RPIM求解点源二维变分问题的最优形状参数

径向基点插值法( RPIM)作为一种高精度的无网格方法,其形函数采用与径向基函数结合的插值方法构造,边界条件可直接加载. 将RPIM用于点源二维变分问题的求解,介绍了RPIM的近似原理;推导了点源二维问题的RPIM总体矩阵表达式,简述了背景网格积分技术,研究了高斯点数目对RPIM计算精度的影响;最后通过数值试验得出了支持域无量纲尺寸α最优选择区间与RPIM形状参数最优值. 研究结果表明:RPIM求解点源二维变分问题具有较好的鲁棒性,α最优区间为1.0~1.2.

Optimal shape parameters of RPIM for resolving point source two-dimensional variational problem

Radial point interpolation method ( RPIM) is a kind of high precision meshfree method. As its shape function is constructed by interpolation method in combination with radial basis function, the boundary conditions can be directly loaded. This paper utilizes RPIM to the calculation of point source two-dimensional electric field. Firstly, the approximate principle of RPIM is introduced in detail and the discrete system matrix expression is deduced corresponding to point source two-dimensional variational problem. Secondly, background grid integral technology is briefly introduced and the influence of different number of gauss points on calculation accuracy of RPIM is discussed. Lastly, the optimal range of support domain dimensionless size and the shape parameter optimal value of RPIM are obtained through numerical experiments. Studies show that RPIM has robustness for solving point source two-dimensional variational problem, and the optimal α range is 1.0 to 1.2.