Friday,
March 25, 12:00 p.m. PSA 113
Jordan Martel
School of Mathematical and Statistical Sciences
Radial Basis Function Methods for Time-Dependent Problems on the Sphere
Abstract
Radial Basis Function Pseudo-Spectral (RBF-PS) methods have become a popular
alternative to traditional Fourier and Chebyshev spectral methods in the
numerical solution of PDEs, particularly in non-standard geometries.
Although RBF-PS methods demonstrate many of the desirable accuracy
properties of traditional spectral methods, they often suffer from severe
instabilies when solving time-dependent problems. Here, we examine how the
flatness of the radial basis functions and the choice of square or
least-square collocation schemes affects the stability of these methods in
the context of time-dependent problems on the sphere. The linear advection
equation and non-linear barotropic vorticity equation are used to study
performance. We conclude that a least-squares collocation scheme using
moderately flat basis functions results in the most desirable stability
properties.
