报告人：胡凯博 研究员（爱丁堡大学）

时 间：2025年1月15日（星期三），下午2:00-4:00

地 点：海纳苑2幢205

摘 要：A fundamental problem in plasma physics is understanding the evolution of magnetic fields with given initial data. Questions include whether a stationary state exists and, if so, what properties it possesses. The Parker hypothesis states that for ‘almost any initial data’, the evolution of magnetic fields develops tangential continuity. This hypothesis remains open and is related to problems such as coronal heating. The topology of magnetic field lines, particularly knots, imposes crucial constraints on the relaxation process. In this talk, we discuss the role of topology preservation, specifically helicity preservation, in computing the long-term evolution of incompressible magnetohydrodynamic (MHD) systems. We derive a scheme using finite element de Rham complexes and compare several methods numerically. In the presence of nontrivial cohomology, we provide a generalized definition of helicity.

报告人简介：胡凯博，2017年博士毕业于北京大学, 曾在挪威奥斯陆大学和美国明尼苏达大学做博士后研究, 任英国牛津大学 Hooke 研究员. 现任爱丁堡大学皇家学会大学研究员 (Royal Society University Research Fellow). 曾获SIAM计算科学与工程早期职业奖 (2023), ERC Starting Grant (2024). 文章入选 SIAM 高影响力文章合集 (SIAM High Impact Article Collection). 研究兴趣包括保结构有限元方法, 离散几何与拓扑及应用.