[1]李订芳,谢 鹏.基于RBF和TSVD正则化求解泊松方程[J].江西师范大学学报(自然科学版),2017,(01):42-45.
 LI Dingfang,XIE Peng.The Gridless Method for Poisson’s Equation Based on RBF and TSVD[J].,2017,(01):42-45.
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基于RBF和TSVD正则化求解泊松方程()
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《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2017年01期
页码:
42-45
栏目:
出版日期:
2017-01-01

文章信息/Info

Title:
The Gridless Method for Poisson’s Equation Based on RBF and TSVD
作者:
李订芳谢 鹏
武汉大学数学与统计学院,湖北 武汉 430072
Author(s):
LI DingfangXIE Peng
1.School of Mathematics and Statistics,Wuhan University,Wuhan Hubei 430000,China
关键词:
TSVD正则化 径向基函数 泊松方程
Keywords:
TSVD regularization radial basis function Poisson’s equation
分类号:
O 175.3
文献标志码:
A
摘要:
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.
Abstract:
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.

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备注/Memo

备注/Memo:
收稿日期:2016-11-20基金项目:国家自然科学基金(61271337)资助项目.作者简介:李订芳(1966-),男,湖南平江人,教授,博士,博士生导师,主要从事计算数学最优化与正则化方面的研究.E-mail:dfli@whu.edu.cn
更新日期/Last Update: 1900-01-01