Spectral transform solutions to the shallow water test set
Journal of Computational Physics
Journal of Computational Physics
The spectral element method for the shallow water equations on the sphere
Journal of Computational Physics
Parallel Semi-Implicit Spectral Element Methods for Atmospheric General Circulation Models
Journal of Scientific Computing
Parallel Implementation Issues: Global versus Local Methods
Computing in Science and Engineering
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
International Journal of High Performance Computing Applications
The NCAR Spectral Element Climate Dynamical Core: Semi-Implicit Eulerian Formulation
Journal of Scientific Computing
Shallow water model on cubed-sphere by multi-moment finite volume method
Journal of Computational Physics
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
Nonlinear operator integration factor splitting for the shallow water equations
Applied Numerical Mathematics
Journal of Computational Physics
A Fully Implicit Domain Decomposition Algorithm for Shallow Water Equations on the Cubed-Sphere
SIAM Journal on Scientific Computing
A Prolate-Element Method for Nonlinear PDEs on the Sphere
Journal of Scientific Computing
Journal of Computational and Applied Mathematics
Nonlinear OIFS for a hybrid galerkin atmospheric model
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part III
High-Order finite element methods for parallel atmospheric modeling
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
CAM-SE: A scalable spectral element dynamical core for the Community Atmosphere Model
International Journal of High Performance Computing Applications
Semi-automatic sparse preconditioners for high-order finite element methods on non-uniform meshes
Journal of Computational Physics
Hermitian Compact Interpolation on the Cubed-Sphere Grid
Journal of Scientific Computing
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A semi-implicit spectral element shallow water model on the cubed-sphere is described and numerical results are compared with an explicit formulation and the traditional spectral transform method using the standard test cases proposed by Williamson et al. (1992). The explicit time step is limited by the phase speed of the fastest gravity waves. Semi-implicit time integration schemes remove this stability restriction but require the solution of an elliptic problem. A weak variational formulation of the governing equations leads to a symmetric Helmholtz operator. The resulting implicit problem for the geopotential is then solved using a block-Jacobi preconditioned conjugate gradient solver. The simulation rate of the semi-implicit model is accelerated relative to the explicit model for practical climate resolutions by a factor of two.