Second-order formulation of a multigrid method for steady Euler equations through defect-correction
Proceedings of the 4th international congress on Computational and applied mathematics
Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions
SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
ICCAM'92 Proceedings of the fifth international conference on Computational and applied mathematics
Multigrid
Directional Agglomeration Multigrid Techniques for High-Reynolds Number Viscous Flows
Directional Agglomeration Multigrid Techniques for High-Reynolds Number Viscous Flows
Nonlinear magnetohydrodynamics simulation using high-order finite elements
Journal of Computational Physics
A fully implicit numerical method for single-fluid resistive magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Calculations of two-fluid magnetohydrodynamic axisymmetric steady-states
Journal of Computational Physics
Journal of Computational Physics
Operator-Based Preconditioning of Stiff Hyperbolic Systems
SIAM Journal on Scientific Computing
Review of implicit methods for the magnetohydrodynamic description of magnetically confined plasmas
Journal of Computational Physics
Hi-index | 31.45 |
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.