Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics
KAUST DepartmentPhysical Sciences and Engineering (PSE) Division
Mechanical Engineering Program
Clean Combustion Research Center
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AbstractMultigrid methods can solve some classes of elliptic and parabolic equations to accuracy below the truncation error with a work-cost equivalent to a few residual calculations so-called "textbook" multigrid efficiency. We investigate methods to solve the system of equations that arise in time dependent magnetohydrodynamics (MHD) simulations with textbook multigrid efficiency. We apply multigrid techniques such as geometric interpolation, full approximate storage, Gauss-Seidel smoothers, and defect correction for fully implicit, nonlinear, second-order finite volume discretizations of MHD. We apply these methods to a standard resistive MHD benchmark problem, the GEM reconnection problem, and add a strong magnetic guide field, which is a critical characteristic of magnetically confined fusion plasmas. We show that our multigrid methods can achieve near textbook efficiency on fully implicit resistive MHD simulations. (C) 2010 Elsevier Inc. All rights reserved.
SponsorsThis work was supported under the DOE SciDAC program (USDOE Contract No. DE-AC02-09CH11466) performed at Princeton Plasma Physics Laboratory, Princeton University, and Columbia University. This research used resources of the National Center for Computational Sciences at Oak Ridge National Laboratory, which is supported by the Office of Science of the US Department of Energy under Contract No. DE-AC05-00OR22725. This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the US Department of Energy under Contract No. DE-AC02-05CH11231. We gratefully acknowledge verification data from the SciDAC Center for Extended MUD Modeling.
JournalJournal of Computational Physics