FINITE ELEMENT APPROXIMATION OF THE MODIFIED MAXWELL'S STEKLOFF EIGENVALUES

被引：5
|
作者：
Gong, Bo [1 ]
Sun, Jiguang [2 ]
Wu, Xinming [3 ]
机构：
[1] Beijing Computat Sci Res Ctr, Beijing 100193, Peoples R China
[2] Michigan Technol Univ, Dept Math Sci, Houghton, MI 49931 USA
[3] Fudan Univ, Sch Math Sci, Shanghai Key Lab Contemporary Appl Math, Shanghai 200433, Peoples R China
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2021年 / 59卷 / 05期
基金：
国家重点研发计划; 中国博士后科学基金;
关键词：
Stekloff eigenvalue; Maxwell's equation; finite element method; tangential trace; INTEGRAL-EQUATION; REGULARITY; TRACES;
D O I：
10.1137/20M1328889
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The modified Maxwell's Stekloff eigenvalue problem arises recently from the inverse electromagnetic scattering theory for inhomogeneous media. This paper contains a rigorous analysis of both the eigenvalue problem and the associated source problem on Lipschitz polyhedra. A new finite element method is proposed to compute Stekloff eigenvalues. By applying the Babuska-Osborn theory, we prove an error estimate without additional regularity assumptions. Numerical results are presented for validation.
引用
收藏
页码：2430 / 2448
页数：19
相关论文
共 50 条
  • [1] FINITE ELEMENT METHODS FOR MAXWELL'S TRANSMISSION EIGENVALUES
    Monk, Peter
    Sun, Jiguang
    SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2012, 34 (03): : B247 - B264
  • [2] THE INCLUSION OF STEKLOFF EIGENVALUES BY BOUNDARY DATA APPROXIMATION
    ENNENBACH, R
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1994, 45 (03): : 399 - 413
  • [3] Non-conforming Crouzeix-Raviart element approximation for Stekloff eigenvalues in inverse scattering
    Yidu Yang
    Yu Zhang
    Hai Bi
    Advances in Computational Mathematics, 2020, 46
  • [4] Non-conforming Crouzeix-Raviart element approximation for Stekloff eigenvalues in inverse scattering
    Yang, Yidu
    Zhang, Yu
    Bi, Hai
    ADVANCES IN COMPUTATIONAL MATHEMATICS, 2020, 46 (06)
  • [5] A Mixed Finite Element Methods Approximation for the Maxwell's Equations in Electromagnetics
    Anees, Asad
    Angermann, Lutz
    2016 IEEE/ACES INTERNATIONAL CONFERENCE ON WIRELESS INFORMATION TECHNOLOGY AND SYSTEMS (ICWITS) AND APPLIED COMPUTATIONAL ELECTROMAGNETICS (ACES), 2016,
  • [6] Superconvergent recovery of edge finite element approximation for Maxwell's equations
    Wu, Chao
    Huang, Yunqing
    Yi, Nianyu
    Yuan, Jinyun
    COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2020, 371
  • [7] Some remarks on finite element approximation of multiple eigenvalues
    Boffi, Daniele
    Gastaldi, Lucia
    APPLIED NUMERICAL MATHEMATICS, 2014, 79 : 18 - 28
  • [8] Error Analysis for the Finite Element Approximation of Transmission Eigenvalues
    Cakoni, Fioralba
    Monk, Peter
    Sun, Jiguang
    COMPUTATIONAL METHODS IN APPLIED MATHEMATICS, 2014, 14 (04) : 419 - 427
  • [9] Nonconforming Finite Element Approximation of Time-Dependent Maxwell's Equations in Debye Medium
    Shi, Dongyang
    Yao, Changhui
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2014, 30 (05) : 1654 - 1673
  • [10] FINITE ELEMENT-GALERKIN APPROXIMATION OF THE EIGENVALUES AND EIGENVECTORS OF SELFADJOINT PROBLEMS
    BABUSKA, I
    OSBORN, JE
    MATHEMATICS OF COMPUTATION, 1989, 52 (186) : 275 - 297
12345