International Journal of applied mathematics and computer science

online read us now

Paper details

Number 3 - September 2022
Volume 32 - 2022

RBF based quadrature on the sphere

Manuel Kindelan, Pedro González-Rodríguez, Diego Álvarez

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-FD, quadrature, sphere