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Efficient Spherical Harmonic Transforms aimed at pseudo-spectral numerical simulations

Nathanaël Schaeffer 1
1 Géodynamo
ISTerre - Institut des Sciences de la Terre
Abstract : In this paper, we report on very efficient algorithms for the spherical harmonic transform (SHT) that can be used in numerical simulations of partial differential equations. Explicitly vectorized variations of the Gauss-Legendre algorithm are discussed and implemented in the open-source library SHTns which includes scalar and vector transforms. This library is especially suitable for direct numerical simulations of non-linear partial differential equations in spherical geometry, like the Navier-Stokes equation. The performance of our algorithms is compared to third party SHT implementations, including fast algorithms. Even though the complexity of the algorithms implemented in SHTns are of order O(N^3) (where N is the maximum harmonic degree of the transform), they perform much better than the available implementations of asymptotically fast algorithms, even for a truncation as high as N=1023. In our performance tests, the best performance for SHT on the x86 platform is delivered by SHTns, which is available at as open source software.
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Contributor : Nathanaël Schaeffer <>
Submitted on : Saturday, December 8, 2012 - 5:29:27 PM
Last modification on : Tuesday, December 29, 2020 - 11:50:03 AM
Long-term archiving on: : Monday, March 11, 2013 - 12:05:54 PM


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  • HAL Id : insu-00675145, version 2
  • ARXIV : 1202.6522


Nathanaël Schaeffer. Efficient Spherical Harmonic Transforms aimed at pseudo-spectral numerical simulations. 2012. ⟨insu-00675145v2⟩



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