Mathematics Graduate Students Organization

Seminar:

Date: November 13

We investigate methods of interpolation and approximation of scattered data in high dimensional spaces and on manifolds. A highly localized basis of functions constructed from radial basis functions is developed and applied to data interpolation, scattered data quadrature, and to the discretization of partial differential equations and integral equations. The basis, which may be constructed in parallel, offers optimal order convergence for interpolation and for scattered data quadrature. We discretize partial differential equations on manifolds and integral equations on domains arising from nonlocal diffusion problems. The acceleration of these methods by graphics processing units (GPUs) and CUDA is studied.