A fast spherical filter with uniform resolution

This paper introduces a fast algorithm for obtaining a uniform resolution representation of a function known at a latitude-longitude grid on the surface of a sphere, equivalent to a triangular, isotropic truncation of the spherical harmonic coefficients for the function. The proposed spectral truncation method, which is based on the fast multipole method and the fast Fourier transform, projects the function to a space with uniform resolution while avoiding surface harmonic transformations. The method requires O(N-2 log N) operations for O(N-2) grid points, as opposed to O(N-3) operations for the standard spectral transform method, providing a reduced-complexity spectral method obviating the pole problem in the integration of time-dependent partial differential equations on the sphere. The filter's performance is demonstrated with numerical examples. (C) 1997 Academic Press.