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We discuss the parallel implementation of a hybrid direct/iterative solver for a special class of saddle point matrices arising from the discretization of the steady Navier-Stokes equations on an Arakawa C-grid, the F-matrices. The two-level method described here has the following properties: (i) it is very robust, even at comparatively high Reynolds Numbers, (ii) a single parameter controls fill...
To understand the physics and dynamics of the ocean circulation, techniques of numerical bifurcation theory such as continuation methods have proved to be useful. Up to now these techniques have been applied to models with relatively few (O(105)) degrees of freedom such as multi-layer quasi-geostrophic and shallow-water models and relatively low-resolution (e.g., 4° horizontal resolution) primitive...
In this paper, we present a new linear system solver for use in a fully-implicit ocean model. The new solver allows to perform bifurcation analysis of relatively high-resolution primitive-equation ocean-climate models. It is based on a block-ILU approach and takes special advantage of the mathematical structure of the governing equations. In implicit models Jacobian matrices have to be constructed...
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