Spherical panel clustering and its numerical aspects

Abstract.

In modern approximation methods, linear combinations in terms of (space localizing) radial basis functions play an essential role. Areas of application are numerical integration formulae on the unit sphere Ω corresponding to prescribed nodes, spherical spline interpolation and spherical wavelet approximation. The evaluation of such a linear combination is a time-consuming task, since a certain number of summations, multiplications and the calculation of scalar products are required. A generalization of the panel clustering method in a spherical setup is presented. The economy and efficiency of panel clustering are demonstrated for three fields of interest, namely upward continuation of the Earth's gravitational potential, geoid computation by spherical splines and wavelet reconstruction of the gravitational potential.