Stability and Error Estimates for Vector Field Interpolation and Decomposition on the Sphere with RBFs

Authors

Edward J. Fuselier, High Point University
Grady Wright, Boise State UniversityFollow

Document Type

Article

Publication Date

10-9-2009

Abstract

A new numerical technique based on radial basis functions (RBFs) is presented for fitting a vector field tangent to the sphere, S², from samples of the field at "scattered" locations on S². The method naturally provides a way to decompose the reconstructed field into its individual Helmholtz–Hodge components, i.e., into divergence-free and curl-free parts, which is useful in many applications from the atmospheric and oceanic sciences (e.g., in diagnosing the horizontal wind and ocean currents). Several approximation results for the method will be derived. In particular, Sobolevtype error estimates are obtained for both the interpolant and its decomposition. Optimal stability estimates for the associated interpolation matrices are also presented. Finally, numerical validation of the theoretical results is given for vector fields with characteristics similar to those of atmospheric wind fields.

Copyright Statement

This document was originally published by Society for Industrial and Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis. Copyright restrictions may apply. DOI: 10.1137/080730901

Publication Information

Fuselier, Edward J. and Wright, Grady. (2009). "Stability and Error Estimates for Vector Field Interpolation and Decomposition on the Sphere with RBFs". SIAM Journal on Numerical Analysis, 47(5), 3213-3239. https://doi.org/10.1137/080730901