TY - JOUR
T1 - A Guide to RBF-Generated Finite Differences for Nonlinear Transport
T2 - Shallow Water Simulations on a Sphere
AU - Flyer, Natasha
AU - Lehto, Erik
AU - Blaise, Sébastien
AU - Wright, Grady
AU - St-Cyr, Amik
PY - 2012/6/1
Y1 - 2012/6/1
N2 - 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. In Appendix A, guidelines are given on how to chose parameters when using RBF-FD to solve hyperbolic PDEs.
AB - 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. In Appendix A, guidelines are given on how to chose parameters when using RBF-FD to solve hyperbolic PDEs.
KW - Finite differences
KW - Hyperbolic PDEs
KW - Radial basis functions
KW - RBF
KW - RBF-FD
KW - Spherical geometry
UR - http://www.scopus.com/inward/record.url?scp=84859212233&partnerID=8YFLogxK
UR - https://scholarworks.boisestate.edu/math_facpubs/95
U2 - 10.1016/j.jcp.2012.01.028
DO - 10.1016/j.jcp.2012.01.028
M3 - Article
SN - 0021-9991
VL - 231
SP - 4078
EP - 4095
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - 11
ER -