An implicit, nonlinear reduced resistive MHD solver
Journal of Computational Physics
A parallel block multi-level preconditioner for the 3D incompressible Navier--Stokes equations
Journal of Computational Physics
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
A comparison of implicit time integration methods for nonlinear relaxation and diffusion
Journal of Computational Physics
High order accurate solution of the incompressible Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
Jacobian---Free Newton---Krylov Methods for the Accurate Time Integration of Stiff Wave Systems
Journal of Scientific Computing
Journal of Computational Physics
Development of a 2-D algorithm to simulate convection and phase transition efficiently
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A monolithic FEM-multigrid solver for non-isothermal incompressible flow on general meshes
Journal of Computational Physics
Journal of Computational Physics
Computers & Mathematics with Applications
Robust, multidimensional mesh-motion based on Monge-Kantorovich equidistribution
Journal of Computational Physics
Predictor-Corrector preconditioned newton-krylov method for cavity flow
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
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Globalized inexact Newton methods are well suited for solving large-scale systems of nonlinear equations. When combined with a Krylov iterative method, an explicit Jacobian is never needed, and the resulting matrix-free Newton--Krylov method greatly simplifies application of the method to complex problems. Despite asymptotically superlinear rates of convergence, the overall efficiency of a Newton--Krylov solver is determined by the preconditioner. High-quality preconditioners can be constructed from methods that incorporate problem-specific information, and for the incompressible Navier--Stokes equations, classical pressure-correction methods such as SIMPLE and SIMPLER fulfill this requirement. A preconditioner is constructed by using these pressure-correction methods as smoothers in a linear multigrid procedure. The effectiveness of the resulting Newton--Krylov-multigrid method is demonstrated on benchmark incompressible flow problems.