报告主题： 奇异Kawarada偏微分方程和六种移动网格思想的数值试验
报告人：Qin Sheng 教授 （Baylor University）
报告时间：2019年5月23日（周四）15：00
报告地点：校本部G507
邀请人：李常品
主办部门：太阳成集团tyc33455数学系
报告摘要：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, nonlinear and singular Kawarada equations 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 test six different designs of monitoring functions targeting at the highly vibrate Kawarada partial differential equation problems 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. Possible collaborations, especially with fractional derivative extensions, in the field Shanghai colleagues and students will also be pursued.
欢迎教师、员工参加！
