The generalized moving least squares technique combined with a Householder transformation for computing the first derivatives on the sphere

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Mohammadi Vahid

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Journal Paper

Paper Information

Journal: Journal of Discrete Mathematics and its Applications Year:2023 | Volume:8 | Issue:1 Page(s): 35-42

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Information Journal Paper

Title

The generalized moving least squares technique combined with a Householder transformation for computing the first derivatives on the sphere

Author(s)

Mohammadi Vahid | Issue Writer Certificate

Keywords

Generalized moving least squares approximation

A Householder reflection

Transport equation

Abstract

We present a new and simple direct approach based on generalized moving least squares (GMLS) for computing the first derivatives of the functions defined on the sphere. The novel method utilizes a Householder transformation (reflection) and a projection onto the tangent plane to compute the first derivatives at the original point on the sphere. The main benefit of this algorithm is that there is no need to use the spherical harmonics for constructing the approximation of the first derivatives. An example of the approximation has been tested to show the ability of the developed method. Moreover, this method has been applied to solve the Transport equation in one example.

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