We simulate the wind driven circulation in oceans. Our aim is to study the impact of short scale wind forcing on the oceanic circulation. We use the isopycnal version of the Spectral Element Ocean Model (SEOM). The modeling of these flows and their climatic impact is complicated by the inherent range of spatial scales involved, which extend from the global scale of O(10,000) km down to the local scale of O(1) km, and by the intrinsic three dimensionality of the dynamics.
SEOM offers an elegant solution to these difficulties. It features advanced algorithms, based on h-p type finite element methods, allowing accurate representation of complex coastline and oceanic bathymetry, variable lateral resolution, and high order solution of the three dimensional oceanic equations of motion.
SEOM's geometrical flexibility permits highly inhomogeneous horizontal grids. An added advantage of the technique is its scalability. Most of the computations are carried out at the element level; only interface information needs to be exchanged between elements. The dual characteristic of dense and structured local computations, and sparse and unstructured communication enhances the locality of the computations. The dual characteristic of dense and structured local computations, and sparse and unstructured communication enhances the locality of the computations, and makes SEOM ideally suited for parallel computers.
In this talk, we define a novel set of techniques that allow us to store relevant matrices for 1/200-th the normal amount that would be expected using normal sparse matrix techniques. A combination of a Schur complement and a parallel algebraic multigrid method is described and compared to a traditional matrix-free preconditioned conjugate gradient solution methodolgy.