A class of bases in L2 for the sparse representations of integral operators
SIAM Journal on Mathematical Analysis
The spectral element method for the shallow water equations on the sphere
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
A new class of time discretization schemes for the solution of nonlinear PDEs
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Adaptive solution of partial differential equations in multiwavelet bases
Journal of Computational Physics
Journal of Computational Physics
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Climate simulation will not grow to the ultrascale without new algorithms to overcome the scalability barriers blocking existing implementations. Until recently, climate simulations concentrated on the question of whether the climate is changing. The emphasis is now shifting to impact assessments, mitigation and adaptation strategies, and regional details. Such studies will require significant increases in spatial resolution and model complexity while maintaining adequate throughput. The barrier to progress is the resulting decrease in time step without increasing single-thread performance. In this paper we demonstrate how to overcome this time barrier for the first standard test defined for the shallow-water equations on a sphere. This paper explains how combining a multiwavelet discontinuous Galerkin method with exact linear part time-evolution schemes can overcome the time barrier for advection equations on a sphere. The discontinuous Galerkin method is a high-order method that is conservative, flexible, and scalable. The addition of multiwavelets to discontinuous Galerkin provides a hierarchical scale structure that can be exploited to improve computational efficiency in both the spatial and temporal dimensions. Exact linear part time-evolution schemes are explicit schemes that remain stable for implicit-size time steps.