Zhiguo Yang, Associate Professor, Shanghai Jiao Tong University

Haijun Yu,Professor

Structure-Preserving Spectral Method for Large-Scale MHD System Simulation

10:00-11:00 August 31 (Thursday), S615

Structure-preserving numerical methods are crucial  for achieving long-time accurate, stable, consistent and physically meaningful simulations. In this talk, we present H^1 and H(div) conforming spectral bases with exact preservation of the incompressibility and magnetic Gauss’s law constraints for the incompressible and resistive magnetohydrodynamic (MHD) systems. 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. Ample 2D and 3D numerical examples illustrate both the accuracy and efficiency of the proposed method.

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。报告人主要研究兴趣包括谱与谱元方法、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。