Accurate Integration of 3D Constant Potential Boundary Element
Zhao Zhenfeng,Shi Xianzhang,Shen ChangYu
(National Engineering Research Center for Advanced Polymer Processing Technology ,Zhengzhou University, Zhengzhou 450002, China)

Abstract: In boundary element methods, the common integrals are divided into three types, regular, nearly singular and singular. A new method to get the acc urate integrals for 3D constant potential elements is proposed. With the aid of an assumed close surface, the certain potential field is taken into the boundary integration equations. The boundary integration is transformed to an assumed closed-surface. It is proved that the integral related to the potential term is equal to the area of a spherical triangle on a unit ball, which leads to a furthe rapplication to the integral of constant derivative term, thus the above menti oned three types of integration can be evaluated by a unified formula.
Keywords: boundary element method, 3D problem, constant potential，accurate integration, numerical integration.