。

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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A Finite Element Method for Hyperbolic Metamaterials with Applications for Hyperlens

SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1420-1442, June 2024.
Abstract. In this paper, we first derive a time-dependent Maxwell’s equation model for simulating wave propagation in anisotropic dispersive media and hyperbolic metamaterials. The modeling equations are obtained by using the Drude–Lorentz model to approximate both the permittivity and permeability. Then we develop a time-domain finite element method and prove its discrete stability and optimal error estimate. This mathematical model and the proposed numerical method can be used to design effective hyperbolic superlenses by the dielectric-metal multilayer metamaterials in different frequency ranges. Extensive two-dimensional (2D) and 3D numerical results are presented to demonstrate the good performance of many 2D and 3D hyperbolic superlenses in different frequency ranges. This is the first finite element paper on solving the hyperbolic metamaterials in a time domain.

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.