报告题目： The discrete de Rham method for geometric partial differential equations
报 告 人： Jia Jia Qian博士 牛津大学
报告时间：2025年12月8日周一上午9：00 – 10：00
报告地点：正新楼306
校内联系人： 张倩 qzhang25@jlu.edu.cn
报告摘要：It is well known that numerical methods that reproduce certain structures of the continuous theory often enjoy nice properties at the discrete level. A prime example is the Maxwell's equations, where the reproduction of the cohomology of the de Rham complex allows us to design a numerical scheme that naturally preserves the constraints. However, once we move to nonlinear equations, the story becomes much more complicated and discretisation dependent. The discrete de Rham (DDR) method is a completely discrete sequence of spaces and operators that exactly replicates certain properties of the continuous complex, in addition to being applicable to general polytopal meshes, and allowing arbitrary-order approximations. In this presentation we will introduce this method, and present its extension to nonlinear problems such as the Yang--Mills equations and the Einstein's equations.
报告人简介：Jia Jia Qian 现为牛津大学数学系的博士后研究员，在胡凯博教授的课题组工作。她于 2025 年在莫纳什大学获得数学博士学位。她的研究兴趣包括任意阶、结构保持的多面体数值方法，以及它们在偏微分方程（如杨–米尔斯方程和爱因斯坦方程）中的应用。目前，她主要研究广义引力模型及其所具有的特殊几何结构.
