Center for Applied Scientific Computing

Lawrence Livermore National Laboratory

P.O. Box 808, L-561

Livermore, CA 94551

Abstract

We will describe a Newton-Krylov-multigrid solver for Richards' equation, a nonlinear parabolic partial differential equation modeling variably saturated groundwater flow. Discretization of Richards' equation leads to a large, coupled system of nonlinear equations which must be solved at each timestep.

Our solver uses a globalized, inexact Newton method for linearization, the restarted form of GMRES as the linear Jacobian system solver and the symmetric part of the Jacobian with a multigrid solver as a preconditioner. Parallel scalability studies for the entire nonlinear solution process will be presented.