題  目：Structure-preserving spectral and spectral-element method for plasma simulation

内容簡介：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.

報告人：楊志國

報告人簡介：2017年博士畢業于新加坡南洋理工大學，2017-2020年于美國普渡大學任職訪問助理教授，2020年加入上海交通大學數學院任副教授。報告人長期從事譜與譜元方法、保結構數值算法的研究。研究成果發表于計算數學的高水平期刊如SIAM系列、JCP、CMAME、JSC等。2020年入選上海海外高層次人才計劃，2021年入選國家高層次青年人才計劃，2024年入選explore x人才計劃，主持揚帆計劃基金、國自然基金，參與中科院先導專項基金等科研項目。

時  間：2024年2月24日（周六）下午14：00開始

地  點：騰訊會議：63129598867

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