Lecture:2018/12/13,14:00-15:00,Qin Sheng,Department of Mathematics and Center for Astrophysics, Space Physics and Engineering Research (CASPER), Baylor University, Texas, USA


Title:Six Corelated Ways of Moving Mesh   Adaptations for Nonlinear Kawarada Problems



It was during the last Banff International   Research Station (BIRS) Workshop on Adaptive Numerical Methods for Partial Differential Equations with   Applications, the topics of different adaptive finite difference procedures   were seriously revisited, reevaluated and reinvested. Among various   kinds of singular partial differential equation problems, Kawarada problems   are particularly attractive to the participants due to their important   theoretical and application features.

In a traditional moving mesh approach, mesh adaptations are   often configurated based on an equidistribution principle. In such a case, a   new mesh is acquired via a monitor function that is equidistributed in some   sense. Typical choices of such monitor functions involve the solution or one   of its many derivatives. The strategy has been proven to be effective and   easy-to-realize in multi-physical applications. However, identifications of optical   core monitoring components are proven to be extremely difficult. To this end,   in this talk, we consider six different designs of monitoring functions   targeting at a highly vibrate nonlinear partial differential equation problem   that exhibits both quenching-type and degeneracy singularities. While the   first a few monitoring designs to be discussed are within the so-called   direct regime, the rest belong to a newer category of the indirect type,   which requires the priori-knowledge of certain important solution features or   characteristics. Computational experiments will be presented to illustrate   our research and conclusions. Continuing collaborations in the field with SEU   colleagues and students will also be aimed.


Dr. Sheng received his BS and MS in Mathematics from Nanjing   University in 1982, 1985,respectively. He then obtained a Ph.D. degree from the   University of Cambridge under the supervision of Professor Arieh   Iserles. After his postdoctoral research with Professor Frank T. Smith,   FRS, in University College London, he joined National University of Singapore   in 1990. Since then, Dr. Sheng was on faculty of several major   universities till his joining Baylor University, which is one of known   research institutions and the second biggest privateuniversity in the   United States. He has been associated with the Mathematics Department andCenter for   Astrophysics, Space Physics and Engineering Research (CASPER). See moredetails from Dr.   Sheng's website https://sites.baylor.edu/qin_sheng/ .

Prof. Sheng has been interested in adaptive and splitting   computations for solvinglinear and nonlinear   partial differential equations. He is also known for the Sheng-Suzuki theoremin numerical analysis.   He has published over 110 refereed articles as well as several joint   research monographs. He has been an Editor-in-Chief of the SCI journal,   International Journal of Computer Mathematics by Taylor and Francis   Group since 2010. He gives invited presentations,including keynote   lectures, in international conferences each year. Dr. Sheng's projects have   beensupported by several research agencies. He currently advises 2   doctoral students and 2postdoctoral research fellows. He also has several academic   visitors from overseas institutions.

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