*主持人：郑海标 副教授

*讲座内容简介：

In this talk, we present H^1-, H(div) and H(curl)-conforming spectral method with exact preservation of the curl/divergence-free constraints for two typical PDEs arising from plasma simulations. One is the incompressible

visco-resistive MHD system and the other one is the Vlaosv Ampere system.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. Besides, several novel second-order energy-stable or energy-conserving time discretization schemes are proposed. Ample 2D and 3D numerical examples illustrate both the

accuracy of the divergence-free basis functions and the efficiency of the proposed schemes.



*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。