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

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-value...

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Bibliographic Details
Published in:Journal of computational physics 2020-09, Vol.417, p.109595, Article 109595
Main Authors: Drake, Kathryn P., Wright, Grady B.
Format: Article
Language:English
Subjects:
Algorithms
Computational physics
Divergence
Divergence-free
Fields (mathematics)
Ill-conditioned problems (mathematics)
Ill-conditioning
QR algorithms
Radial basis function
Radial basis functions
RBFQR
Shape parameter
Sphere
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Summary: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.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2020.109595