Abstract
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 proposedspectral 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 requiresO(N2logN) operations forO(N2) grid points, as opposed toO(N3) 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.
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