SHTnsKit.jl

High-Performance Spherical Harmonic Transforms for Julia

CPU | GPU | MPI Distributed | Auto-Differentiation

Features

Core Transforms

Forward & backward spherical harmonic transforms
Scalar, vector, and complex field support
In-place operations for memory efficiency

GPU Acceleration

CUDA/cuFFT for NVIDIA GPUs
KernelAbstractions.jl backend
Automatic CPU fallback

MPI Distributed

PencilArrays domain decomposition
Scalable to thousands of cores
Efficient communication patterns

Analysis Tools

Power spectrum analysis
Energy diagnostics
Wigner D-matrix rotations

Quick Start

Installation

using Pkg

# Basic installation
Pkg.add("SHTnsKit")

# With GPU support
Pkg.add(["SHTnsKit", "CUDA", "KernelAbstractions"])

# With MPI support
Pkg.add(["SHTnsKit", "MPI", "PencilArrays", "PencilFFTs"])

Hello World

using SHTnsKit

# Create configuration for lmax=16
cfg = create_gauss_config(16, 18)

# Create a test pattern on the sphere
spatial = zeros(cfg.nlat, cfg.nlon)
for i in 1:cfg.nlat
    x = cfg.x[i]  # cos(θ)
    spatial[i, :] .= (3*x^2 - 1)/2  # Y_2^0 pattern
end

# Transform: spatial → spectral → spatial
Alm = analysis(cfg, spatial)
recovered = synthesis(cfg, Alm)

# Verify roundtrip accuracy
println("Error: ", maximum(abs.(spatial - recovered)))  # ~1e-14

Pro Tip

For large problems (lmax > 64), use GPU acceleration with gpu_analysis() and gpu_synthesis() for significant speedup.

GPU Example

using SHTnsKit, CUDA

cfg = create_gauss_config(128, 130)
spatial = rand(cfg.nlat, cfg.nlon)

# GPU-accelerated transforms
Alm = gpu_analysis(cfg, spatial)
recovered = gpu_synthesis(cfg, Alm)

# Safe version with automatic CPU fallback
Alm_safe = gpu_analysis_safe(cfg, spatial)

Scientific Applications

Climate Science

Atmospheric dynamics, weather prediction, ocean circulation

Geophysics

Gravitational fields, magnetic anomalies, Earth surface modeling

Astrophysics

CMB analysis, stellar dynamics, gravitational waves

Fluid Dynamics

Vorticity-divergence decomposition, turbulence on spheres

Documentation

Quick Start

Get started in minutes

GPU Guide

CUDA acceleration

Distributed

MPI parallelization

API Reference

Complete documentation

Installation Options

Setup	Command	Use Case
Basic	`Pkg.add("SHTnsKit")`	Single CPU, getting started
GPU	`+ CUDA, KernelAbstractions`	NVIDIA GPU acceleration
MPI	`+ MPI, PencilArrays, PencilFFTs`	Cluster computing
Full	All of the above	Maximum flexibility

Requirements

Julia 1.10 or later
For GPU: NVIDIA GPU with CUDA support
For MPI: OpenMPI or MPICH installed

Contributing

We welcome contributions! See our GitHub repository for:

Bug reports and feature requests
Documentation improvements
Pull requests

Citation

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

@software{shtnskit,
  author = {Kar, Subhajit},
  title = {SHTnsKit.jl: High-Performance Spherical Harmonic Transforms},
  url = {https://github.com/subhk/SHTnsKit.jl},
  year = {2024}
}

License

SHTnsKit.jl is released under the GNU General Public License v3.0.

Made for the scientific computing community