首页> 外文期刊>Engineering analysis with boundary elements >Solving potential problems by a boundary-type meshless method-the boundary point method based on BIE
【24h】

Solving potential problems by a boundary-type meshless method-the boundary point method based on BIE

机译:边界型无网格法-基于BIE的边界点法求解潜在问题

获取原文
获取原文并翻译 | 示例

摘要

In this paper, a novel boundary-type meshless method, the boundary point method (BPM), is developed via an approximation procedure based on the idea of Young et al. [Novel meshless method for solving the potential problems with arbitrary domain. J Comput Phys 2005;209:290-321] and the boundary integral equations (BIE) for solving two- and three-dimensional potential problems. In the BPM, the boundary of the solution domain is discretized by unequally spaced boundary nodes, with each node having a territory (the point is usually located at the centre of the territory) where the field variables are defined. The BPM has both the merits of the boundary element method (BEM) and the method of fundamental solution (MFS), both of these methods use fundamental solutions which are the two-point functions determined by the source and the observation points only. In addition to the singular properties, the fundamental solutions have the feature that the greater the distance between the two points, the smaller the values of the fundamental solutions will be. In particular, the greater the distances, the smaller the variations of the fundamental solutions. By making use of this feature, most of the off-diagonal coefficients of the system matrix will be computed by one-point scheme in the BPM, which is similar to the one in the MFS. In the BPM, the 'moving elements' are introduced by organizing the relevant adjacent nodes tentatively, so that the source points are placed on the real boundary of the solution domain where the resulting weak singular, singular and hypersingular kernel functions of the diagonal coefficients of the system matrix can be evaluated readily by well-developed techniques that are available in the BEM. Thus difficulties encountered in the MFS are removed because of the coincidence of the two points. When the observation point is close to the source point, the integrals of kernel functions can be evaluated by Gauss quadrature over territories.rnIn this paper, the singular and hypersingular equations in the indirect and direct formulations of the BPM are presented corresponding to the relevant BIE for potential problems, where the indirect formulations can be considered as a special form of the MFS. Numerical examples demonstrate the accuracy of solutions of the proposed BPM for potential problems with mixed boundary conditions where good agreements with exact solutions are observed.
机译:在本文中,基于Young等人的思想,通过近似程序开发了一种新的边界类型无网格方法,边界点方法(BPM)。 [新颖的无网格方法,用于解决任意域的潜在问题。 J Comput Phys 2005; 209:290-321]和用于解决二维和三维潜在问题的边界积分方程(BIE)。在BPM中,解决方案域的边界由不等距的边界节点离散化,每个节点都有一个定义变量的区域(该点通常位于区域的中心)。 BPM具有边界元法(BEM)和基本解法(MFS)的优点,这两种方法都使用基本解,这是仅由源点和观察点确定的两点函数。除了奇异性质外,基本解还具有以下特征:两点之间的距离越大,基本解的值就越小。尤其是,距离越大,基本解的变化就越小。通过使用此功能,系统矩阵的大部分非对角线系数将通过BPM中的单点方案进行计算,这与MFS中的对角系数相似。在BPM中,通过暂时组织相关的相邻节点来引入“运动元素”,以便将源点放置在解域的实边界上,在该边界上,得到对角线系数的弱奇异,奇异和超奇异核函数。系统矩阵可以通过BEM中可用的发达技术轻松进行评估。由于这两点的重合,因此消除了MFS中遇到的困难。当观测点靠近源点时,可以通过在区域上进行高斯求积来评估核函数的积分。rn本文针对相应的BIE提出了BPM间接公式和直接公式中的奇异和超奇异方程对于潜在问题,可以将间接配方视为MFS的一种特殊形式。数值示例证明了对于混合边界条件下潜在问题的拟议BPM解决方案的准确性,在这种情况下可以观察到与精确解决方案的良好协议。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱:kefu@zhangqiaokeyan.com

京公网安备:11010802029741号 ICP备案号:京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有
  • 客服微信

  • 服务号