THE LEAST SQUARES TREFFTZ METHOD AND THE METHOD OF EXTERNAL SOURCE FOR THE EIGENFREQUENCIES OF WAVEGUIDES

被引:3
|
作者
Fang, Hui-Ming
Fan, Chia-Ming [1 ]
Liu, Yan-Cheng
Hsiao, Sung-Shan
机构
[1] Natl Taiwan Ocean Univ, Dept Haber & River Engn, Keelung, Taiwan
来源
JOURNAL OF MARINE SCIENCE AND TECHNOLOGY-TAIWAN | 2013年 / 21卷 / 06期
关键词
least squares Trefftz method; eigenfrequencies problem; Helmholtz equation; boundary-type meshless method; RADIAL BASIS FUNCTIONS; MESHLESS COLLOCATION METHOD; FUNDAMENTAL-SOLUTIONS; EIGENVALUE PROBLEMS; HELMHOLTZ-EQUATION; LAPLACE EQUATION; DOMAINS; EIGENPROBLEMS;
D O I
10.6119/JMST-013-0626-1
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
In this study, the least squares Trefftz method (LSTM) is adopted for analyzing the eigenfrequencies problems governed by homogeneous Helmholtz equations. The Trefftz method, one kind of boundary-type meshless collocation methods, does not need mesh generation and numerical quadrature. Since the system of linear algebraic equations obtained by Trefftz method is highly ill-conditioned, the least squares method is adopted to stabilize the numerical scheme in this study. In the eigenproblem, the response amplitudes from an external source are used to determine the resonant frequencies. By adding an external source, the homogeneous boundary condition becomes inhomogeneous. Then we can employ the LSTM to easily solve this problem. In this paper, the LSTM and the method of external source are used to solve this eigenfrequencies problems governed by Helmholtz equations. Several numerical examples are provided to verify the accuracy and the simplicity of the proposed numerical scheme.
引用
收藏
页码:703 / 710
页数:8
相关论文
共 50 条
  • [1] METHOD OF FUNDAMENTAL SOLUTIONS WITH EXTERNAL SOURCE FOR THE EIGENFREQUENCIES OF WAVEGUIDES
    Fan, Chia-Ming
    Young, Der-Liang
    Chu, Chia-Lin
    JOURNAL OF MARINE SCIENCE AND TECHNOLOGY-TAIWAN, 2009, 17 (03): : 164 - 172
  • [2] Solving the Eigenfrequencies Problem of Waveguides by Localized Method of Fundamental Solutions with External Source
    Sun, Ke
    Ding, Shuang
    Zhang, Junli
    Liu, Yan-Cheng
    MATHEMATICS, 2022, 10 (07)
  • [3] Effective condition number for weighted linear least squares problems and applications to the Trefftz method
    Wei, Yi-min
    Lu, Tzon-Tzer
    Huang, Hung-Tsai
    Li, Zi-Cai
    ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2012, 36 (01) : 53 - 62
  • [4] Least squares linear source approach in method of characteristics
    Liang, Liang
    Zhang, Qian
    Chen, Ying
    Song, Peitao
    Zhang, Zhijian
    Zhao, Qiang
    Wu, Hongchun
    Cao, Liangzhi
    ANNALS OF NUCLEAR ENERGY, 2020, 138
  • [5] Least Squares Method for Diffusion Source Localization in Complex Networks
    Lalou, Mohammed
    Kheddouci, Hamamache
    COMPLEX NETWORKS & THEIR APPLICATIONS V, 2017, 693 : 473 - 485
  • [6] A least squares method for identification of unknown groundwater pollution source
    He, Zhukun
    Zuo, Rui
    Zhang, Dan
    Ni, Pengcheng
    Han, Kexue
    Xue, Zhenkun
    Wang, Jinsheng
    Xu, Donghui
    HYDROLOGY RESEARCH, 2021, 52 (02): : 450 - 460
  • [7] LEAST-SQUARES METHOD FOR SOURCE SOUND SEPARATION.
    Nakamichi, Kohji
    Nomura, Yasuo
    Yanagida, Masuzo
    Kakusho, Osamu
    Technology Reports of Kansai University, 1985, (26): : 51 - 59
  • [8] CALCULATION OF DIELECTRIC WAVEGUIDES WITH A COMPLEX PROFILE BY THE LEAST-SQUARES METHOD.
    Voytovich, N.N.
    Radio engineering & electronic physics, 1979, 24 (05): : 120 - 122
  • [9] A SUCCESSIVE LEAST SQUARES METHOD FOR STRUCTURED TOTAL LEAST SQUARES
    Plamen Y.Yalamov
    JournalofComputationalMathematics, 2003, (04) : 463 - 472
  • [10] A property of the method of least squares
    Vernotte, P
    COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES, 1927, 185 : 1246 - 1247