Monolithic multigrid methods for two-dimensional resistive magnetohydrodynamics

Adler, James H.; Benson, Thomas R.; Cyr, Eric C.; MacLachlan, Scott P.; Tuminaro, Raymond S.

doi:10.1137/151006135

Title: Monolithic multigrid methods for two-dimensional resistive magnetohydrodynamics

Journal Article · Wed Jan 06 00:00:00 EST 2016 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/151006135· OSTI ID:1263651

Adler, James H. ^[1]; Benson, Thomas R. ^[1]; Cyr, Eric C. ^[2]; MacLachlan, Scott P. ^[3]; Tuminaro, Raymond S. ^[4]

Tufts Univ., Medford, MA (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Memorial Univ. of Newfoundland, St. John's (Canada)
Sandia National Lab. (SNL-CA), Livermore, CA (United States)

Magnetohydrodynamic (MHD) representations are used to model a wide range of plasma physics applications and are characterized by a nonlinear system of partial differential equations that strongly couples a charged fluid with the evolution of electromagnetic fields. The resulting linear systems that arise from discretization and linearization of the nonlinear problem are generally difficult to solve. In this paper, we investigate multigrid preconditioners for this system. We consider two well-known multigrid relaxation methods for incompressible fluid dynamics: Braess--Sarazin relaxation and Vanka relaxation. We first extend these to the context of steady-state one-fluid viscoresistive MHD. Then we compare the two relaxation procedures within a multigrid-preconditioned GMRES method employed within Newton's method. To isolate the effects of the different relaxation methods, we use structured grids, inf-sup stable finite elements, and geometric interpolation. Furthermore, we present convergence and timing results for a two-dimensional, steady-state test problem.

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Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1263651

Report Number(s):: SAND-2015-9123J; 644878

Journal Information:: SIAM Journal on Scientific Computing, Vol. 38, Issue 1; ISSN 1064-8275

Publisher:: SIAMCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 28 works

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Local Fourier analysis of block-structured multigrid relaxation schemes for the Stokes equations: Local Fourier analysis of block-structured multigrid relaxation schemes for the Stokes equations He, Yunhui; MacLachlan, Scott P. Numerical Linear Algebra with Applications, Vol. 25, Issue 3 https://doi.org/10.1002/nla.2147	journal	February 2018
A face‐based monolithic approach for the incompressible magnetohydrodynamics equations Ata, Kayhan; Sahin, Mehmet International Journal for Numerical Methods in Fluids, Vol. 92, Issue 5 https://doi.org/10.1002/fld.4786	journal	May 2020

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