地点：行健楼学术活动室665

Abstract：This talk is an overview of the framework of MARS(mapping and adjusting regular semianalytic sets)for numerically solving the incompressible Navier-Stokes equations (INSE) on moving domains with fourth-order accuracy.We propose GePUP-ES,a fourth-order energy-stable adaptive projection method for solving INSE on a square box.To augment GePUP-ES to irregular and moving domains with arbitrarily complex topology and geometry, we have employed tools from algebraic topology, differential geometry, and artificial intelligence. Different from current methods that avoid topology and geometry by converting them into numerical ODEs/PDEs, we tackle topological and geometric problems with tools in topology and geometry. We show that the coupling of numerical analysis with (even elementary)concepts in topology and geometry could be powerful for realworld applications.

CV：浙江大学求是特聘教授，国家级科技创新领军人才，浙江大学数学科学学院计算数学系主任。清华大学学士及硕士，美国康奈尔大学博士，美国劳伦斯伯克利国家实验室博士后。主要研究方向为动边界不可压流体的理论建模和数值计算，工作聚焦点为应用拓扑、界面追踪和高阶数值方法。

Qinghai Zhang got his bachelor and master degrees both at Tsinghua University and obtained his Ph.D. at Cornell University. He did his postdocs at Lawrence Berkeley National Lab and University of Utah. He is now a Qiushi distinguished professor of mathematics at Zhejiang University, where he also serves as the department chair of computational mathematics. His work focuses on numerical algorithms of multiphase flows and one of his main research themes is to tackle geometrical and topological problems with tools in geometry and topology. He has published papers in prestigeous journals such as SIAM Review, PNAS, Math. Comput., SIAM J. Numer. Anal., SIAM J. Sci. Comput., CMAME, J. Comput. Phys., and Coastal Engr.