Semi-implicit method for long time scale magnetohydrodynamic computations in three dimensions
Journal of Computational Physics
Any Nonincreasing Convergence Curve is Possible for GMRES
SIAM Journal on Matrix Analysis and Applications
Iterative methods for solving linear systems
Iterative methods for solving linear systems
Journal of Computational Physics
A solution-adaptive upwind scheme for ideal magnetohydrodynamics
Journal of Computational Physics
An implicit, nonlinear reduced resistive MHD solver
Journal of Computational Physics
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Globalized Newton-Krylov-Schwarz Algorithms and Software for Parallel Implicit CFD
International Journal of High Performance Computing Applications
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
Newton-Krylov-FAC methods for problems discretized on locally refined grids
Computing and Visualization in Science
A fully implicit numerical method for single-fluid resistive magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
Implicit adaptive mesh refinement for 2D reduced resistive magnetohydrodynamics
Journal of Computational Physics
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
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We introduce an operator-based scheme for preconditioning stiff components encountered in implicit methods for hyperbolic systems of PDEs posed on regular grids. The method is based on a directional splitting of the implicit operator, followed by a characteristic decomposition of the resulting directional parts. This approach allows for the solution of any number of characteristic components, from the entire system to only the fastest, stiffness-inducing waves. We apply the preconditioning method to stiff hyperbolic systems arising in magnetohydrodynamics and gas dynamics. We then present numerical results showing that this preconditioning scheme works well on problems where the underlying stiffness results from the interaction of fast transient waves with slowly-evolving dynamics, scales well to large problem sizes and numbers of processors, and allows for additional customization based on the specific problems under study.