Fourier Series on Spheres

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Abstract
Spectral methods for the numerical solution of problems in spherical (and spheroidal) geometries are discussed. A new class of expansions based on special Fourier series are shown to lead to efficient and accurate simulations. A detailed exposition is given of the properties of surface harmonic series and transform methods and their relation to the new Fourier series on spheres. With resolution 1/N in both longitude and latitude, spectral methods using surface harmonics require 0(N) arithmetic operations per retained mode per time step while those based on Fourier series on spheres require only 0(logN) operations per retained mode per time step.

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