Regular Article: Computing Fourier Transforms and Convolutions on the 2-Sphere
Advances in Applied Mathematics
Computing challenges of the cosmic microwave background
Computing in Science and Engineering
A Recurrence Technique for Expanding a Function in Spherical Harmonics
IEEE Transactions on Computers
Spherical harmonic transforms for discrete multiresolution applications
The Journal of Supercomputing
Discrete Spherical Harmonic Transforms: Numerical Preconditioning and Optimization
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part II
Spherical harmonic transforms using quadratures and least squares
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part III
Optimization of spherical harmonic transform computations
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
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Most boundary value problems of the geopotential field have integral and series solutions in terms of Green's convolution kernels. These solutions are advantageously evaluated using fast Spherical Harmonic Transforms (SHTs) for regular arrays of simulated or observed global data. However, the computational complexity and numerical conditioning of SHTs for relatively dense data are quite challenging and recent algorithmic developments warrant further investigations for geodetic and geophysical applications. Global multiresolution applications for scalar, vector and tensor fields on the Earth and its neighborhood require spherical harmonic analysis and synthesis using convolution filters with data decimation and dilation. For global spherical grid applications, efficient and reliable SHTs are needed just as Fast Fourier Transforms (FFTs) are used in regional planar applications. With the availability of enormous quantities of space, surface and subsurface data, extensive data structuring and management are unavoidable for most array computations. Different methodologies imply very different strategies and conflicting claims often appear in the literature. Discussions of the implicit and other assumptions with simulated results would undoubtedly help to clarify the situation and help decide on appropriate data structuring strategies for different computational applications.