The Applications of Hypersingular Meshless Method for Waveguide and Electromagnetic Wave Problems
Date Issued
2006
Date
2006
Author(s)
Wang, Yu-Fei
DOI
en-US
Abstract
In this thesis, a numerical algorithm for solving the ElectroMagnetic (EM) waveguide, EM resonator and electromagnetic wave scattering problems, involving 2-D and 3-D Helmholtz equation, is described and implemented. In the Method of Fundamental Solutions (MFS), seeding location of the source points on a fictitious boundary off-setting from the real boundary is necessary. However, in the proposed method the double-layer potential kernel functions are employed as the alternative radial basis functions (RBFs) in the conventional MFS which uses the fundamental solutions, seeding the source points on the real boundary, and the source points coincide with the boundary points, causing hypersingularity occurs. The purpose of above-mentioned statements is to derive the diagonal terms of the influence matrices by using a desingularization technique to regularize the singularity and hypersingularity of the Green’s functions. Applying the proposed method in which the meshless features of the MFS are maintained yields a reliable solution. Numerical simulations consist of the solutions of electromagnetic waveguide, resonator and 3-D electromagnetic wave scattering problems. Numerical examples are performed, and compared the present numerical results with the analytical solutions, results of conventional MFS and other numerical methods. The validity and accuracy of the proposed method are well demonstrated.
Subjects
無網格數值方法
徑向基底函數
基本解法
雙層勢能核函數
奇異性
超強奇異性
赫姆霍茲方程式
波導管
空腔共振器
散射
meshless method
radial basis functions
MFS
double layer potential
singularity
hypersingularity
Helmholtz equation
waveguide
scattering
Type
thesis
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