Mathematics Colloquium 10/07/22

Abstract:  Computer simulations of evolutionary multiscale multiphysics partial differential equations are important in many areas of science and engineering. Algorithms for time integration of these systems face important challenges. Multiscale problems have components evolving at different rates. No single time step can solve all components efficiently (e.g., when an explicit discretization is used, and the spatial discretization uses both fine and coarse mesh patches). Multiphysics problems are driven by multiple simultaneous processes with different dynamic characteristics. No single time discretization method is best suited to solve all processes (e.g., when some are stiff and others non-stiff). In order to address these challenges, multimethods have been proposed. Multimethods are time integration approaches that use different solution strategies for different subsystems have been developed. For example, different processes are discretized with different numerical schemes, and different components of the system are solved with different time steps. We discuss several general aspects of multimethods for the integration for multiphysics systems, as well as new developments in the field.

Biosketch: Prof. Sandu received his PhD degree from the University of Iowa in 1997. Before joining VT, he was a postdoc at Courant Institute, NYU (1997-1998) and an assistant professor at Michigan Tech (1998-2003). He is the founding member and director of Computational Science Laboratory at VT. His selected honors include NSF CAREER award (2001), Fellow of Virginia Tech College of Engineering (2008), Distinguished Scientist of ACM (2015), and Honorary Fellow of the European Society of Computational Methods in Science and Engineering (2016). He has been a recipient of numerous grants from funding agencies, including NSF, AFOSR, NIH, NASA, DOE, NOAA. He has supervised over 20 PhD students and 7 postdocs. His research interests are in the area of computational science and engineering. In particular, he mainly focuses on time integration, data assimilation, and HPC.

For more information, please contact:  Dr. Vu Thai Luan (luan@math.msstate.edu).