A Multigrid Method for Helmholtz Transmission Eigenvalue Problems

被引：65
|
作者：
Ji, Xia [1 ]
Sun, Jiguang [2 ]
Xie, Hehu [1 ]
机构：
[1] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC,NCMIS, Beijing 100190, Peoples R China
[2] Michigan Technol Univ, Dept Math Sci, Houghton, MI 49931 USA
来源：
JOURNAL OF SCIENTIFIC COMPUTING | 2014年 / 60卷 / 02期
基金：
中国国家自然科学基金; 美国国家科学基金会;
关键词：
Transmission eigenvalue; Multigrid method; Finite element method; ITERATIVE METHODS;
D O I：
10.1007/s10915-013-9794-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we analyze the convergence of a finite element method for the computation of transmission eigenvalues and corresponding eigenfunctions. Based on the obtained error estimate results, we propose a multigrid method to solve the Helmholtz transmission eigenvalue problem. This new method needs only linear computational work. Numerical results are provided to validate the efficiency of the proposed method.
引用
收藏
页码：276 / 294
页数：19
相关论文
共 50 条
  • [1] A Multigrid Method for Helmholtz Transmission Eigenvalue Problems
    Xia Ji
    Jiguang Sun
    Hehu Xie
    Journal of Scientific Computing, 2014, 60 : 276 - 294
  • [2] A new multigrid finite element method for the transmission eigenvalue problems
    Han, Jiayu
    Yang, Yidu
    Bi, Hai
    APPLIED MATHEMATICS AND COMPUTATION, 2017, 292 : 96 - 106
  • [3] A full multigrid method for eigenvalue problems
    Chen, Hongtao
    Xie, Hehu
    Xu, Fei
    JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 322 : 747 - 759
  • [4] Adaptive multigrid method for quantum eigenvalue problems
    Xu, Fei
    Wang, Bingyi
    Luo, Fusheng
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2024, 436
  • [5] A full multigrid method for nonlinear eigenvalue problems
    JIA ShangHui
    XIE HeHu
    XIE ManTing
    XU Fei
    ScienceChina(Mathematics), 2016, 59 (10) : 2037 - 2048
  • [6] A full multigrid method for nonlinear eigenvalue problems
    Jia, ShangHui
    Xie, HeHu
    Xie, ManTing
    Xu, Fei
    SCIENCE CHINA-MATHEMATICS, 2016, 59 (10) : 2037 - 2048
  • [7] A full multigrid method for nonlinear eigenvalue problems
    ShangHui Jia
    HeHu Xie
    ManTing Xie
    Fei Xu
    Science China Mathematics, 2016, 59 : 2037 - 2048
  • [8] Local and Parallel Multigrid Method for Nonlinear Eigenvalue Problems
    Fei Xu
    Qiumei Huang
    Journal of Scientific Computing, 2020, 82
  • [9] Adaptive multigrid for Helmholtz problems
    Bartsch, G
    Wulf, C
    THEORETICAL AND COMPUTATIONAL ACOUSTICS 2001, 2002, : 535 - 544
  • [10] Adaptive multigrid for Helmholtz problems
    Bartsch, G
    Wulf, C
    JOURNAL OF COMPUTATIONAL ACOUSTICS, 2003, 11 (03) : 341 - 350
12345