Past Event: Oden Institute Seminar

Techniques to derive discrete elasticity complexes

Jay Gopalakrishnan, Professor, Mathematics, Portland University

Abstract

*** This seminar will be presented both live in POB 6.304 and via Zoom.***

In view of recent developments in finite element exterior calculus, it is now possible to gain a unified understanding of the varied attempts to obtain finite elements for the Cauchy stress tensor. In this talk, we will study the elasticity complex as an example of how complicated exact sequences of spaces can be built from simpler ones.  Lining up two simpler complexes, we start by performing a "diagram chase", which often goes by the name of Bernstein-Gelfand-Gelfand resolution. Then, we show how this process can be perfectly mimicked at the discrete level on a three-dimensional mesh of macroelements of Alfeld's type. It results in a discrete elasticity complex, complete with unisolvent degrees of freedom for each of the finite elements involved, together with accompanying global commuting interpolants. This is joint work with S. Christiansen, J. Guzman and K. Hu.

Biography

Jay Gopalakrishnan is a computational mathematician whose research centers around the design of numerical methods for partial differential equations.  He has co-authored over ninety publications, including the first papers on HDG methods and DPG methods.  He has worked at Bell Labs, University of Minnesota, Medtronic Inc, and for over a decade, at University of Florida.  He currently works at Portland State University.