Lecturer:Ju Lili

Abstract:

Maximum bound principle (MBP) is an important property for a large class of semilinear parabolic equations, in the sense that their solution preserves for all time a uniform pointwise bound in absolute value imposed by the initial and boundary conditions. It has been a challenging problem on how to design unconditionally MBP-preserving time stepping schemes for these equations, especially the ones with order greater than one. We combine the integrating factor Runge-Kutta (IFRK) method with the linear stabilization technique to develop a stabilized IFRK (sIFRK) method, and successfully derive the sufficient conditions for the proposed method to preserve MBP unconditionally in the discrete setting. We then elaborate some sIFRK schemes with up to the third order accuracy, which are proven to be unconditionally MBP-preserving by verifying these conditions. In addition, it is shown that many strong stability preserving sIFRK (SSP-sIFRK) schemes do not satisfy these conditions, except the first-order one. Various numerical experiments are also carried out to demonstrate the performance of the proposed method.

Introduction to the Lecturer:

Ju Lili, professor at the University of South Carolina, U.S.A. He received B.S. degree in mathematics from Wuhan University in 1995, M.S. degree in computational mathematics from the Institute of Computational Mathematics and Scientific/Engineering Computing of Chinese Academy of Sciences in 1998, and Ph.D. degree in applied mathematics from Iowa State University in 2002. He was engaged in post-doctoral research at the Institute of Mathematics and Applications, University of Minnesota, U.S.A., from 2002 to 2004. Later, he began working at the University of South Carolina, U.S.A. successively as an assistant professor (2004/08-2008/08), associate professor (2008/08-2012/12), and professor (2013/12-present) in the Department of Mathematics. He is mainly engaged in researches on numerical methods for partial differential equations, image processing and computer vision, non-local models, high performance computing, and their applications in materials and earth sciences. So far, he has more than 120 scientific papers published, with about 3600 Google Scholar Citations. Since 2006, he has led consecutively many scientific research programs of US National Science Foundation and Department of Energy. From 2012-2017, he served as an associate editor at SIAM Journal on Numerical Analysis, and currently is an editorial board member for Numerical Mathematics: Theory, Methods and Applications. His phase field simulation work of alloy microstructure evolution on "Sunwai TaihuLight" supercomputer was shortlisted for the 2016 Gordon Bell Prize in the field of high performance computing.

Invitee:

Zhao Weidong, Professor from School of Mathematics

Time:

9:00-11:00, June 11 (Friday)

Venue:

Tencent Meeting, ID: 169 738 423, Password: 210611

https://meeting.tencent.com/s/q7BK6jmKFUxW

Hosted by the School of Mathematics, Shandong University