This library demonstrates enhanced performance and accuracy in spherical harmonic transformations, suggesting significant speed improvements over traditional methods.
This paper introduces parallALT — a fully spectral spherical harmonic transform library. Developed for modern massively parallel accelerators, such as GPUs, parallALT combines close to machine-precision accuracy with exceptional performance. This paper demonstrates that our fully spectral algorithm has \(O(√L) \) (with L being the spherical harmonic degree) round trip accuracy scaling compared to O ( L ) scaling of the conventional quadrature approach. We also show that parallALT implementation for high L ∈ [512, 16384] is up to three times faster on an Nvidia H100 GPU than the most efficient open source quadrature implementation, SHTns. Developed with the help of the in-house cross-platform runtime code generation platform, PfSolve and VkFFT libraries, parallALT will be released as an open source library in the future.
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Dmitrii Tolmachev (2026) studied this question.
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