@TechReport{	  it:2011-020,
  author	= {Natasha Flyer and Erik Lehto and S{\'e}bastien Blaise and
		  Grady B. Wright and Amik St-Cyr},
  title		= {{RBF}-Generated Finite Differences for Nonlinear Transport
		  on a Sphere: Shallow Water Simulations},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2011},
  number	= {2011-020},
  month		= sep,
  abstract	= {The current paper establishes the computational efficiency
		  and accuracy of the RBF-FD method for large-scale
		  geoscience modeling with comparisons to state-of-the-art
		  methods as high-order discontinuous Galerkin and spherical
		  harmonics, the latter using expansions with close to
		  300,000 bases. The test cases are demanding fluid flow
		  problems on the sphere that exhibit numerical challenges,
		  such as Gibbs phenomena, sharp gradients, and complex
		  vortical dynamics with rapid energy transfer from large to
		  small scales over short time periods. The computations were
		  possible as well as very competitive due to the
		  implementation of hyperviscosity on large RBF stencil sizes
		  (corresponding roughly to 6th to 9th order methods) with up
		  to O($10^5$) nodes on the sphere. The RBF-FD method scaled
		  as O($N$) per time step, where $N$ is the total number of
		  nodes on the sphere.}
}