Structure/asymptotic-preserving high-order matrix-free spectral methods for plasma simulations
数学专题报告
报告题目(Title)：Structure/asymptotic-preserving high-order matrix-free spectral methods for plasma simulations
报告人(Speaker)：杨志国 副教授(上海交通大学)
地点(Place)：后主楼1220
时间(Time)：2023年4月12日 (周三), 9:00-10:00
邀请人(Inviter)：蔡勇勇
报告摘要
In this talk, we present H^1-, H(div)- and H(curl)-conforming spectral methods with exact preservation of the curl/divergence-free constraints for discretization of typical PDEs arising from plasma simulations. 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. Fast matrix-free solution algorithm particularly designed for scalable and parallel computations are proposed. Besides, we present efficient asymptotic-preserving schemes, which guarantee that the asymptotic limiting of the discrete scheme is a consistent and stable discretization of the quasi-neutral limit of the continuous model. Ample numerical examples in 2D and 3D illustrate both the accuracy and efficiency of the proposed methods.
主讲人简介
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、保结构数值算法及其在电磁、流体、相场模拟中的应用。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年上海海外高层次人才引进计划，2021年入选国家高层次青年人才计划，主持扬帆计划基金、国自然青年科学基金，参与中科院先导专项等。
