Abstract

Many complex nonlinear systems have intrinsic structures such as energy dissipation or conservation, and/or positivity/maximum principle preserving. It is desirable, sometimes necessary, to preserve these structures in a numerical scheme.

I will present some recent advances on using the scalar auxiliary variable (SAV) approach to develop highly efficient and accurate structure preserving schemes for a large class of complex nonlinear systems. These schemes can preserve energy dissipation/conservation as well as other global constraints and/or are positivity/bound preserving, only require solving decoupled linear equations with constant coefficients at each time step, and can achieve higher-order accuracy.

About the speaker

Jie Shen obtained his bachelor degree in computational mathematics from Peking University in 1982, PhD degree in numerical analysis at Paris-Sud University (University of Paris -- XI) in 1987. After leaving his postdoc position at Indiana University, he worked at Pennsylvania State University first as assistant professor (Aug. 1991 -- June 1997), then associate professor (July 1997 -- June 2001), and professor (July 2001 -- June 2003).  He was appointed as professor at Purdue University in August 2002. Since February 2012, he serves as director of the Center for Computational and Applied Mathematics at Purdue University. Prof Shen's research interest lies in numerical analysis, scientific computing. He makes tremendous contribution in spectral methods, computational fluid dynamics and computational material sciences. He has published two monographs and over two hundred journal articles, and serves as editor-in-chief/associate editor for more than eight top journals. He is selected as Fellow (class 2017) of the American Mathematical Society (AMS) , and Fellow (class 2020) of Society of Industrial and Applied Mathematics (SIAM).