A Novel Mixed Spectral Method and Error Estimates for Maxwell Transmission Eigenvalue Problems

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2024-05-03 DOI:10.1137/23m1544830

Jing An, Waixiang Cao, Zhimin Zhang

{"title":"A Novel Mixed Spectral Method and Error Estimates for Maxwell Transmission Eigenvalue Problems","authors":"Jing An, Waixiang Cao, Zhimin Zhang","doi":"10.1137/23m1544830","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1039-1066, June 2024. <br/> Abstract. In this paper, a novel mixed spectral-Galerkin method is proposed and studied for a Maxwell transmission eigenvalue problem in a spherical domain. The method utilizes vector spherical harmonics to achieve dimension reduction. By introducing an auxiliary vector function, the original problem is rewritten as an equivalent fourth-order coupled linear eigensystem, which is further decomposed into a sequence of one-dimensional fourth-order decoupled transverse-electric (TE) and transverse-magnetic (TM) modes. Based on compact embedding theory and the spectral approximation property of compact operators, error estimates for both eigenvalue and eigenfunction approximations are established for the TE mode. For the TM mode, an efficient essential polar condition and a high-order polynomial approximation method are designed to cope with the singularity and complexity caused by the coupled boundary conditions. Numerical experiments are presented to demonstrate the efficiency and robustness of our algorithm.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"42 1","pages":""},"PeriodicalIF":2.8000,"publicationDate":"2024-05-03","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/10.1137/23m1544830","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 1039-1066, June 2024.
Abstract. In this paper, a novel mixed spectral-Galerkin method is proposed and studied for a Maxwell transmission eigenvalue problem in a spherical domain. The method utilizes vector spherical harmonics to achieve dimension reduction. By introducing an auxiliary vector function, the original problem is rewritten as an equivalent fourth-order coupled linear eigensystem, which is further decomposed into a sequence of one-dimensional fourth-order decoupled transverse-electric (TE) and transverse-magnetic (TM) modes. Based on compact embedding theory and the spectral approximation property of compact operators, error estimates for both eigenvalue and eigenfunction approximations are established for the TE mode. For the TM mode, an efficient essential polar condition and a high-order polynomial approximation method are designed to cope with the singularity and complexity caused by the coupled boundary conditions. Numerical experiments are presented to demonstrate the efficiency and robustness of our algorithm.

查看原文本刊更多论文

麦克斯韦传输特征值问题的新型混合谱法和误差估计值

SIAM 数值分析期刊》第 62 卷第 3 期第 1039-1066 页，2024 年 6 月。摘要本文针对球面域中的麦克斯韦传输特征值问题，提出并研究了一种新颖的混合谱-Galerkin 方法。该方法利用矢量球面谐波实现降维。通过引入辅助矢量函数，原始问题被改写为等效的四阶耦合线性特征系统，并进一步分解为一维四阶解耦横向电（TE）和横向磁（TM）模式序列。基于紧凑嵌入理论和紧凑算子的谱近似特性，建立了 TE 模式的特征值和特征函数近似的误差估计。对于 TM 模式，设计了一种高效的基本极性条件和一种高阶多项式近似方法，以应对耦合边界条件引起的奇异性和复杂性。数值实验证明了我们算法的效率和稳健性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.