Talk by Dr. Abedi from Tennessee Space Institute “Space and spacetime discontinuous Galerkin methods for dynamic problems”

Monday 26 December 2016, 10:30-12

Seminar room, School of Mechanical Engineering

Abstract: The multi-scale, multi-physics, and complex nature of many modern problems as well as rapid advances in supercomputing call for more accurate, stable, and scalable computational methods. I briefly discuss and compare a few popular numerical methods such as continuous and discontinuous Galerkin (DG) finite element methods in terms of their accuracy, efficiency, and stability for discontinuous solution features and dynamic problems. The discussion shows why the development of new computational methods is still an active research topic albeit widespread use of commercial software packages. Some metrics for this discussion will be on high order methods, adaptive schemes, and parallel computing. Next, I will present the Spacetime Discontinuous Galerkin (SDG) finite element method, in which space and time are directly discretized by elements that employ discontinuous basis functions. The SDG’s element-wise balance property, local solution scheme, and inherent stability yield a method that strongly satisfies the aforementioned criteria and delivers exceptionally accurate results for problems with severe nonlinearities and singular features. Examples will be shown from elastodynamics, electromagnetics, and thermal and fluid mechanics.

About the Speaker: Reza Abedi received his B.S. in Civil Engineering and M.S. in Structural Engineering from Sharif University of Technology, Tehran, Iran, in 1999 and 2001 respectively. He obtained his M.S. in Mathematics and Ph.D. in Theoretical and Applied Mechanics from the University of Illinois at UrbanaChampaign in 2006 and 2010, respectively. He then joined the department of Mechanical Science and Engineering at the University of Illinois as a postdoctoral fellow. Since August 2012, he has been a professor in the department of Mechanical, Aerospace and Biomedical Engineering at the University of Tennessee Space Institute (UTSI) and the University of Tennessee Knoxville (UTK). Among his research interests are computational solid, electromagnetics, fluid, and thermal mechanics, fracture and failure modeling, structural health monitoring, and scientific computing.