HEPL SEMINAR - Matthew West

HEPL SEMINAR Matthew West, Assistant Professor of Aeronautics and Astronautics.

Variational integrators and conservation laws

A central difficulty in simulating many complex dynamic problems is the preservation of quantities that are exactly conserved by the model system. Examples include energy and momentum for solid mechanics, circulation and vorticity for inviscid fluids, and the four constraint PDEs of Einstein's equations of general relativity.

In this talk we will describe a new framework for deriving coupled time and space discretizations which explicitly ties the conservation properties of the discretization to the symmetries of the system that are the underlying cause of the conservation laws. The key idea is to directly discretize the variational Lagrangian form of the system, resulting in variational integrators with many useful properties.

Specific applications to solid mechanics will be presented, including asynchronous space-time discretizations and conservative impact mechanics methods. Future work relating to fluids and relativity will be discussed.

Matthew West is an assistant professor in Aeronautics and Astronautics at Stanford University. He holds a B.Sc. in Pure and Applied Mathematics from the University of Western Australia and a Ph.D. in Control and Dynamical Systems from Caltech. His research uses geometric mechanics to develop novel numerical methods for computational mechanics, including

fluid/structure interaction and contact/impact dynamics.