Fast Spherical Filter Gets Diverse Application
January 1998
An 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 latitude-longitude
grid on the surface of a sphere. For a grid containing N2 points, the
new spectral truncation method performs a projection to a uniform-resolution
function space in time proportional to N2 log(N), compared with N3 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."
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