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Fast Spherical Filter Gets Diverse ApplicationJanuary 1998An algorithm recently developed by researchers in ITL's Mathematical and Computational Sciences Division and the University of Colorado is receiving attention from diverse quarters in industry and government, for applications ranging from microwave modeling in electromagnetics to weather and climate modeling. The work, which was reported in the Journal of Computational Physics in September 1997, involved constructing a fast algorithm for obtaining a uniform resolution representation of a function known at a latitudelongitude grid on the surface of a sphere. For a grid containing N^{2} points, the new spectral truncation method performs a projection to a uniformresolution function space in time proportional to N^{2} log(N), compared with N^{3} for the equivalent projection via the spherical harmonics transformation. This represents a very significant cost reduction, allowing the practical solution of problems on much finer grids than previously possible. For example, the new, fast algorithm reduces the computational complexity of the step that is a computational bottleneck in standard weather and climate models, and is being tested at the National Center for Atmospheric Research (NCAR), Boulder, for integration into existing computational routines. In another case, an enhanced implementation of the algorithm built by researchers at Yale University is now in use at Boeing in recently developed electromagnetics modeling software, where the current application is simulation of radar scattering and aircraft "signatures."
