径向点插值法局部形参的改进校准方法

The optimized calibration method for the local shape factors of radial point interpolation method

径向点插值法(Radial Point Interpolation Method,RPIM)中基函数形参、支持域大小和平均节点间距等因素直接影响算法的精度与计算效率,而过小形参会引起插值不稳定现象.针对此问题,提出一种基于局部形参校准法(Local Shape Factor Calibration Method,LSFCM)改进的形参优化算法,研究RPIM应用于电磁场问题中插值精度的影响因素,在不同形参、支持域大小和节点距离时的全局均方根插值误差曲线上,根据插值精度和计算效率灵活选择全局形参,简化形参设置与节点插值计算过程,提高计算效率.数值试验结果验证了所提方法的有效性.

In the radial point interpolation method （RPIM）, the shape factors such as the parameters of basis function, the support domain size and the average node distance directly affect the interpolation precision and computational efficiency, and the small shape parameter may lead to interpolation instability. In order to optimize parameter selection in RPIM, the algorithm based on the local shape factor calibration method（LSFCM）is proposed in the electromagnetic field problem. The global root mean square （RMS） in- terpolation error curve with different support domain size, node distance and different parameters can sim- plify the process of the shape parameter selection and node interpolation. The numerical results show the algorithm has improved the interpolation precision and computational efficiency.