活动时间：2025-04-07 09:30
活动地点：二号学院楼2432报告厅
主讲人：Xiaoming Wang
主讲人中文简介：
王晓明教授现为宁波东方理工大学讲席教授。他本硕毕业于复旦大学，在美国印第安纳大学布卢明顿分校获博士学位，为国家级高层次人才。曾任职于纽约大学库朗研究所，普林斯顿高等研究院，复旦大学（特聘教授），南方科技大学（讲席教授，系主任），美国佛罗里达州立大学（系主任），美国密苏里科技大学（首任Havener Endowed Chair）等。王晓明教授的主要研究方向是应用和计算数学，特别是和流体运动、湍流、地下水、以及气候变化相关的数学问题，他的工作的一个显著特点是严谨的数学和真实应用的有机结合，已在CPAM、JFM、SINUM、JCP等杂志发表论文100多篇，在剑桥大学出版社出版专著一部。
活动内容摘要：
Since the time of Kolmogorov, it has been recognized that physical laws governing turbulent and chaotic systems are often revealed through their statistical properties. When they exist, invariant measures describe the long-time statistical behavior of such systems. However, efficiently and accurately approximating invariant measures, especially for high-dimensional systems, remains a significant challenge. Classical numerical methods that perform well for short-time simulations may fail to capture the correct long-time dynamics. In this talk, I will present a novel and highly efficient second-order accurate numerical scheme based on the BDF2-Gear method and the Scalar Auxiliary Variable (SAV) approach, tailored for a class of finite-dimensional nonlinear models arising in geophysical fluid dynamics. The scheme achieves efficiency by requiring the solution of only a fixed symmetric positive definite linear system at each time step. Under uniformly bounded external forcing, the scheme yields uniformly bounded solutions for all time. Furthermore, we show that the proposed scheme can be viewed as a small perturbation of the classical BDF2-Gear extrapolation method in the forcing term, resulting in a modest change in the generalized Grashof number. We prove that, under appropriate assumptions, the global attractors and invariant measures of the numerical scheme converge to those of the original continuous system, thus faithfully capturing its long-time statistical behavior.
主持人：孙春友