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 URL/nschaeff/shtns as open source software.
In this paper, we report on very efficient algorithms for the spherical harmonic transform (SHT) . Explicitly vectorized variations of the algorithm based on the Gauss-Legendre quadrature are discussed and implemented in the SHTns library which includes scalar and vector transforms. The main breakthrough is to achieve very efficient on-the-fly computations of the Legendre associated functions, even for very high resolutions, by taking advantage of the specific properties of the SHT and the advanced capabilities of current and future computers. This allows us to simultaneously and significantly reduce memory usage and computation time of the SHT. We measure the performance and accuracy of our algorithms . Even though the complexity of the algorithms implemented in SHTns are in O(N^3) (where N is the maximum harmonic degree of the transform), they perform much better than any third party implementation, including lower complexity algorithms, even for truncations as high as N=1023. SHTns is available at URL/nschaeff/shtns as open source software.
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that can be used in numerical simulations of partial differential equations
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Gauss-Legendre algorithm
algorithm based on the Gauss-Legendre quadrature
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open-source library SHTns
SHTns library
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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
The main breakthrough is to achieve very efficient on-the-fly computations of the Legendre associated functions, even for very high resolutions, by taking advantage of the specific properties of the SHT and the advanced capabilities of current and future computers. This allows us to simultaneously and significantly reduce memory usage and computation time of the SHT. We measure the performance and accuracy
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is compared to third party SHT implementations, including fast algorithms
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of order
in
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the available implementations of asymptotically fast
any third party implementation, including lower complexity
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a truncation
truncations
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In our performance tests, the best performance for SHT on the x86 platform is delivered by SHTns , which
SHTns