双互易边界元法域内自适应布点方法及布点位置对计算精度的影响

An adaptive domain node arrangement method in the domain of dual reciprocity boundary element method and the influence of the node location on the calculation accuracy

边界元法以积分方程理论为数学基础,可通过加权残余量法建立起积分方程的先进数值方法,是一种半数值半解析的方法,计算精度很高。但是传统的边界元法不能处理域内积分问题,双互易法的引入巧妙地将域内积分转化成边界上的积分,其中径向基函数(radial basis functions, RBF)起到了重大作用。但是数值算例表明径向基函数不稳定,阻碍了边界元法在工程实际中的应用。探讨了域内点的布置位置对计算精度的影响,并提出可让精度得到进一步提高的一种自适应布点方法,以较少的点达到较高的精度,并用算例进行验证。

Based on the theory of integral equation, the boundary element method(BEM) is an advanced numerical method of integral equation, which can be established by weighted residual method. It is a seminumerical and semi-analytical method with high calculation accuracy. The traditional BEM cannot deal with the problem of domain integral. The introduction of the dual reciprocity method can transform the domain integral into the integral on the boundary, in which the radial basis function(RBF) plays a significant role. However,numerical examples show that the radial basis function is unstable, which hinders the application of BEM in engineering practice. The main work of this paper is to discuss the influence of the position of the nodes in the domain on the calculation accuracy, and to propose an adaptive domain node arrangement method. Higher accuracy can be achieved with fewer nodes, which is verified by examples.