中文摘要：

基于镜像技术,通过在圆形孔内外镜像点布置单位正源或负源,重新构造了满足圆孔内边界上的两类边界（Dirichlet,Neumann）的基本解函数.进一步将重构的基本解函数应用于含圆孔有限多连域调和方程边界值问题的基本解方法的计算.研究表明,通过应用重构的基本解函数,无需考虑圆孔内边界,极大减少了输入数据,计算效率得到较大提高,最大限度提高数值解精度.

英文摘要：

Based on the image technology, the fundamental solutions were reconstructed for the multi-connected region, by assigning unit positive or negative sources at mirror positions inside and outside the circular hole. The rebuilt fundamental functions satisfy the two types of boundary conditions（Dirichlet, Neumann） on the circular hole boundary. The method of fundamental solution （MFS） with reconstructed fundamental functions was consequently introduced to solve the boundary problems of harmonic equations in the finite multi-connected region with a circular hole. It concluded that the numerical calculation with reconstructed fundamental solutions can avoid considering the inside hole boundary, greatly reduce input the data, improve the calculation efficiency, and maximize the accuracy of numerical solutions.