Semi-implicit method for long time scale magnetohydrodynamic computations in three dimensions
Journal of Computational Physics
VODE: a variable-coefficient ODE solver
SIAM Journal on Scientific and Statistical Computing
Hybrid Krylov methods for nonlinear systems of equations
SIAM Journal on Scientific and Statistical Computing
An implicit scheme for nonideal magnetohydrodynamics
Journal of Computational Physics
A solution-adaptive upwind scheme for ideal magnetohydrodynamics
Journal of Computational Physics
A Polyalgorithm for the Numerical Solution of Ordinary Differential Equations
ACM Transactions on Mathematical Software (TOMS)
An Alternative Implementation of Variable Step-Size Multistep Formulas for Stiff ODEs
ACM Transactions on Mathematical Software (TOMS)
Application of parallel implicit methods to edge-plasma numerical simulations
Journal of Computational Physics
An implicit, nonlinear reduced resistive MHD solver
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
Nonlinear magnetohydrodynamics simulation using high-order finite elements
Journal of Computational Physics
Journal of Computational Physics
Globalized Newton-Krylov-Schwarz Algorithms and Software for Parallel Implicit CFD
International Journal of High Performance Computing Applications
Journal of Computational Physics
An unsplit Godunov method for ideal MHD via constrained transport
Journal of Computational Physics
SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Journal of Computational Physics
ELLAM for resolving the kinematics of two-dimensional resistive magnetohydrodynamic flows
Journal of Computational Physics
An iterative semi-implicit scheme with robust damping
Journal of Computational Physics
Short Note: ADI-SGS scheme on ideal magnetohydrodynamics
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
A finite volume spectral element method for solving magnetohydrodynamic (MHD) equations
Applied Numerical Mathematics
Operator-Based Preconditioning of Stiff Hyperbolic Systems
SIAM Journal on Scientific Computing
A Fully Implicit Domain Decomposition Algorithm for Shallow Water Equations on the Cubed-Sphere
SIAM Journal on Scientific Computing
Review of implicit methods for the magnetohydrodynamic description of magnetically confined plasmas
Journal of Computational Physics
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
Hi-index | 31.49 |
We present a nonlinearly implicit, conservative numerical method for integration of the single-fluid resistive MHD equations. The method uses a high-order spatial discretization that preserves the solenoidal property of the magnetic field. The fully coupled PDE system is solved implicitly in time, providing for increased interaction between physical processes as well as additional stability over explicit-time methods. A high-order adaptive time integration is employed, which in many cases enables time steps ranging from one to two orders of magnitude larger than those constrained by the explicit CFL condition. We apply the solution method to illustrative examples relevant to stiff magnetic fusion processes which challenge the efficiency of explicit methods. We provide computational evidence showing that for such problems the method is comparably accurate with explicit-time simulations, while providing a significant runtime improvement due to its increased temporal stability.