Non-symmetric magnetohydrostatic equilibria: a multigrid approach

MacTaggart, D. , Elsheikh, A., McLaughlin, J.A. and Simitev, R.D. (2013) Non-symmetric magnetohydrostatic equilibria: a multigrid approach. Astronomy and Astrophysics, 556, A40. (doi:10.1051/0004-6361/201220458)

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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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Mactaggart, Dr David and Simitev, Dr Radostin
Authors: MacTaggart, D., Elsheikh, A., McLaughlin, J.A., and Simitev, R.D.
College/School:College of Science and Engineering > School of Mathematics and Statistics
College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Astronomy and Astrophysics
Publisher:EDP Sciences
ISSN:0004-6361
ISSN (Online):1432-0746
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