Applied Mathematics Seminar——The discrete de Rham method for geometric partial differential equations
报告人：Jia Jia Qian (University of Oxford)
时间：2025-12-10 15:30-16:30
地点：智华楼-王选报告厅-101
Abstract:
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.
Bio:
Jia Jia Qian is a postdoctoral fellow at the mathematics department of the University of Oxford, working in the research group of Kaibo Hu. She graduated with a PhD in Mathematics from Monash University in 2025. Her research interests include general-order and structure preserving polytopal methods, and their applications to partial differential equations such as the Yang--Mills and Einstein's equations. She is currently investigating generalised gravity models and their particular geometric structures.
