{"title":"A Finite Element Method for Hyperbolic Metamaterials with Applications for Hyperlens","authors":"Fuhao Liu, Wei Yang, Jichun Li","doi":"10.1137/23m1591207","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1420-1442, June 2024. <br/> 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.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"63 1","pages":""},"PeriodicalIF":2.8000,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Numerical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1591207","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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.
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