skip to main content

Title: 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 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.
Authors:
 [1] ;  [2] ;  [3]
  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)
Publication Date:
OSTI Identifier:
1223367
Report Number(s):
DOE-Columbia--25783
TRN: US1500822
DOE Contract Number:
FC02-06ER25783
Resource Type:
Technical Report
Research Org:
Columbia Univ., New York, NY (United States)
Sponsoring Org:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Country of Publication:
United States
Language:
English
Subject:
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