基于RBF和TSVD正则化求解泊松方程
The Gridless Method for Poisson’s Equation Based on RBF and TSVD

针对泊松方程的数值解,提出了一种基于截断奇异值分解(TSVD)的正则化和径向基函数(RBF)的改进的无网格方法.由于通过RBF拟合方程所产生的系数矩阵经常是病态的,TSVD正则化方法可以改善RBF无网格方法而获得更精确的数值解,与传统的RBF方法相比能够获得更好的数值结果,而且通过选择恰当的径向基函数,也能够提高数值解的精度.
An improved gridless method based on radical basis function(RBF)for the numerical solution of Poisson’equation is proposed.Since the coefficient matrix generated by the RBF approximation is usually ill-conditioned,the truncated singular value decomposition(TSVD)regularization method is used to obtain a more accurate numerical solution.Compared to common RBF,better numerical results will be achieved.What’s more,the accuracy of numerical solution can be improved by choosing proper radial basis functions