Non-symmetric magnetohydrostatic equilibria: a multigrid approach

David MacTaggart, A. Elsheikh, J. A. McLaughlin, R. D. Simitev

Research output: Contribution to journalArticle

2 Citations (Scopus)
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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.
Original languageEnglish
Article number40
Number of pages6
JournalAstronomy and Astrophysics
Volume556
Early online date23 Jul 2013
DOIs
Publication statusPublished - Aug 2013

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magnetohydrostatics
magnetic field
plasma pressure
plasma
finite difference method
scalars
multigrid methods
pressure gradient
solar magnetic field
Lorentz force
stratification
pressure gradients
magnetic fields
gravity
plasma density
current density
gravitation
method
speed

Cite this

MacTaggart, David ; Elsheikh, A. ; McLaughlin, J. A. ; Simitev, R. D. / Non-symmetric magnetohydrostatic equilibria : a multigrid approach. In: Astronomy and Astrophysics. 2013 ; Vol. 556.
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Non-symmetric magnetohydrostatic equilibria : a multigrid approach. / MacTaggart, David; Elsheikh, A.; McLaughlin, J. A.; Simitev, R. D.

In: Astronomy and Astrophysics, Vol. 556, 40, 08.2013.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Non-symmetric magnetohydrostatic equilibria

T2 - a multigrid approach

AU - MacTaggart, David

AU - Elsheikh, A.

AU - McLaughlin, J. A.

AU - Simitev, R. D.

PY - 2013/8

Y1 - 2013/8

N2 - 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.

AB - 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.

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