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 the latitude-azimuth coordinate system, and the function is integrated over eachrectangle using RBF interpolation. The method is easy to implement and its accuracy is comparable to that based on SPHexpansions. One advantage of the proposed method is its abilityto handle non-uniformnode 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 algorithmwith a non-uniform distribution of electrical charges. We show that, using node clustering, the accuracy of the method canbe significantly improved.

RBF based quadrature on the sphere Articles