Efficient spherical harmonic transforms aimed at pseudospectral numerical simulations
Efficient spherical harmonic transforms aimed at pseudospectral numerical simulations
复制标题
针对伪谱数值模拟的高效球谐变换
DOI：
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发表时间：
2012
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通讯作者：
N. Schaeffer
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作者：
N. Schaeffer
本文报道了球面谐波变换（SHT）的几种高效算法。本文讨论了基于高斯-勒让德正交的显式矢量化算法，并在SHTns库中实现，其中包括标量变换和矢量变换。主要的突破是通过利用SHT的特定特性和当前和未来计算机的先进功能，实现非常高效的Legendre相关函数的实时计算，即使是非常高的分辨率。这使我们能够同时显著减少SHT的内存使用和计算时间。我们衡量算法的性能和准确性。尽管在SHTns中实现的算法的复杂性在ON3（其中N是变换的最大谐波度），但它们比任何第三方实现（包括低复杂度算法）都要好得多，即使对于截断高达N = 1023。SHTns作为开源软件可在https://bitbucket.org/nschaeff/shtns上获得。
In this paper, we report on very efficient algorithms for 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. Although the complexity of the algorithms implemented in SHTns are in ON3 (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 https://bitbucket.org/nschaeff/shtns as open source software.