Applied Math Colloquium: Sean Carney
Wednesday, January 31, 2024 · 12 - 1 PM
Title: Far-fields, laws of the wall, and addressing system uncertainties
Speaker: Sean Carney (George Mason University)
Abstract: The direct numerical simulation of many problems in science and engineering that exhibit a wide range of active spatiotemporal scales is prohibitively expensive. As a result, specially designed, multiscale numerical methods are needed. This is especially true, for example, for optimal control problems and for problems that contain uncertainties in system parameters. The differential equations that describe multiscale physical systems generically require boundary conditions (BCs) to be well-posed (i.e. for their solutions to exist and to be unique); however, multiscale numerical methods typically require additional, artificial computational BCs for well-posedness. Developing and analyzing such computational BCs can lead to many intriguing mathematical questions related to their accuracy and stability, as well as the computational efficiency that they afford. In this talk we explore how and where these computational BCs arise, we discuss their implications for solving stochastic optimization problems.
