Semi-implicit method for long time scale magnetohydrodynamic computations in three dimensions
Journal of Computational Physics
3D nonlinear MHD calculations using implicit and explicit time integration schemes
Journal of Computational Physics
Semi-implicit magnetohydrodynamic calculations
Journal of Computational Physics
Compressible linear and nonlinear resistive MHD calculations in toroidal geometry
Journal of Computational Physics
Derivation of implicit difference schemes by the method of differential approximation
Journal of Computational Physics
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
An implicit scheme for nonideal magnetohydrodynamics
Journal of Computational Physics
NITSOL: A Newton Iterative Solver for Nonlinear Systems
SIAM Journal on Scientific Computing
Stability of algorithms for waves with large flows
Journal of Computational Physics
Fluctuation effects on 3D Lagrangian mean and Eulerian mean fluid motion
Physica D - Special issue originating from the 18th Annual International Conference of the Center for Nonlinear Studies, Los Alamos, NM, May 11&mdash ;15, 1998
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
Nonlinear magnetohydrodynamics simulation using high-order finite elements
Journal of Computational Physics
A triangular finite element with first-derivative continuity applied to fusion MHD applications
Journal of Computational Physics
Modelling of heat transport in magnetised plasmas using non-aligned coordinates
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
Journal of Computational Physics
An iterative semi-implicit scheme with robust damping
Journal of Computational Physics
The XTOR code for nonlinear 3D simulations of MHD instabilities in tokamak plasmas
Journal of Computational Physics
Bézier surfaces and finite elements for MHD simulations
Journal of Computational Physics
Calculations of two-fluid magnetohydrodynamic axisymmetric steady-states
Journal of Computational Physics
On the partial difference equations of mathematical physics
IBM Journal of Research and Development
Accurate semi-implicit treatment of the Hall effect in magnetohydrodynamic computations
Journal of Computational Physics
Analysis of a mixed semi-implicit/implicit algorithm for low-frequency two-fluid plasma modeling
Journal of Computational Physics
Toward textbook multigrid efficiency for fully implicit resistive magnetohydrodynamics
Journal of Computational Physics
Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods
Journal of Computational Physics
XTOR-2F: A fully implicit Newton-Krylov solver applied to nonlinear 3D extended MHD in tokamaks
Journal of Computational Physics
Computational Methods in Plasma Physics
Computational Methods in Plasma Physics
Operator-Based Preconditioning of Stiff Hyperbolic Systems
SIAM Journal on Scientific Computing
Hi-index | 31.45 |
Implicit algorithms are essential for predicting the slow growth and saturation of global instabilities in today's magnetically confined fusion plasma experiments. Present day algorithms for obtaining implicit solutions to the magnetohydrodynamic (MHD) equations for highly magnetized plasma have their roots in algorithms used in the 1960s and 1970s. However, today's computers and modern linear and non-linear solver techniques make practical much more comprehensive implicit algorithms than were previously possible. Combining these advanced implicit algorithms with highly accurate spatial representations of the vector fields describing the plasma flow and magnetic fields and with improved methods of calculating anisotropic thermal conduction now makes possible simulations of fusion experiments using realistic values of plasma parameters and actual configuration geometry. This article is a review of these developments.