Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Using MPI: portable parallel programming with the message-passing interface
Using MPI: portable parallel programming with the message-passing interface
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Parallel Newton--Krylov--Schwarz Algorithms for the Transonic Full Potential Equation
SIAM Journal on Scientific Computing
An adaptive finite element method for magnetohydrodynamics
Journal of Computational Physics
A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems
SIAM Journal on Scientific Computing
An implicit, nonlinear reduced resistive MHD solver
Journal of Computational Physics
Nonlinearly Preconditioned Inexact Newton Algorithms
SIAM Journal on Scientific Computing
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
Journal of Computational Physics
Journal of Computational Physics
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
A fully implicit numerical method for single-fluid resistive magnetohydrodynamics
Journal of Computational Physics
ICCS '09 Proceedings of the 9th International Conference on Computational Science: Part I
Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods
Journal of Computational Physics
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
Hi-index | 31.46 |
A parallel, fully coupled, nonlinearly implicit Newton-Krylov-Schwarz algorithm is proposed for the numerical simulation of a magnetic reconnection problem described by a system of resistive Hall magnetohydrodynamics equations in slab geometry. A key component of the algorithm is a restricted additive Schwarz preconditioner defined for problems with doubly periodic boundary conditions. We show numerically that with such a preconditioned nonlinearly implicit method the time step size is no longer constrained by the CFL number or the convergence of the Newton solver. We report the parallel performance of the algorithm and software on machines with thousands of processors.