Preconditioning of linear systems in an ocean flow model

The climate is largely determined by the ocean flow, which in itself is driven by wind and by gradients in temperature and salinity. Nowadays numerical models exist that are able to describe the occurring phenomena not only qualitatively but also quantitatively. At the Institute for Marine and Atmospheric research Utrecht (IMAU) a so-called thermohaline circulation model is developed in which methods of dynamical systems theory are used to study the stability of ocean flows. Here bifurcation diagrams are constructed by varying the strength of the forcing, for instance the amount of fresh water coming in from the north due to melting. For every value of the strength we have to solve a nonlinear system, which is handled by a Newton-type method. This produces many linear systems to be solved. 

In the talk the following will be addressed: the form of the system of equations, a special purpose method which uses Trilinos and MRILU. The latter is a multilevel ILU preconditioner developed at Groningen University. Results of the approach obtained on the Dutch national supercomputer will be shown.