FORTVSH: A Fortran Module For Vector Spherical Harmonics Computations

arXiv:2608.08419 · astro-ph.SR, astro-ph.IM, physics.comp-ph · Submitted 2026-08-16 · Read on arXiv

Justin G. Elfritz

astro-ph.SR, astro-ph.IM, physics.comp-ph

Submitted: 2026-08-16

Updated: 2026-08-18

Comments: 22 pages with 10 figures

Code: https://github.com/justinelfritz/FORTVSH

License: http://creativecommons.org/licenses/by/4.0/

The gist: The vector spherical harmonics (VSH) are crucial ingredients for representation of arbitrary vector fields in curvilinear coordinate systems throughout mathematical physics.

Terminology

Adam — 3× in this paper · explained in 2 episodes
Benchmark — 3× in this paper · explained in 2 episodes
Benchmarking — 3× in this paper · explained in 3 episodes
Core — 3× in this paper · explained in 2 episodes
Consistency — 2× in this paper · explained in 3 episodes
Magnetohydrodynamics (MHD) — 2× in this paper · explained in 3 episodes
Verification — 2× in this paper · explained in 2 episodes
Abstraction — 1× in this paper · explained in 1 episode
Reconstruction Error — 1× in this paper · explained in 2 episodes

Abstract

The vector spherical harmonics (VSH) are crucial ingredients for representation of arbitrary vector fields in curvilinear coordinate systems throughout mathematical physics. Performant, efficient computations of the VSH are essential to high-performance computing applications that utilize spectral analysis, including magnetohydrodynamics (MHD) simulations for geophysics and astrophysics. The open-source FORTVSH package provides a catalog of numerical routines for evaluating various VSH forms and related mathematical functions. This manuscript establishes the theoretical basis, addresses the computational need for efficient VSH solvers, and presents a comprehensive overview of the FORTVSH routines.

Terminology

Abstract

Related papers