On spherical harmonics based numerical quadrature over the surface of a sphere

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(NlogN) operations.

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