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Title: Monolithic multigrid methods for two-dimensional resistive magnetohydrodynamics

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.
Authors:
 [1] ;  [1] ;  [2] ;  [3] ;  [4]
  1. Tufts Univ., Medford, MA (United States)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  3. Memorial Univ. of Newfoundland, St. John's (Canada)
  4. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Publication Date:
OSTI Identifier:
1263651
Report Number(s):
SAND--2015-9123J
Journal ID: ISSN 1064-8275; 644878
Grant/Contract Number:
AC04-94AL85000
Type:
Accepted Manuscript
Journal Name:
SIAM Journal on Scientific Computing
Additional Journal Information:
Journal Volume: 38; Journal Issue: 1; Journal ID: ISSN 1064-8275
Publisher:
SIAM
Research Org:
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY monolithic multigrid; magnetohydrodynamics; Braess-Sarazin relaxation; Vanka relaxation