Semi-implicit method for long time scale magnetohydrodynamic computations in three dimensions
Journal of Computational Physics
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Semi-implicit magnetohydrodynamic calculations
Journal of Computational Physics
Finite difference schemes and partial differential equations
Finite difference schemes and partial differential equations
Accurate semi-implicit treatment of the hall effect in magnetohydrodynamic computations
Journal of Computational Physics
Hybrid Krylov methods for nonlinear systems of equations
SIAM Journal on Scientific and Statistical Computing
Derivation of implicit difference schemes by the method of differential approximation
Journal of Computational Physics
An implicit scheme for nonideal magnetohydrodynamics
Journal of Computational Physics
Efficient management of parallelism in object-oriented numerical software libraries
Modern software tools for scientific computing
Enhanced Nonlinear Iterative Techniques Applied to a Nonequilibrium Plasma Flow
SIAM Journal on Scientific Computing
An improved convection scheme applied to recombining divertor plasma flows
Journal of Computational Physics
A multilevel iterative field solver for implicit, kinetic, plasma simulation
Journal of Computational Physics
A Multigrid Preconditioned Newton--Krylov Method
SIAM Journal on Scientific Computing
An implicit energy-conservative 2D Fokker-Planck algorithm: II. Jacobian-free Newton—Krylov solver
Journal of Computational Physics
Physics-based preconditioning and the Newton-Krylov method for non-equilibrium radiation diffusion
Journal of Computational Physics
A multigrid tutorial: second edition
A multigrid tutorial: second edition
On Newton-Krylov multigrid methods for the imcompressible Navier-Stokes equations
Journal of Computational Physics
A Multigrid-Preconditioned Newton--Krylov Method for the Incompressible Navier--Stokes Equations
SIAM Journal on Scientific Computing
On Preconditioning Newton--Krylov Methods in Solidifying Flow Applications
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
On balanced approximations for time integration of multiple time scale systems
Journal of Computational Physics
A 2D high-ß Hall MHD implicit nonlinear solver
Journal of Computational Physics
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
A comparison of implicit time integration methods for nonlinear relaxation and diffusion
Journal of Computational Physics
Jacobian---Free Newton---Krylov Methods for the Accurate Time Integration of Stiff Wave Systems
Journal of Scientific Computing
A fully implicit, nonlinear adaptive grid strategy
Journal of Computational Physics
Self-adaptive time integration of flux-conservative equations with sources
Journal of Computational Physics
A fully implicit numerical method for single-fluid resistive magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
An iterative semi-implicit scheme with robust damping
Journal of Computational Physics
Implicit adaptive mesh refinement for 2D reduced resistive magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Short Note: ADI-SGS scheme on ideal magnetohydrodynamics
Journal of Computational Physics
Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods
Journal of Computational Physics
Robust, multidimensional mesh-motion based on Monge-Kantorovich equidistribution
Journal of Computational Physics
Operator-Based Preconditioning of Stiff Hyperbolic Systems
SIAM Journal on Scientific Computing
First-Order System Least Squares for Incompressible Resistive Magnetohydrodynamics
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Efficiency Based Adaptive Local Refinement for First-Order System Least-Squares Formulations
SIAM Journal on Scientific Computing
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
Hi-index | 31.52 |
Implicit time differencing of the resistive magnetohydrodynamic (MHD) equations can step over the limiting time scales--such as Alfvén time scales--to resolve the dynamic time scales of interest. However, nonlinearities present in these equations make an implicit implementation cumbersome. Here, viable paths for an implicit, nonlinear time integration of the MHD equations are explored using a 2D reduced viscoresistive MHD model. The implicit time integration is performed using the Newton-Raphson iterative algorithm, employing Krylov iterative techniques for the required algebraic matrix inversions, implemented Jacobian-free (i.e., without ever forming and storing the Jacobian matrix). Convergence in Krylov techniques is accelerated by preconditioning the initial problem. A "physics-based" preconditioner, based on a semi-implicit approximation to the original set of partial differential equations, is employed. The preconditioner employs low-complexity multigrid techniques to invert approximately the resulting elliptic algebraic systems. The resulting 2D reduced resistive MHD implicit algorithm is shown to be successful in dealing with large time steps (on the order of the dynamical time scale of the problem) and fine grids. The algorithm is second-order accurate in time and scalable under grid refinement. Comparison of the implicit CPU time with an explicit integration method demonstrates CPU savings even for moderate (64 × 64) grids, and close to an order of magnitude in fine grids (256 × 256).