Applied Seminar: Dr. Mauro Perego
Dr. Mauro Perego
Monday, September 23, 2019 -
3:30pm to 4:30pm
Title: Generalized Moving Least Squares: Advances in Approximation Theory and Applications
Authors: M. Perego, P. Bochev, P. Kuberry, K. Peterson, N. Trask
In this talk we present existence and approximation results for the reconstruction of a few classes of linear functionals, including differential and integral functionals, using the Generalized Moving Least Square (GMLS) method. These results extend or specialize classical MLS theoretical results, and rely both on the classic approximation theory for finite elements and on existence/approximation results for scattered data. In particular, we will consider the reconstruction of vector fields in Sobolev spaces and the reconstruction of differential k-forms. We show how these results can be applied to data transfer problems, operator learning problems and to design collocation and variational meshless schemes for the solution of partial differential equations.