Semi-implicit method for long time scale magnetohydrodynamic computations in three dimensions
Journal of Computational Physics
Semi-implicit magnetohydrodynamic calculations
Journal of Computational Physics
Accurate semi-implicit treatment of the hall effect in magnetohydrodynamic computations
Journal of Computational Physics
Derivation of implicit difference schemes by the method of differential approximation
Journal of Computational Physics
Iterative solution methods
Implicit-explicit methods for time-dependent partial differential equations
SIAM Journal on Numerical Analysis
Stability of algorithms for waves with large flows
Journal of Computational Physics
An implicit, nonlinear reduced resistive MHD solver
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
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
The behaviour of the local error in splitting methods applied to stiff problems
Journal of Computational Physics
A Technique for Accelerating the Convergence of Restarted GMRES
SIAM Journal on Matrix Analysis and Applications
Jacobian---Free Newton---Krylov Methods for the Accurate Time Integration of Stiff Wave Systems
Journal of Scientific Computing
Journal of Computational Physics
A fully implicit numerical method for single-fluid resistive magnetohydrodynamics
Journal of Computational Physics
Analysis of a mixed semi-implicit/implicit algorithm for low-frequency two-fluid plasma modeling
Journal of Computational Physics
Review of implicit methods for the magnetohydrodynamic description of magnetically confined plasmas
Journal of Computational Physics
Hi-index | 31.46 |
An efficient, iterative semi-implicit (SI) numerical method for the time integration of stiff wave systems is presented. Physics-based assumptions are used to derive a convergent iterative formulation of the SI scheme which enables the monitoring and control of the error introduced by the SI operator. This iteration essentially turns a semi-implicit method into a fully implicit method. Accuracy, rather than stability, determines the timestep. The scheme is second order accurate and shown to be equivalent to a simple preconditioning method. We show how the diffusion operators can be handled so as to yield the property of robust damping, i.e. dissipating the solution at all values of the parameter D@Dt, where D is a diffusion operator and @Dt the timestep. The overall scheme remains second order accurate even if the advection and diffusion operators do not commute. In the limit of no physical dissipation, and for a linear test wave problem, the method is shown to be symplectic. The method is tested on the problem of Kinetic Alfven wave mediated magnetic reconnection. A Fourier (pseudo-spectral) representation is used. A two-field gyrofluid model is used and an efficacious k-space SI operator for this problem is demonstrated. CPU speed-up factors over a CFL-limited explicit algorithm ranging from ~20 to several hundreds are obtained, while accurately capturing the results of an explicit integration. Possible extension of these results to a real-space (grid) discretization is discussed.