An Acceleration Procedure for the Spectral Element Ocean Model Formulation of the Shallow Water Equations

We develop an overlapping block preconditioner based on an additive Schwarz method for preconditioning the system of equations arising from discretizing the shallow water equations using the spectral ocean element method approach. The system is complicated by being sparse, but having a very large number of nonzeroes in any row of the matrix, which is never stored. The resulting coupled system of equations will be reduced to a Schur complement system with a special structure of the Schur complement. A major section of the computation is shown to be speeded up by a factor of approximately 3, independent of the number of processors used (within reason).