Fall 2014, Thursdays, Blocker 506A, 4:00-4:50 PM

Date: November 13

"  Meshfree Methods Using Localized Kernel Bases "
  Stephen Rowe  


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.