An Innovation of 3-D non-singular boundary integral equations

• Main Authors: Ting-Ying Chou, 周鼎贏
• Other Authors: Hwang, Wei- Shien
• Format: Others
• Language: en_US
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/46715525216160269347

碩士 === 國立臺灣大學 === 工程科學及海洋工程學研究所 === 93 === The main purpose of this thesis is to present an efficient analysis for singular integrals of three dimensional boundary integral equations. Numerical analysis is used for this discussion. In treating a high order element which has a singular integral, most three dimensional boundary element methods use adaptive integration or polar coordinates transformation. This thesis also includes an alternative method for calculating boundary integral equations. The method transforms the singular integral into a desingularized integral plus a linear integral which is along the boundary of the element; thus, it is more accurate and simple. Two kinds of eliminating the singularity are mentioned. One is for Green’s function in elements by using linear integrals; the other is for its normal derivative by the divergence theorem. The method is to add a term into the original singular kernel while it subtracts its analytical solution from the original equation. Since the singularity of Green’s function can be eliminated by such a mathematical technique, shape function does not need to be supposed while solving the unknown. The calculation can be directly applied to the real shape of the object by taking the integral points distributed on the object as nodes that satisfy boundary conditions. Hence, not only the calculation is significantly simplified but also singularity terms do not require special processing. Therefore, the numerical programming is much easier. Applications of numerical theoretic analysis on smooth and non-smooth boundary models will be proposed and discussed at the end.