Multiscale Approaches in Electrodynamics of Heterogeneous Materials





报告摘要:In this talk, we will introduce our recent advances in the multiscale analysis and algorithms for the electromagnetic properties of heterogeneous materials. First, we will briefly talk about the fundamental physical questions and the mathematical models from the classical electrodynamics to the semi-quantum models, then to the quantum electrodynamics (QED) and the quantum chromodynamics (QCD). Meanwhile, we will introduce some important studies about the multiscale analysis and algorithms for the classical Maxwell's equations and for the semi-quantum models. Second, we focus on discussing the multiscale method for the Maxwell's equations in the heterogeneous dispersion media including metamaterials and negative index materials. Third, the homogenization method and the multiscale asymptotic method for the semi-quantum models such as Schr?dinger-Poisson equations and Maxwell- Schr?dinger equations with rapidly oscillating discontinuous coefficients are presented. It originates from the interaction of the matter field and the electromagnetic field in materials science. Finally, the numerical results and some unsolved questions are reported.

This talk is based on the joint work with Dr. Lei Zhang, Dr. Chupeng Ma, Dr. Yongwei Zhang and Prof. Yanping Lin.    

报告人简介:曹礼群,男,中国科学院数学与系统科学研究院研究员,博士生导师,现任中科院数学院计算数学与科学工程计算所副所长,中国计算物理学会常务理事,中国计算数学学会理事,中国计算力学专业委员会委员,北京市计算数学学会副理事长。研究方向:多尺度建模与算法。代表性成果有:1.部分解决世界数学联盟前主席,法国著名数学家 J.L.Lions 1981年就谱多尺度分析提出的一个公开问题,并获得中科院数学院突出科研成果奖;2. 在尺度间隙、尺度不变性和弱关联体系键合关联效应等方面取得若干原创性结果,被973项目组推荐为三项代表性成果之一;3.提出了复合材料与界面纳米结构热传输问题的分子动力学与连续介质跨尺度模型和算法,被多尺度领域国际权威刊物Multiscale Modeling and Simulation推选为“Featured Article”;4.发展了有效质量近似的Schr?dinger-Poisson非线性耦合系统的均匀化和多尺度方法,该结果被美国工业与应用数学学会(SIAM)展板采用。