Numerical Quadrature over the Surface of a Sphere

摘要

Large-scale simulations in spherical geometries require associated quadrature formulas. Classical approaches based on tabulated weights are limited to specific quasi-uniform distributions of relatively low numbers of nodes. By using a radial basis function-generated finite differences (RBF-FD)-based approach, the proposed algorithm creates quadrature weights for N arbitrarily scattered nodes in only O(N log N) operations.