<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The paper describes a new RBF-FD based technique to compute quadrature weights on the sphere. In the proposed method, the sphere is divided into rectangles in the latitude-azimuth coordinate system, and the function is integrated over each rectangle using RBF interpolation. The method is easy to implement and its accuracy is comparable to that based on SPH expansions. One advantage of the proposed method is its ability to handle non-uniform node distributions. On this respect, we propose a new algorithm to cluster nodes in regions of steep changes in the function. It is a repulsion-based algorithm with a non-uniform distribution of electrical charges. We show that, using node clustering, the accuracy of the method can be significantly improved.</p>
</abstract>

The paper describes a new RBF-FD based technique to compute quadrature weights on the sphere. In the proposed method, the sphere is divided into rectangles in the latitude-azimuth coordinate system, and the function is integrated over each rectangle using RBF interpolation. The method is easy to implement and its accuracy is comparable to that based on SPH expansions. One advantage of the proposed method is its ability to handle non-uniform node distributions. On this respect, we propose a new algorithm to cluster nodes in regions of steep changes in the function. It is a repulsion-based algorithm with a non-uniform distribution of electrical charges. We show that, using node clustering, the accuracy of the method can be significantly improved.

RBF Based Quadrature on the Sphere

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"RBF Based Quadrature on the Sphere"}

The paper describes a new RBF-FD based technique to compute quadrature weights on the sphere. In the proposed method, the sphere is divided into rectangles in...

RBF Based Quadrature on the Sphere

Published Online: Oct 08, 2022

Page range: 467 - 478

Received: Oct 04, 2021

Accepted: Apr 11, 2022

DOI: https://doi.org/10.34768/amcs-2022-0034

Keywords
RBF-FD, quadrature, sphere

© 2022 Manuel Kindelan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

RBF Based Quadrature on the Sphere

Published Online: Oct 08, 2022

Page range: 467 - 478

Received: Oct 04, 2021

Accepted: Apr 11, 2022

DOI: https://doi.org/10.34768/amcs-2022-0034

KeywordsRBF-FD, quadrature, sphere

© 2022 Manuel Kindelan et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
RBF-FD, quadrature, sphere