Speaker: Brendan Keith (Brown University)
Time:
Thursday, August 22, 2024: 2:00 PM - 3:00 PM
Friday, August 23, 2024: 2:00 PM - 3:00 PM
Place: Room 615 (ASTC)
Title: Proximal Galerkin: A Structure-Preserving Finite Element Method for Pointwise Bound Constraints
Abstract:
The proximal Galerkin finite element method is a high-order, low iteration complexity, nonlinear numerical method for solving variational inequalities that arise from pointwise bound constraints in infinite-dimensional function spaces. The first talk in this series will introduce the proximal Galerkin method and demonstrate how it preserves the geometric and algebraic structure of pointwise bound constraints, leading to robust, mesh-independent algorithms to solve free boundary and optimal design problems. The second talk will focus on the mathematical theory developed to understand the Proximal Galerkin method. As the audience will see, new mathematical techniques are required to understand this finite element method.
This series of talks is mainly based on [1] but will include new results and applications.
[1] B. Keith, T.M. Surowiec. Proximal Galerkin: A structure-preserving finite element method for pointwise bound constraints. Foundations of Computational Mathematics (to appear), 2024.
Bio:
Brendan Keith is the Morton E. Gurtin Assistant Professor of Applied Mathematics in the Division of Applied Mathematics at Brown University in Providence, Rhode Island. His research mainly relates to modeling, predicting, and optimizing for events arising in natural sciences and engineering, focusing on numerical methods for partial differential equations, scientific machine learning, and PDE-constrained optimization. In 2018, Brendan received his Ph.D. in Computational Science, Engineering, and Mathematics from the Oden Institute for Computational Engineering and Sciences at the University of Texas at Austin. Before Brown, he held postdoctoral positions at TU Munich, ICERM, and Lawrence Livermore National Laboratory. Most recently, he was awarded a 2023 US DOE Office of Science Early Career Research Award and featured in Popular Science Magazine's 2023 ``Brilliant 10'' list of early career researchers.