报告人：胡凯博 皇家学会大学研究员 爱丁堡大学
报告时间：2024年9月12日15:00-16:00
报告地点：红瓦楼726
报告内容简介：Finite Element Exterior Calculus (FEEC) provides a cohomology framework for structure-preserving discretisation of a large class of PDEs. In FEEC, de Rham complexes for problems involving differential forms have been extensively discussed. A canonical construction of finite elements exists, which has a discrete topological interpretation and can be generalized to other discrete structures, e.g., graph cohomology.
There has been significant interest in extending FEEC to tensor-valued problems with applications in continuum mechanics, differential geometry and general relativity etc. In this talk, we first review the de Rham sequences and their canonical discretisation with Whitney forms. Then we provide an overview of some efforts towards Finite Element Tensor Calculus. On the continuous level, we characterise algebraic and differential structures of tensors using the Bernstein-Gelfand-Gelfand (BGG) machinery. On the discrete level, we discuss analogies of the Whitney forms. A special case is Christiansen’s finite element interpretation of Regge calculus, a discrete geometric scheme for metric and curvature. We present a correspondence between algebra (BGG sequences), continuum mechanics (microstructure), Riemann-Cartan geometry (curvature and torsion) and discretization (de Rham’s currents).
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, 美国明尼苏达大学做博士后研究. 现为爱丁堡大学 Royal Society University Research Fellow. 研究方向包括保结构离散, 有限元外形式 (Finite element exterior calculus)等. 曾获 SIAM Computational Science and Engineering Early Career Prize, 牛津大学 Hooke Research Fellowship.
报告邀请人：黄学海