Non-symmetric magnetohydrostatic equilibria: a multigrid approach

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

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)
    55 Downloads (Pure)


    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
    Early online date23 Jul 2013
    Publication statusPublished - Aug 2013


    • Magnetic fields
    • Magnetohydrodynamics
    • MHD
    • Graphical processing unit
    • GPU


    Dive into the research topics of 'Non-symmetric magnetohydrostatic equilibria: a multigrid approach'. Together they form a unique fingerprint.

    Cite this