Vector field approximation using radial basis functions

详细信息    查看全文

• 作者：Daniel A. Cervantes Cabrera^a ; Pedro Gonzá ; lez-Casanova^b ; Christian Gout^c ; ^{christian.gout@insa-rouen.fr} ; L. Hé ; ctor Juá ; rez^d ; L. Rafael Resé ; ndiz^d
• 关键词：Vector field approximation ; Radial basis functions ; Runge phenomenon
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2013
• 出版时间：1 March, 2013
• 年：2013
• 卷：240
• 期：Complete
• 页码：163-173
• 全文大小：289 K

文摘

In this article, we investigate the performance of RBF-PDE methods for approximating solenoidal fields. It is well known that global RBF collocation methods present a trade-off principle, which means that smoothness implies high convergence order plus ill-conditioning. On the other hand, local methods for solving this problem have recently appeared in the literature. In this paper, we perform a numerical investigation of the differences between RBF global and local methods, in order to investigate the possible advantage of using local methods for the approximation of vector fields. More precisely, we compare the local Hermite interpolation technique using inverse multiquadrics against the non-symmetric collocation method of Kansa.