{"title":"Analysis and Application of an Orthogonal Nodal Basis on Triangles for Discontinuous Spectral Element Methods","authors":"Shaozhong Deng, Wei Cai","doi":"10.1002/anac.200510007","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we propose and analyze an orthogonal non-polynomial nodal basis on triangles for discontinuous spectral element methods (DSEMs) for solving Maxwell's equations. It is based on the standard tensor product of the Lagrange interpolation polynomials and a “collapsing” mapping between the standard square and the standard triangle. The basis produces diagonal mass matrices for the DSEMs and is easy to implement. Numerical results for electromagnetic scattering in heterogeneous media are provided to demonstrate the exponential convergence of the proposed basis, and its application to the simulation of optical coupling by whispering gallery modes between two microcylinders is presented as well. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)</p>","PeriodicalId":100108,"journal":{"name":"Applied Numerical Analysis & Computational Mathematics","volume":"2 3","pages":"326-345"},"PeriodicalIF":0.0000,"publicationDate":"2005-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/anac.200510007","citationCount":"15","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Numerical Analysis & Computational Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/anac.200510007","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 15
Abstract
In this paper, we propose and analyze an orthogonal non-polynomial nodal basis on triangles for discontinuous spectral element methods (DSEMs) for solving Maxwell's equations. It is based on the standard tensor product of the Lagrange interpolation polynomials and a “collapsing” mapping between the standard square and the standard triangle. The basis produces diagonal mass matrices for the DSEMs and is easy to implement. Numerical results for electromagnetic scattering in heterogeneous media are provided to demonstrate the exponential convergence of the proposed basis, and its application to the simulation of optical coupling by whispering gallery modes between two microcylinders is presented as well. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
不连续谱元法中三角形正交节点基的分析与应用
本文提出并分析了求解麦克斯韦方程组的不连续谱元法在三角形上的正交非多项式节点基。它是基于拉格朗日插值多项式的标准张量积和标准正方形和标准三角形之间的“坍缩”映射。该基为DSEMs生成对角质量矩阵，易于实现。本文给出了非均质介质中电磁散射的数值计算结果，证明了该方法的指数收敛性，并将其应用于两个微柱间低语通道模式光耦合的模拟。(©2005 WILEY-VCH Verlag GmbH &KGaA公司，Weinheim)
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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