A multigrid preconditioned Newton-Krylov method

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 n onlinear systems while not requiring the explicit formation or storage of t he complete Jacobian. However, the standard algorithmic scaling of Krylov m ethods is nonoptimal, with increasing linear system dimension. This motivat es our use of multigrid-based preconditioning. It is demonstrated that a si mple multigrid-based preconditioner can effectively limit the growth of Kry lov iterations as the dimension of the linear system is increased. Differen t performance aspects of the proposed algorithm are investigated on three n onlinear, nonsymmetric, boundary value problems. Our goal is to develop a h ybrid methodology which has Newton-Krylov nonlinear convergence properties and multigrid-like linear convergence scaling for large scale simulation.