GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Numerical grid generation: foundations and applications
Numerical grid generation: foundations and applications
ACM Transactions on Mathematical Software (TOMS)
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
An adaptive grid with directional control
Journal of Computational Physics
Choosing the forcing terms in an inexact Newton method
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Efficient management of parallelism in object-oriented numerical software libraries
Modern software tools for scientific computing
Enhanced Nonlinear Iterative Techniques Applied to a Nonequilibrium Plasma Flow
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
Conjugate gradient methods for partial differential equations.
Conjugate gradient methods for partial differential equations.
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
A Computational Differential Geometry Approach to Grid Generation (Scientific Computation)
A Computational Differential Geometry Approach to Grid Generation (Scientific Computation)
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Computational Methods in Plasma Physics
Computational Methods in Plasma Physics
Robust, multidimensional mesh-motion based on Monge-Kantorovich equidistribution
Journal of Computational Physics
Hi-index | 31.45 |
Numerical simulations of the four-field extended magnetohydrodynamics (MHD) equations with hyper-resistivity terms present a difficult challenge because of demanding spatial resolution requirements. A time-dependent sequence of r-refinement adaptive grids obtained from solving a single Monge-Ampere (MA) equation addresses the high-resolution requirements near the x-point for numerical simulation of the magnetic reconnection problem. The MHD equations are transformed from Cartesian coordinates to solution-defined curvilinear coordinates. After the application of an implicit scheme to the time-dependent problem, the parallel Newton-Krylov-Schwarz (NKS) algorithm is used to solve the system at each time step. Convergence and accuracy studies show that the curvilinear solution requires less computational effort than a pure Cartesian treatment. This is due both to the more optimal placement of the grid points and to the improved convergence of the implicit solver, nonlinearly and linearly. The latter effect, which is significant (more than an order of magnitude in number of inner linear iterations for equivalent accuracy), does not yet seem to be widely appreciated.