报告时间：2021年4月27日上午10:00-11:00

报告地点：Zoom网址：https://umassd.zoom.us/j/6339263022，密码：123456

报告题目：The Fourier pseudo-spectral numerical schemes for nonlinear PDEs and their stabilitysegmentation problems

报告人：马萨诸塞大学达特茅斯分校 Dr. Wang Cheng

邀请人：杨旭光

报告人简介：Dr. Cheng Wang is a professor in Department of  Mathematics at the University of Massachusetts Dartmouth  (UMassD). He obtained hid Ph.D degree from Temple University in 2000, under the supervision of Prof. Jian-Guo Liu. Prior to joining UMassD in 2008 as an assistant professor, he was a Zorn postdoc at Indiana University from 2000 to 2003, under the supervision of Roger Temam and Shouhong Wang, and he worked as an assistant professor at University of Tennessee at Knoxville from 2003 to 2008. Dr. Wang’s research interests include development of stable, accurate numerical algorithms for partial differential equations and numerical analysis. He has published more than 90 papers with more than 4000 citations. He also serves in the Editorial Board of “Numerical Mathematics: Theory, Methods and Applications”.

报告摘要：The Fourier pseudo-spectral numerical schemes are considered for nonlinear partial differential equations (PDE). Stability and convergence analysis are analyzed in details, such as viscous Burgers' equation and incompressible fluid equations. Related applications to incompressible quasi-geostrophic equation will also be addressed, in both 2-D and 3-D, for smooth and vortex sheet initial data. In addition, high order time stepping schemes (up to fourth order accuracy order) will be explored in detail. Unconditional stability is established for the implicit time stepping algorithms.