Upcoming Event: Oden Institute Seminar
Jie Shen, Professor, Department of Mathematics, Purdue University
3:30 – 5PM
Tuesday Nov 8, 2022
POB 6.304 & Zoom
Solutions for a large class of partial differential equations (PDEs) arising from sciences and engineering applications are required to be positive to be positive or within a specified bound, and/or energy dissipative.
It is of critical importance that their numerical approximations preserve these structures at the discrete level, as violation of these structures may render the discrete problems ill posed or inaccurate.
I will review the existing approaches for constructing positivity/bound preserving schemes, and then present several efficient and accurate approaches: (i) through reformulation as Wasserstein gradient flows; (ii) through a suitable functional transform; and (iii) through a Lagrange multiplier. These approaches have different advantages and limitations, are all relatively easy to implement and can be combined with most spatial discretizations.
Professor Jie Shen received his B.S. in Computational Mathematics from Peking University in 1982, and his Ph.D in Numerical Analysis from Universite de Paris-Sud (currently Paris Saclay University) at Orsay in 1987. Before joining the Purdue Faculty in Fall 2002, he was a faculty member at Penn State University (1991-2001) and University of Central Florida (2001-2002).
Since Jan. 2012 he serves as the Director of Center for Computational and Applied Mathematics at Purdue University. He is a recipient of the Fulbright “Research Chair” Award in 2008 and the Inaugural Research Award of the College of Science at Purdue University in 2013, and an elected Fellow of AMS and SIAM.
His main research interests are numerical analysis, spectral methods and scientific computing with applications in computational fluid dynamics and materials science.