Application of Helmholtz Equation by the Boundary Element Method to the Waveguide and Scattering Propagation Problems

• Main Authors: Guo-Qing Chen, 陳國清
• Other Authors: Der-Liang Young
• Format: Others
• Language: zh-TW
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/20359331834154651626

碩士 === 國立臺灣大學 === 土木工程學研究所 === 90 === In this study, we use the Boundary Element Method to simulate the electromagnetic fields. The corresponding governing equations are the Maxwell’s equations. By separation of time variable, it can be transformed to the Helmholtz equation. This is the main equation of the discretization in the numerical simulation. After the discretization is determined, it would be applied in some electromagnetic problems. First, the rectangular waveguide with a metal insert will be considered. Because the rectangular waveguide with a metal insert is symmetric, we can consider only the quarter domain. And the known boundary conditions of the waveguide are all zero, we then will use the Singular Value Decomposition (SVD) to find out the non-trivial solution. Furthermore, the homogeneous scattering problems also are considered. When the incident plane wave passes through the perfect electrical conductor, it will produce a scattering field. And the perfect electrical conductor will be considered as a cylinder in 2D and sphere in 3D. Finally, comparisons of our numerical simulations with the analytical solutions and the other numerical methods are made, and we find that our numerical model is a good tool for the analysis in the field of electromagnetic wave propagation.