改进的平均源边界节点法模拟平面位势问题

Improved average source boundary node method for plane potential problems

平均源边界节点法ASBNM是一种最近提出的边界型无网格法。该方法仅使用边界节点不涉及任何单元和积分的概念,具有方法简单和程序设计容易等特点。但是,对于依赖于边界积分方程的边界型无网格法,关键问题是如何准确高效地估计影响矩阵的对角元。本文提出直接计算影响矩阵对角元的方法,是已有ASBNM法的改进,将对角元的计算转化为一个纯几何问题,因此适用于任何二维边值问题。数值算例证明了本文方法的有效性和准确性。

Average Source Boundary Node Method(ASBNM)is a recently proposed boundary-type meshless method.This method only uses the boundary nodes in the implementation and does not involve any element and integration notion,which is efficient,accurate,easy to implement and truly meshless.It is worth noting that for boundary-type meshless methods depending on boundary integral equations,regardless of their forms,a crucial but difficult issue is to estimate the diagonal elements of influence matrices accurately and efficiently.In this study,based on,a new scheme for directly calculating the diagonal elements of the influence matrices is proposed by the average source technique,which is an important improvement of the existing ASBNM.The new scheme transforms the calculation of diagonal elements into a purely geometric problem with respect to the boundary of solution domain.Therefore,it can be extended to any two-dimensional boundary value problems,such as elasticity problems,Stokes problems,etc.The numerical examples show the accuracy,convergence and computational efficiency of the proposed method.