Title:Exponential, Non-Exponential Splitting and Their Applications for Solving Singular PDEs

Speaker:Qin SHENG

Abstract:This talk will begin from two interactive facts. Firstly, we will pay a special attention to optimized operator splitting strategies, such as the non-exponential ADI and exponential LOD methods, and explore their modernizations. Secondly, we will focus at interesting issues involving the constructions and analysis of highly-effective and highly-efficient finite difference approximations of singular PDEs which are crucial to multiple industrial designs. The quenching phenomenon involved will be explored. Based on the two facts, adaptive splitting approaches will be introduced. Mathematical analysis on solution positivity, monotonicity and stability will be discussed. We will also present the latest ideas on moving mesh strategies which can be extended for solving many multi-physics problems including those from beam propagations, laser-materials interactions, oil pipeline decay detections and finance.

Introduction of speaker:Professor Qin Sheng, Department of Mathematics, Center for Astrophysics, Space Physics and Engineering Research (CASPER), Baylor University, Texas, USA. Dr. Sheng received his BS and MS in Mathematics from Nanjing University in 1982, 1985, respectively. Then he acquired his Ph.D. from the University of Cambridge. He joined National University of Singapore in 1990. Dr. Sheng has been interested in splitting and adaptive numerical methods for solving linear and nonlinear partial differential equations. He is also known for the Sheng-Suzuki theorem in numerical analysis. He has been an Editor-in-Chief of the SCI journal, International Journal of Computer Mathematics since 2010.

Inviter:Aijie CHENG

Time:11:00-12:00,May 28(Tuesday)

Location:Hall 808, Block B, Zhixin Building, Central Campus

Hosted by: School of Mathematics, Shandong University