HealpixMPI.jl: an MPI-parallel implementation of the Healpix tessellation scheme in Julia

Abstract

Spherical Harmonic Transforms (SHTs) can be seen as Fourier Transforms’ spherical, two-dimensional counterparts, casting real-space data to the spectral domain and vice versa. As in Fourier analysis where a function is decomposed into a set of amplitude coefficients, an SHT allows any spherically-symmetric field, defined in real space, to be decomposed into a set of complex harmonic coefficients 𝑎 ℓ,𝑚 , commonly referred to as alms, where each quantifies the contribution of the corresponding spherical harmonic function.