parallALT: Fully Spectral GPU Accelerated Spherical Harmonic Transform Library

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 \(O(\sqrt {L}) \) (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.