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{\large Carol Woodward \\
{\bf Introducing Multilevel Preconditioning to an Existing Variably Saturated Subsurface Flow Code}}

P O Box 808 \\ L-561 \\ Livermore \\ CA 94551
\\
{\tt cswoodward@llnl.gov}\\
Daniel Osei-Kuffuor\\
Glenn Hammond\end{center}

Variably saturated subsurface flow is modeled with a scalar, highly
nonlinear equation. After spatial and temporal discretization, the
nonlinearities in this equation are often solved by application of
Newton's method within each time step. For large-scale problems, the
Newton method is combined with a preconditioned Krylov method for
solution of the linear systems within each nonlinear iteration. In this
talk, we discuss both software and mathematical issues related to
transitioning the variably saturated flow module within the PNNL
subsurface simulation code, STOMP, from use of a block ILU preconditioner
to use of a multigrid preconditioner. Results related to tuning the
multigrid preconditioner will be shown as well as weak scaling studies.


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