报 告 人：Cheng Wang 教授 麻省大学达特茅斯分校
报告时间：2023年12月25日14:00-15:00
报告地点：上海财经大学红瓦楼826
报告摘要：A few positivity-preserving, energy stable numerical schemes are proposed and analyzed for certain type reaction-diffusion systems involving the Law of Mass Action with the detailed balance condition. The energetic variational formulation is applied, in which the reaction part is reformulated in terms of reaction trajectories. The fact that both the reaction and the diffusion parts dissipate the same free energy opens a path of an energy stable, operator splitting scheme for these systems. At the reaction stage, equations of reaction trajectories are solved by treating all the logarithmic terms in the reformulated form implicitly due to their convex nature. The positivity-preserving property and unique solvability can be theoretically proved. Moreover, the energy stability of this scheme at the reaction stage can be proved by a careful convexity analysis. Similar techniques are used to establish the positivity-preserving property and energy stability for the standard semi-implicit solver at the diffusion stage. As a result, a combination of these two stages leads to a positivity-preserving and energy stable numerical scheme for the original reaction-diffusion system. It is the first time to report an energy-dissipation-law-based operator splitting scheme to a nonlinear PDE with variational structures. Several numerical examples are also presented.
报告人简介：Cheng Wang，University of Massachusetts Dartmouth（UMassD）数学系教授。2000年博士毕业于Temple University，导师为Jian-Guo Liu教授。2000-2003年于Indiana University从事博士后研究工作（Zorn postdoc），合作导师为Roger Temam与Shouhong Wang。2003-2008年在University of Tennessee at Knoxvill担任助理教授。2008年进入UMassD任教至今。Cheng Wang教授的研究领域为偏微分方程的稳定高阶算法机器数值分析。已发表70余篇论文，引用达1800余次，入选ESI高被引论文库。担任国际期刊Numerical Mathematics: Theory, Methods and Applications的编委。
报告邀请人：严阅 副教授