Abstract
The scalability of a fully implicit global shallow water solver is studied in this paper. In the solver a conservative second-order finite volume scheme is used to discretize the shallow water equations on a cubed-sphere mesh which is free of pole-singularities. Instead of using the popular explicit or semi-implicit methods in climate modeling, we employ a fully implicit method so that the restrictions on the time step size can be greatly relaxed. Newton-Krylov-Schwarz method is then used to solve the nonlinear system of equations at each time step. Within each Newton iteration, the linear Jacobian system is solved by using a Krylov subspace method preconditioned with a Schwarz method. To further improve the scalability of the algorithm, we use multilevel hybrid Schwarz preconditioner to suppress the increase of the iteration number as the mesh is refined or more processors are used. We show by numerical experiments on the Rossby-Haurwitz problem that the fully implicit solver scales well to thousands of processors on an IBM BlueGene/L supercomputer.
This research was supported in part by DOE under DE-FC-02-06ER25784, in part by NSF under EAR 0934647 and DMS 0913089, in part by NSFC under 10801125 and in part by 863 program of China under 2010AA012300.
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Yang, C., Cai, XC. (2011). Scalability Studies of an Implicit Shallow Water Solver for the Rossby-Haurwitz Problem. In: Palma, J.M.L.M., Daydé, M., Marques, O., Lopes, J.C. (eds) High Performance Computing for Computational Science – VECPAR 2010. VECPAR 2010. Lecture Notes in Computer Science, vol 6449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19328-6_18
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DOI: https://doi.org/10.1007/978-3-642-19328-6_18
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