Past Event: Oden Institute Seminar

Structure-preserving finite-element schemes for coupled hyperbolic systems

Prof. Matthias Maier, Associate Professor in the Department of Mathematics at Texas A&M

Abstract

Structure preserving numerical methods provide theoretical guarantees of reliability for situations where ad-hoc stabilization techniques can fail. In this talk we present fully discrete approximation techniques for coupled hyperbolic systems. The schemes are structure preserving in the sense that it maintains a discrete energy law, as well as hyperbolic invariant domain properties, such as positivity of the density and a minimum principle of the specific entropy.

We discuss the underlying algebraic discretization technique based on collocation, convex limiting, and an IMEX splitting technique on two
concrete examples: the compressible Navier-Stokes equations, and the repulsive and attractive Euler-Poisson equations.

Biography

Matthias Maier is an Associate Professor in the Department of Mathematics at Texas A&M University. His research centers around scientific computation and analysis of numerical methods for optics and fluid dynamics with an emphasis on simulating multiscale phenomena. He is a principal developer of the finite element software deal.II.

MM has master's degrees (Diplomen) in both Mathematics and Physics from Heidelberg University (Germany). He earned a doctorate in mathematics from Heidelberg University in 2015, and was a Dunham Jackson Assistant Professor at the University of Minnesota (Twin Cities) from 2015 to 2018. He joined the Texas A&M faculty in 2018, and was promoted to Associate Professor in 2022.