Astable algorithm for divergence-free radial basis functions in the flat limit

JOURNAL OF COMPUTATIONAL PHYSICS

卷:417

Article

Drake, Kathryn P.¹  Wright, Grady B.¹ 

[1] Boise State Univ, Dept Math, 1910 Univ Dr, Boise, ID 83725 USA

关键词: Radial basis functions;    Shape parameter;    Ill-conditioning;    RBFQR;    Divergence-free;    Sphere;   

DOI  :  10.1016/j.jcp.2020.109595

来源: Elsevier

【 摘 要 】

The direct method used for calculating smooth radial basis function (RBF) interpolants in the flat limit becomes numerically unstable. The RBF-QR algorithm bypasses this ill-conditioning using a clever change of basis technique. We extend this method for computing interpolants involving matrix-valued kernels, specifically surface divergence-free RBFs on the sphere, in the flat limit. Results illustrating the effectiveness of this algorithm are presented for a divergence-free vector field on the sphere from samples at scattered points. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free