A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
Spectral transform solutions to the shallow water test set
Journal of Computational Physics
Choosing the forcing terms in an inexact Newton method
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Journal of Computational Physics
A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems
SIAM Journal on Scientific Computing
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Journal of Computational Physics
A Fully Implicit Domain Decomposition Algorithm for Shallow Water Equations on the Cubed-Sphere
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
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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.