The generalized moving least squares technique combined with a Householder transformation for computing the first derivatives on the sphere
Publish Year: 1402
Type: Journal paper
Language: English
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Document National Code:
JR_JDMA-8-1_005
Index date: 22 October 2023
The generalized moving least squares technique combined with a Householder transformation for computing the first derivatives on the sphere 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.
The generalized moving least squares technique combined with a Householder transformation for computing the first derivatives on the sphere Keywords:
The generalized moving least squares technique combined with a Householder transformation for computing the first derivatives on the sphere authors
Vahid Mohammadi
Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University
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