Non-symmetric magnetohydrostatic equilibria: a multigrid approach

¹ School of Engineering, Computing and Applied Mathematics, University of Abertay Dundee, Kydd Building, Dundee, DD1 1HG UK
e-mail: D.MacTaggart@abertay.ac.uk
² Department of Mathematics and Information Sciences, Northumbria University, Newcastle Upon Tyne, NE1 8ST, UK
³ School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QW, UK

Received: 6 May 2013
Accepted: 23 June 2013

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 ×30 are readily achievable.