Title: Maximum Bound Principles for Semilinear Parabolic Equations and Exponential Time Differencing Schemes

Keynote Speaker: Ju Lili

Abstract:

The ubiquity of semilinear parabolic equations has been illustrated in their numerous applications ranging from physics, biology, to materials and social sciences. In this talk, we consider a practically desirable property for a class of semilinear parabolic equations of the abstract form with a time-invariant maximum bound principle by its initial and boundary conditions. We first study an analytical framework for some sufficient conditions that lead to such a maximum bound principle for the time-continuous dynamic system of infinite or finite dimensions. Then, we utilize a suitable exponential time differencing approach with a properly chosen generator of contraction semigroup to develop first- and second-order accurate temporal discretization schemes, that satisfy the maximum bound principle unconditionally in the time-discrete setting. Error estimates of the proposed schemes are derived along with their energy stability. Extensions to vector- and matrix-valued systems are also discussed. We demonstrate that the abstract framework and analysis techniques developed here offer an effective and unified approach to study the maximum bound principle of the abstract evolution equation, that covers a wide variety of well-known models and their numerical discretization schemes. Some numerical experiments are also carried out to verify the theoretical results.

Introduction to the Speaker:

Ju Lili, Professor of the University of South Carolina, graduated from Wuhan University and was awarded the bachelor's degree in mathematics in 1995, the master degree in computational mathematics by the Institute of Computational Mathematics and Scientific/Engineering Computing of Chinese Academy of Sciences in 1998, and the doctoral degree in applied mathematics by Iowa State University in 2002. From 2002 to 2004, he was engaged in postdoctoral research in the Institute for Mathematics and Its Applications of the University of Minnesota. He then worked at the University of South Carolina, where he successively served as the Assistant Professor (2004-2008), Associate Professor (2008-2012) and Professor (2013-now) of the Department of Mathematics. Prof. Ju mainly studies the numerical methods and analysis, high-performance scientific computing, mesh optimization, non-local model, image processing, deep learning and its application in materials and earth sciences. So far, he has published more than 100 scientific research papers, with about 3,200 citations counted by the Google Scholar Citations. Since 2006, he has presided over a number of scientific research programs funded by the National Science Foundation (NSF) and the United States Department of Energy Department of Energy (DOE). He is a member of the Society for Industrial and Applied Mathematics (SIAM), and served as the President of the Southeast Atlantic Branch of SIAM from 2008 to 2009, and the editorial board member of SIAM Journal on Numerical Analysis - an important international journal in numerical analysis, during the period of 2012 to 2017. He has been repeatedly invited to serve as a member of the peer review group of the Foundation for the Field of Computational Mathematics, NSF. Prof. Ju, together with others, made great achievements in the phase-field simulation of alloy microstructure evolution on "Sunway Taihu Light" supercomputer, which was nominated for the grand prize of 2016 international high-performance computing application - "Gordon Bell Prize".

Inviter:

Zhao Weidong Professor in the School of Mathematics

Time:

8:30-9:30 on October 8 (Thursday)

Location:

Tencent Conference, ID: 773 499 793, Conference Password: 364735

https://meeting.tencent.com/s/bX6QLWLGvuq5

Sponsored by: School of Mathematics, Shandong University