Non-symmetric magnetohydrostatic equilibria: a multigrid approach

TL;DR

This paper presents an efficient multigrid numerical method for calculating non-symmetric magnetohydrostatic equilibria in solar magnetic fields, incorporating plasma pressure, gravity, and Lorentz forces, with significant speed-up via GPU parallelization.

Contribution

The paper introduces a multigrid approach to solve scalar elliptic equations for non-symmetric MHS equilibria, demonstrating high computational efficiency and GPU acceleration.

Findings

Multigrid method effectively computes non-symmetric MHS equilibria.

GPU parallelization achieves up to 30x speed-up.

The approach handles both force-free and non-force-free cases.

Abstract

Aims. Linear magnetohydrostatic (MHS) models of solar magnetic fields balance plasma pressure gradients, gravity and Lorentz forces where the current density is composed of a linear force-free component and a cross-field component that depends on gravitational stratification. In this paper, we investigate an efficient numerical procedure for calculating such equilibria. Methods. The MHS equations are reduced to two scalar elliptic equations - one on the lower boundary and the other within the interior of the computational domain. The normal component of the magnetic field is prescribed on the lower boundary and a multigrid method is applied on both this boundary and within the domain to find the poloidal scalar potential. Once solved to a desired accuracy, the magnetic field, plasma pressure and density are found using a finite difference method. Results. We investigate the effects of the cross-field currents on the linear MHS equilibria. Force-free and non-force-free examples are given to demonstrate the numerical scheme and an analysis of speed-up due to parallelization on a graphics processing unit (GPU) is presented. It is shown that speed-ups of x30 are readily achievable.