Past Event: Oden Institute Seminar

The entropic finite element method

Prof. Brendan Keith, Brown University

Abstract

A great challenge in finite element analysis is developing a stable, high-order Galerkin method that strictly enforces pointwise bound constraints. The entropic finite element method (EFEM) is a nonlinear, structure-preserving method with these properties. This talk will introduce EFEM and describe its capabilities for treating free-boundary problems, enforcing discrete maximum principles, and designing scalable, mesh-independent algorithms for inverse design. The overall methodology combines ideas from nonlinear programming, functional analysis, and differential geometry and can potentially lead to new synergies among these areas. This talk and the companion paper written with Thomas Surowiec are dedicated to Leszek.

Biography

Brendan Keith is an Assistant Professor in the Division of Applied Mathematics at Brown University in Providence, Rhode Island. His research interests mainly relate to modeling, predicting, and designing 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. He has held postdoctoral positions at TU Munich, ICERM, and Lawrence Livermore National Laboratory.