Abstract
The chapter discusses the parallel atmospheric modeling with high-order continuous and discontinuous Galerkin methods. The chapter reviews high-order finite element methods for the atmospheric shallow water equations. The accuracy and efficiency of nodal continuous and discontinuous Galerkin spectral elements are evaluated using standard test problems proposed by Williamson et al. The relative merits of strong-stability preserving (SSP) explicit Runge–Kutta and multistep time discretizations are discussed in the chapter. Distributed memory MPI implementations are compared on the basis of the total computation time required, sustained performance, and parallel scalability. Because a discontinuous Galerkin method permits the overlap of computation and communication, higher sustained execution rates are possible at large processor counts. The discontinuous Oalerkin method converges exponentially for smooth solutions, and standard error metrics compare favorably with the continuous Galerkin spectral element model.
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