Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics

Technical Report · Sat Dec 14 00:00:00 EST 2013

DOI:https://doi.org/10.2172/1223367· OSTI ID:1223367

Adams, Mark F. ^[1]; Samtaney, Ravi ^[2]; Brandt, Achi ^[3]

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1. Columbia Univ., New York, NY (United States)
2. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
3. Weizmann Inst. of Science, Rehovot (Israel)

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.

• Research Organization: Columbia Univ., New York, NY (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• DOE Contract Number: FC02-06ER25783
• OSTI ID: 1223367
• Report Number(s): DOE-Columbia-25783; TRN: US1500822
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
MAGNETOHYDRODYNAMICS
EFFICIENCY
INTERPOLATION
TIME DEPENDENCE
EQUATIONS
COMPUTERIZED SIMULATION
NONLINEAR PROBLEMS
ACCURACY
BENCHMARKS
CORRECTIONS
DEFECTS
PLASMA
MAGNETIC FIELDS
nonlinear multigrid
defect correction
implicit magnetohydrodynamics