Efficient Spherical Harmonic Transforms aimed at pseudo-spectral numerical simulations

摘要: In this paper, we report on very efficient algorithms for the spherical harmonic transform (SHT). Explicitly vectorized variations of algorithm based Gauss-Legendre quadrature are discussed and implemented in SHTns library which includes scalar vector transforms. The main breakthrough is to achieve on-the-fly computations Legendre associated functions, even high resolutions, by taking advantage specific properties SHT advanced capabilities current future computers. This allows us simultaneously significantly reduce memory usage computation time SHT. We measure performance accuracy our algorithms. Even though complexity $O(N^3)$ (where N maximum degree transform), they perform much better than any third party implementation, including lower algorithms, truncations as N=1023. available at https URL open source software.