Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics

Multigrid 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 depen...

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Bibliographic Details
Published in:Journal of computational physics 2010-09, Vol.229 (18), p.6208-6219
Main Authors: Adams, Mark F., Samtaney, Ravi, Brandt, Achi
Format: Article
Language:English
Subjects:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Computational efficiency
Computational techniques
Computer simulation
Computing time
Defect correction
Exact sciences and technology
Fluid flow
Implicit magnetohydrodynamics
Magnetohydrodynamics
Mathematical analysis
Mathematical methods in physics
MHD
Nonlinear multigrid
Physics
Textbooks
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Summary:Multigrid 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.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2010.04.024