Mimetic Methods for Lagrangian Relaxation of Magnetic Fields

TL;DR

This paper introduces a GPU-accelerated mimetic numerical scheme for magnetic field relaxation to force-free states, preserving magnetic flux and topology with higher accuracy than traditional methods.

Contribution

The authors develop a novel mimetic Lagrangian relaxation method that improves accuracy and computational speed for simulating force-free magnetic fields.

Findings

Higher accuracy in approximating force-free states.

Enhanced computational speed using GPU implementation.

Strict preservation of magnetic flux and topology.

Abstract

We present a new code that performs a relaxation of a magnetic field towards a force-free state (Beltrami field) using a Lagrangian numerical scheme. Beltrami fields are of interest for the dynamics of many technical and astrophysical plasmas as they are the lowest energy states that the magnetic field can reach. The numerical method strictly preserves the magnetic flux and the topology of magnetic field lines. In contrast to other implementations we use mimetic operators for the spatial derivatives in order to improve accuracy for high distortions of the grid. Compared with schemes using direct derivatives we find that the final state of the simulation approximates a force-free state with a significantly higher accuracy. We implement the scheme in a code which runs on graphical processing units (GPU), which leads to an enhanced computing speed compared to previous relaxation codes.