Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 417, Issue -, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2020.109595
Keywords
Radial basis functions; Shape parameter; Ill-conditioning; RBFQR; Divergence-free; Sphere
Funding
- SMART Scholarship
- Under Secretary of DefenseResearch and Engineering, National Defense Education Program/BA-1, Basic Research
- National Science Foundation [CCF 1717556]
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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.
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