中文摘要：

将重构核粒子法和势问题的边界积分方程方法结合，提出了势问题的重构核粒子边界无单元法。推导了势问题的重构核粒子边界无单元法的公式，研究其数值积分方案，建立了重构核粒子边界无单元法的离散化边界积分方程，并推导了重构核粒子边界无单元法的内点位势的积分公式。重构核粒子法形成的形函数具有重构核函数的光滑性，且能再现多项式在插值点的精确值，所以该方法具有更高的精度。最后给出了数值算例，验证了所提方法的有效性和正确性。

英文摘要：

Reproducing kernel particle method （RKPM） shape functions in meshless （or mesh-free） methods. In this is one of the important methods to obtain the paper, combining the reproducing kernel particle method and boundary integral equations for two-dimensional potential problems, the reproducing kernel particle boundary element-free （RKP-BEF） method for two-dimensional potential problems is presented. The formulae of the RKP-BEF method for two-dimensional potential problems based on Poisson＇s equation are obtained. The discrete boundary integral equations of the RKP-BEF method are formed, and the corresponding numerical integral methods are discussed. The boundary integral equations of the RKP-BEF method for the potentials at interior points are obtained. The smoothness of the shape function of the RKPM is the same as that of the reproducing kernel function, and the values of polynomials at interpolating points can be exactly reconstructed, then the RKP-BEF method has higher precision. In comparison with other existing meshless boundary integral equation methods, such as boundary node method （BNM） and local boundary integral equation（LBIE） method, the RKP-BEF method is a direct numerical method, in which the basic unknown quantity is the real solution of the nodal variables, of meshless boundary integral equation methods. And the boundary conditions can be implemented directly. The numerical examples of 2-D potential problems are given for verifying the effectiveness and correctness of the method in this paper.