Divergence-free RBFs on surfaces

Francis J. Narcowich; Joseph D. Ward; Grady B. Wright

doi:10.1007/s00041-006-6903-2

Divergence-free RBFs on surfaces

Francis J. Narcowich
, Joseph D. Ward
, Grady B. Wright

Mathematics Department

Texas A&M University

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

This article presents a new tool for fitting a divergence-free vector field tangent to a two-dimensional orientable surface P ∈ℝ³ to samples of such a field taken at scattered sites on P. This method, which involves a kernel constructed from radial basis functions, has applications to problems in geophysics, and has the advantage of avoiding problems with poles. Numerical examples testing the method on the sphere are included.

Original language	English
Pages (from-to)	643-663
Number of pages	21
Journal	Journal of Fourier Analysis and Applications
Volume	13
Issue number	6
DOIs	https://doi.org/10.1007/s00041-006-6903-2
State	Published - Dec 2007

Keywords

Incompressible fluid
Numerical modeling
Radial basis function
Sphere
Vector fields

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10.1007/s00041-006-6903-2

Cite this

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title = "Divergence-free RBFs on surfaces",

abstract = "This article presents a new tool for fitting a divergence-free vector field tangent to a two-dimensional orientable surface P ∈ℝ3 to samples of such a field taken at scattered sites on P. This method, which involves a kernel constructed from radial basis functions, has applications to problems in geophysics, and has the advantage of avoiding problems with poles. Numerical examples testing the method on the sphere are included.",

keywords = "Incompressible fluid, Numerical modeling, Radial basis function, Sphere, Vector fields",

author = "Narcowich, \{Francis J.\} and Ward, \{Joseph D.\} and Wright, \{Grady B.\}",

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AU - Narcowich, Francis J.

AU - Ward, Joseph D.

AU - Wright, Grady B.

PY - 2007/12

Y1 - 2007/12

N2 - This article presents a new tool for fitting a divergence-free vector field tangent to a two-dimensional orientable surface P ∈ℝ3 to samples of such a field taken at scattered sites on P. This method, which involves a kernel constructed from radial basis functions, has applications to problems in geophysics, and has the advantage of avoiding problems with poles. Numerical examples testing the method on the sphere are included.

AB - This article presents a new tool for fitting a divergence-free vector field tangent to a two-dimensional orientable surface P ∈ℝ3 to samples of such a field taken at scattered sites on P. This method, which involves a kernel constructed from radial basis functions, has applications to problems in geophysics, and has the advantage of avoiding problems with poles. Numerical examples testing the method on the sphere are included.

KW - Incompressible fluid

KW - Numerical modeling

KW - Radial basis function

KW - Sphere

KW - Vector fields

UR - https://www.scopus.com/pages/publications/35548941391

U2 - 10.1007/s00041-006-6903-2

DO - 10.1007/s00041-006-6903-2

M3 - Article

AN - SCOPUS:35548941391

SN - 1069-5869

VL - 13

SP - 643

EP - 663

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

IS - 6

ER -

Divergence-free RBFs on surfaces

Abstract

Keywords

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