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{\large Dana Knoll \\
{\bf Physics-based Preconditioning of JFNK for Free-surface Ocean Modeling}}

Los Alamos National Laboratory \\ PO BOX 1663 \\ MS B216 \\ Los Alamos \\ NM 87545
\\
{\tt nol@lanl.gov}\\
Samet Kadioglu\\
Wilbert Weijer\end{center}

Global ocean model equation systems contain a variety of normal modes and thus
a variety of time-scales. The 3-D hydrostatic free-surface model with
salinity and temperature contains: external gravity waves and Rossby
waves, internal gravity waves and Rossby waves, dissipation, and
advection. The Parallel Ocean Program (POP) uses knowledge of these
various normal modes to execute an operator split, semi-implicit, time
integration of this system. There is motivation to develop a fully
implicit, unsplit, version of POP, imPOP. The JFNK method
is currently used for the nonlinear solution required at each time step.

In this study we consider a reduced 2-D hydrostatic system of three
equations for surface height, horizontal momentum, and temperature. This
system contains external and internal gravity waves, dissipation, and
advection. We develop and study operator split semi-implicit methods as a
preconditioner to JFNK. These preconditioners are developed from the
normal mode time scale knowledge embedded within the current POP time
integration process.


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