Friday,
March 30, 12:00 p.m. GWC 487
Grady Wright
Boise State University
A high-order kernel method for partial differential equations on surfaces
Abstract
Kernel methods such as those based on radial basis functions (RBFs)
are becoming increasingly popular for numerically solving partial
differential equations (PDEs) because they are geometrically flexible,
algorithmically accessible, and can be highly accurate. There have
been many successful applications of these techniques to various types
of PDEs defined on planar regions in two and higher dimensions, and
more recently to PDEs defined on the surface of a sphere. In this talk
we describe a kernel method based on RBFs for numerically solving PDEs
defined on more general surfaces, specifically on smooth surfaces
embedded in R^3 with no boundary. We describe the accuracy and
stability of the method and its application to certain biologically
relevant, non-linear reaction diffusion equations on various surfaces.
