Moving Trefftz method for the Helmholtz equation

• Main Authors: Fu-Sheng Deng, 鄧福勝
• Other Authors: W. Yeih
• Format: Others
• Language: zh-TW
• Published: 2001
• Online Access: http://ndltd.ncl.edu.tw/handle/55116416887795992165

碩士 === 國立海洋大學 === 河海工程學系 === 89 === In this thesis, the moving Trefftz methods are derived to deal with the eigenproblem of the Helmholtz equation. Unlike the conventional Trefftz method having only one origin, the moving Trefftz method allows many origins in its configuration. Due to this property, the moving Trefftz method is more flexible than the conventional one especially when a multiply connected domain with holes more than one is considered. Since only zeroth order Bessel and/or Neumann functions are adopted as the base functions, in order to have enough bases in the moving Trefftz method one should move the origins to construct enough constraint equations. Although the location of origins are movable, it is proved that every bases of this configuration is independent of others, and the current approach is equivalent to the conventional Trefftz method by equivalency of bases. Furthermore, it is proved that the indirect moving Trefftz method proposed in this work is equivalent to the direct moving Trefftz method. There exists no spurious eigensolution in both direct moving and indirect moving Trefftz methods. However, the moving Trefftz methods suffer from the ill-posed behaviors like other regular BEM formulations do. We adopt the Tikhonov’s regularization technique and the generalized singular-value decomposition method to extract the polluted information out and have the true eigensolution. The numerical examples show that the current approach is an acceptable method.