报告人：盛秦
报告时间：2018年9月19日（星期三）
报告地点：宁夏大学怀远校区宁远楼（原数学楼）
报告题目On mesh adaptations for the numerical solution of singular reaction-diffusion equations
报告人简介：
盛秦，南京大学获得数学学士和硕士学位，英国剑桥大学获得数学博士学位，现为Baylor大学(美国第二大私立大学)数学系和天体物理、空间物理及工程研究中心终身教授。主要从事应用和计算数学研究，具体的研究方向包括：偏微分方程数值解法、算子分裂及区域分解法、自适应方法、高频振荡问题的数值分析、逼近论及方法、矩阵分析、计算金融、多物理场应用、并行计算、以工程应用为目标的软件设计等。2010年至今，担任国际计算机数学杂志《International Journal of Computer Mathematics》主编。出版学术专著6部，发表学术论文110余篇。
报告摘要：
Many finite difference methods that involve spatial adaptation employ an equidistribution principle. In these cases, a new mesh is constructed such that a given monitor function is equidistributed in some sense. Typical choices of the monitor function involve the solution or one of its many derivatives. This constructive strategy has been proven to be extremely effective and easy-to-use in multiphysical computations. However, selections of core monitoring functions are often challenging and crucial to the computational success. This talk concerns several different designs of the monitoring function that targets a highly nonlinear partial differential equation 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. Experimental computations will be presented to illustrate our study and conclusions. Further research collaborations with Ningxia colleagues will be discussed.
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宁夏大学数学统计学院
2018年9月18日
