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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
投稿时间:2019-01-28  修订日期:2019-04-20
DOI:
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:Pane 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).
作者单位E-mail
逄泽慧 山东理工大学数学与统计学院 1297650940@qq.com 
张耀明 山东理工大学数学与统计学院 zymfc@163.com 
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中文摘要:
      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,程序设计容易等特点。需指出的是,对于依赖于边界积分方程的边界型无网格法,无论它们的形式是什么,一个关键但困难的问题是准确高效地估计影响矩阵的对角元。ASBNM法通过耦合规则化边界积分方程与平均源技术来估计影响矩阵的对角元。本提出直接计算影响矩阵对角元的方法,是已有ASBNM法的改进。该方法将对角元的计算问题转化为一个纯几何问题,不使用问题的规则化边界积分方程,因此它通用于任何二维边值问题,如弹性力学问题、Stokes问题等。数值算例表明了本文方法的准确性、收敛性和计算效率。
英文摘要:
      Abstract: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. It has the characteristics of simple method and easy programming. It should be pointed out 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. The ASBNM method estimates the diagonal elements of the influence matrices by coupling the regularized boundary integral equation with the average source technique. In this paper, 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. Other than the previous method which uses the regularized boundary integral equation of the considered problem, the new scheme transforms the calculation of diagonal elements into a pure geometric problem with respect to the boundary of solution domain. Therefore, so 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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