A Newton-Krylov-Multigrid Solver for Variably Saturated Flow Problems

Carol S. Woodward

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.