Globally convergent Newton methods for nonsmooth equations
Mathematics of Operations Research
A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Convergence analysis of some algorithms for solving nonsmooth equations
Mathematics of Operations Research
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
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
The spectral element method for the shallow water equations on the sphere
Journal of Computational Physics
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
High-performacne parallel implicit CFD
Parallel Computing - Special issue on parallel computing in aerospace
Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations
Journal of Computational Physics
Semi-Implicit Spectral Element Atmospheric Model
Journal of Scientific Computing
Journal of Computational Physics
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Convergence analysis of additive Schwarz for the Euler equations
Applied Numerical Mathematics
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
Nonlinear operator integration factor splitting for the shallow water equations
Applied Numerical Mathematics
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
Finite-volume transport on various cubed-sphere grids
Journal of Computational Physics
Shallow water model on cubed-sphere by multi-moment finite volume method
Journal of Computational Physics
A Fully Implicit Jacobian-Free High-Order Discontinuous Galerkin Mesoscale Flow Solver
ICCS 2009 Proceedings of the 9th International Conference on Computational Science
A Scalable and Adaptable Solution Framework within Components of the Community Climate System Model
ICCS 2009 Proceedings of the 9th International Conference on Computational Science
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
Journal of Computational Physics
A peta-scalable CPU-GPU algorithm for global atmospheric simulations
Proceedings of the 18th ACM SIGPLAN symposium on Principles and practice of parallel programming
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High resolution and scalable parallel algorithms for the shallow water equations on the sphere are very important for modeling the global climate. In this paper, we introduce and study some highly scalable multilevel domain decomposition methods for the fully implicit solution of the nonlinear shallow water equations discretized with a second-order well-balanced finite volume method on the cubed-sphere. With the fully implicit approach, the time step size is no longer limited by the stability condition, and with the multilevel preconditioners, good scalabilities are obtained on computers with a large number of processors. The investigation focuses on the use of semismooth inexact Newton method for the case with nonsmooth topography and the use of two- and three-level overlapping Schwarz methods with different order of discretizations for the preconditioning of the Jacobian systems. We test the proposed algorithm for several benchmark cases and show numerically that this approach converges well with smooth and nonsmooth bottom topography, and scales perfectly in terms of the strong scalability and reasonably well in terms of the weak scalability on machines with thousands and tens of thousands of processors.