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逄泽慧,张耀明.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[J].计算力学学报,2020,37(1):108~112
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
Improved average source boundary node method for plane potential problems
投稿时间:2019-01-28  修订日期:2019-04-20
DOI:10.7511/jslx20190128001
中文关键词:  平面位势问题  平均源边界节点法  平均源技术  无网格法
英文关键词:plane potential problem  Average Source Boundary Node Method(ASBNM)  average source technology  meshless/meshfree method
基金项目:山东省自然科学基金(ZR2017MA021)资助项目.
作者单位E-mail
逄泽慧 山东理工大学 数学与统计学院, 淄博 255049  
张耀明 山东理工大学 数学与统计学院, 淄博 255049 zymfc@163.com 
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中文摘要:
      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。
英文摘要:
      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.
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