An implicit, nonlinear reduced resistive MHD solver
Journal of Computational Physics
An implicit particle-in-cell method for granular materials
Journal of Computational Physics
A 2D high-ß Hall MHD implicit nonlinear solver
Journal of Computational Physics
Journal of Computational Physics
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
A fully implicit, nonlinear adaptive grid strategy
Journal of Computational Physics
Journal of Computational Physics
Efficient nonlinear solvers for Laplace-Beltrami smoothing of three-dimensional unstructured grids
Computers & Mathematics with Applications
Journal of Computational Physics
Computers & Mathematics with Applications
Robust, multidimensional mesh-motion based on Monge-Kantorovich equidistribution
Journal of Computational Physics
Journal of Computational Physics
A Jacobian-free Newton Krylov method for mortar-discretized thermomechanical contact problems
Journal of Computational Physics
Generalized Monge-Kantorovich Optimization for Grid Generation and Adaptation in $L_{p}$
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
Hi-index | 0.06 |
We study multigrid preconditioning of matrix-free Newton--Krylov methods as a means of developing more efficient nonlinear iterative methods for large scale simulation. Newton--Krylov methods have proven dependable in solving nonlinear systems while not requiring the explicit formation or storage of the complete Jacobian. However, the standard algorithmic scaling of Krylov methods is nonoptimal, with increasing linear system dimension. This motivates our use of multigrid-based preconditioning. It is demonstrated that a simple multigrid-based preconditioner can effectively limit the growth of Krylov iterations as the dimension of the linear system is increased. Different performance aspects of the proposed algorithm are investigated on three nonlinear, nonsymmetric, boundary value problems. Our goal is to develop a hybrid methodology which has Newton--Krylov nonlinear convergence properties and multigrid-like linear convergence scaling for large scale simulation.