A Treffz's Method for the Solution of the Two-Dimensional Helmholtz Problem

• Main Author: 林柏樹
• Other Authors: 鍾弘光
• Format: Others
• Language: en_US
• Published: 1997
• Online Access: http://ndltd.ncl.edu.tw/handle/32169682953316360896

碩士 === 中原大學 === 土木工程學系 === 85 === 　　The main objective of this research is to use Trefftz method to solve two-dimensional Helmholtz equation. The complete solution of two-dimensional Helmholtz equation is caleld complete Trefftz function. It is a set of terms which are the solutions of two-dimensional Helmholtz equation. In this paper, it is assumed that the solutions of two-dimensinal Helmholtz equation can be represented by the summation of terms of Trefftz functions. The weighted coefficient of each Trefftz function has to be determined. The Trefftz boundary integral equation is derived to calculate the values of those coefficients. When using Trefftz boundary integral equation to solve Helmholtz problem, there is no singular integration problem. the traditional boundary integral method with Green's funcitons has numerical difficulties on its singular integration and hence, Trefftz boundary integral equaiton is more convenient. For the problems of high and irregular frequencies, the traditional boundary integral method is difficult to reach a unique result for numerical solution. the Trefftz boundary integral equation can overcome the difficulty. In this paper, the standard examples include radiative problem of two dimensional cylinder, and the radiative problem of box waveguide. The numerical results are compared with exact solutions, and to guarantee the correct results of Trefftz boundary integral equation and the weighted coefficients are plotted. At the same time, the results for high and irregular frequencies are calculated and compared with exact solutions. the multiple radiative-scattering problems are also discussed. Finally, the conclusions and suggestions are presented.