三维Laplace方程的虚边界配点求解法

Virtual Boundary Collocation Method for 3D Laplace Equation

针对三维Laplace方程的几种边值问题,采用基于单层位势和双层位势2种方式,利用分布在虚拟边界上的密度函数和矩密度函数,建立三维Laplace方程的虚边界元计算公式,并用常单元和等额配点法计算.该方法避免了传统边界元法中奇异积分的计算,采用较少的边界节点即可达到较高的精度.数值算例证明了此方法的有效性和可行性.

Based on the single and double layer potentials, this paper gives the virtual boundary integral equations of 3D Laplace equation for different boundary value problems 3D Laplace equation with the help of the density function and moment density on the virtual boundary. The virtual boundary collocation method （VBCM） is applied with constant elements on virtual boundary and equal collocation nodes on real boundary, which avoids the singular integral calculation of traditional boundary element method. A good accuracy can be obtained with less boundary nodes. Numerical examples demonstrate the efficiency and the feasibility of this method.