报告人：杨志国

邀请人：刘文杰

报告题目：Structure-Preserving Spectral and Spectral-Element Method for Plasma Simulation

摘要：In this talk, I will present our recent progress on structure-preserving spectral and spectral-element methods, which are crucial for achieving long-time accurate, stable, consistent and physically meaningful plasma simulations. We first present H^1 and H(div) conforming spectral bases with exact preservation of the incompressibility constraint. Two key ingredients, i.e. exact de Rham complexes and their commuting diagram, and the derivative property of the generalized Jacobi polynomials, are essential for the derivation of the desired basis functions. We propose a fast matrix-free iterative solution algorithm based on the tensorial structure of the resultant linear system and a novel simultaneous multiple-matrices diagonalisation technique. This algorithm may serve as an essential building block for developing scalable high order spectral-element method for large-scale simulations. Next, we extend these ideas to a mixed divergence-free spectral-element method for the curl-curl problem. We then present some numerical examples of 7-dimensional Vlasov-Maxwell system and 3 dimensional MHD system to illustrate both the accuracy and efficiency of the proposed method.

报告时间：2023年12月26 日10：00—11：00 

报告地点：理学楼609

报告人简介：杨志国，2017年博士毕业于新加坡南洋理工大学，2017-2020年于美国普渡大学任职访问助理教授，2020年加入上海交通大学数学院任副教授。报告人长期从事谱与谱元方法、保结构数值算法的研究。研究成果发表于计算数学的高水平期刊如SIAM系列、JCP、CMAME、JSC等。入选2020年上海***********，2021年入选国家高层次青年人才计划，主持扬帆计划基金、国自然基金，参与中科院先导专项等。