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Paper details
Number 3 - September 2022
Volume 32 - 2022
RBF based quadrature on the sphere
Manuel Kindelan, Pedro González-Rodríguez, Diego Álvarez
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.
Keywords
RBF-FD, quadrature, sphere