Domain decomposition algorithms with small overlap
SIAM Journal on Scientific Computing
A positive finite-difference advection scheme
Journal of Computational Physics
Journal of Computational Physics
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Parallel Newton--Krylov--Schwarz Algorithms for the Transonic Full Potential Equation
SIAM Journal on Scientific Computing
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems
SIAM Journal on Scientific Computing
Spatial discretization of the Shallow water equations in spherical geometry using Osher's scheme
Journal of Computational Physics
Semi-Implicit Spectral Element Atmospheric Model
Journal of Scientific Computing
On balanced approximations for time integration of multiple time scale systems
Journal of Computational Physics
Journal of Computational Physics
A Schwarz Preconditioner for the Cubed-Sphere
SIAM Journal on Scientific Computing
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Studies on the accuracy of time-integration methods for the radiation-diffusion equations
Journal of Computational Physics
A comparison of implicit time integration methods for nonlinear relaxation and diffusion
Journal of Computational Physics
Towards an Efficient and Scalable Discontinuous Galerkin Atmospheric Model
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 13 - Volume 14
Journal of Computational Physics
Journal of Computational Physics
International Journal of High Performance Computing Applications
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
A wave propagation method for hyperbolic systems on the sphere
Journal of Computational Physics
Journal of Computational Physics
A fully implicit numerical method for single-fluid resistive magnetohydrodynamics
Journal of Computational Physics
High-order Galerkin methods for scalable global atmospheric models
Computers & Geosciences
A spectral finite volume transport scheme on the cubed-sphere
Applied Numerical Mathematics
Journal of Computational Physics
Finite-volume transport on various cubed-sphere grids
Journal of Computational Physics
Optimized Schwarz methods with an overset grid for the shallow-water equations: preliminary results
Applied Numerical Mathematics
Shallow water model on cubed-sphere by multi-moment finite volume method
Journal of Computational Physics
Journal of Computational Physics
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Popular approaches for solving shallow water equations (SWEs) for climate modeling are explicit and semiimplicit methods, and both have certain constraints on the time step size. In this paper, we propose and study a fully implicit method which imposes no limit on the time step size but requires the solution of a large sparse nonlinear system of equations at every time step. The focus of the paper is a parallel, fully coupled, Newton-Krylov-RAS algorithm with a Jacobian matrix explicitly calculated on a weakly nonmatching cubed-sphere mesh. Here, RAS is a restricted additive Schwarz method. We show numerically that with such a preconditioned, nonlinearly implicit method the time step size is no longer constrained by the CFL condition, and we report superlinear speedup of the algorithm on machines with thousands of processors for problems with smooth and nonsmooth solutions.