Non-symmetric magnetohydrostatic equilibria: a multigrid approach

D. MacTaggart, A. Elsheikh, J. A. McLaughlin, R. D. Simitev
School of Engineering, Computing and Applied Mathematics, University of Abertay Dundee, Kydd Building, Dundee, DD1 1HG, Scotland, UK
University of Glasgow, 2013


   title={Non-symmetric magnetohydrostatic equilibria: a multigrid approach},

   author={MacTaggart, D and Elsheikh, A and McLaughlin, JA and Simitev, RD},



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AIMS. Neukirch and Rastatter (1999) re-formulate the linear magnetohydrostatic model (MHS) model of Low (1991) into a form that only requires the solution of two scalar elliptic partial differential equations. In this paper, we investigate an efficient numerical procedure for calculating MHS equilibria based on this representation. 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.
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