SHTnsKit.jl

High-Performance Spherical Harmonic Transforms in Julia

SHTnsKit.jl provides a pure-Julia implementation of spherical harmonic transforms with serial CPU, CUDA, AMDGPU, and MPI/PencilArrays execution.

Key Features

High-Performance Computing

• Pure Julia: No C dependencies, seamless Julia ecosystem integration
• Multi-threading: Optimized with Julia threads and FFTW parallelization
• MPI Parallel: Distributed computing with MPI + PencilArrays + PencilFFTs
• GPU Native: CUDA and AMDGPU device-array transforms through package extensions
• SIMD Optimized: Vectorization with LoopVectorization.jl support
• Extensible: Modular architecture for CPU/GPU/distributed computing

Complete Scientific Functionality

• Transform Types: Scalar, vector, and complex field transforms
• Grid Support: Gauss-Legendre, regular Fejér, pole-inclusive, and Driscoll-Healy grids
• Conventions: Orthonormal, four-pi, and Schmidt normalization with configurable Condon-Shortley phase
• Vector Analysis: Spheroidal-toroidal decomposition for flow fields
• Differential Operators: Laplacian, gradient, divergence, vorticity
• Spectral Analysis: Power spectra, correlation functions, filtering

Advanced Capabilities

• Automatic Differentiation: Native ForwardDiff.jl and Zygote.jl support
• Field Rotations: Wigner D-matrix rotations and coordinate transforms
• Matrix Operators: Efficient spectral differential operators
• Performance Tuning: Comprehensive benchmarking and optimization tools

Installation

Basic Installation (Serial Computing)

using Pkg
Pkg.add("SHTnsKit")

Full Installation (Parallel Computing)

For high-performance parallel computing on clusters:

using Pkg
Pkg.add(["SHTnsKit", "MPI", "PencilArrays", "PencilFFTs", "LoopVectorization"])

GPU Extensions

using Pkg
Pkg.add(["SHTnsKit", "CUDA", "GPUArrays", "GPUArraysCore", "KernelAbstractions"])   # NVIDIA
Pkg.add(["SHTnsKit", "AMDGPU", "GPUArrays", "GPUArraysCore", "KernelAbstractions"]) # AMD

Generic analysis(cfg, device_array) and synthesis(cfg, coefficients) calls preserve the vendor device. Strict GPU() dispatch never silently falls back to CPU execution.

System Requirements

MPI Setup (for parallel computing):

# Ubuntu/Debian
sudo apt-get install libopenmpi-dev

# macOS  
brew install open-mpi

# Configure Julia MPI
julia -e 'using Pkg; Pkg.build("MPI")'

Citation

If you use SHTnsKit.jl in your research, please cite:

@article{schaeffer2013efficient,
  title={Efficient spherical harmonic transforms aimed at pseudospectral numerical simulations},
  author={Schaeffer, Nathana{\"e}l},
  journal={Geochemistry, Geophysics, Geosystems},
  volume={14},
  number={3},
  pages={751--758},
  year={2013},
  publisher={Wiley Online Library}
}

License

SHTnsKit.jl is released under the GNU General Public License v3.0 (GPL-3.0), ensuring compatibility with the underlying SHTns library.

References

• SHTns Documentation: Original C library
• Spherical Harmonics Theory: Mathematical background