Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics

• 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
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2010.04.024

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.