江苏省应用数学（中国矿业大学）中心系列学术报告
题目：Fast Eigensolver for 3D Photonic Crystals in Oblique Coordinate System
报告人：李铁香 教授 单位： 东南大学 数学学院
时 间：2023年9月23日（周六）下午 16:30-17:30
地点：数学学院 A310
报告内容简介：
Abstract: In this talk, we consider studying the eigen-decomposition and developing the fast solver for 3D Maxwell’s equations for photonic crystals. The fast algorithm for Maxwell’s equations (FAME) is proposed for band structure calculations of 3D isotopic/anisotropic photonic crystals(PCs), especially with non-orthogonal Bravais lattices. By directly working with the intrinsic coordinate system with Bravais translation lattices/inverse lattices as basis/inverse basis and covariant/contravariant formulations, the frequency domain Maxwell’s equations are discretized into a genralized eigenvalue problem (GEP). With an alternative understanding of nullspace-deflation techniques, this GEP is transformed into several equivalent nullspace free GEPs (NFGEPs), whose smallest few positive eigenvalues and associated eigenvectors are solved by an iterative eigensolver of the inner-outer type. Comparison with other methods for band structure calculations of 3D anisotropic/isotropic PCs is made to demonstrate the effectiveness and strength of our present approach.
报告人简介：李铁香，东南大学教授，博士生导师，南京应用数学中心主任助理，东南大学丘成桐中心主任助理，江苏省数学学会计算数学分会第二届理事会理事，不确定性系统分析与仿真专业委员会委员，江苏省“青蓝工程”中青年学术带头人。主要研究方向为大规模矩阵计算及应用、电磁场高效计算、三维计算几何等，主持多项国家级科研项目，发表五十余篇学术论文，获 2017 年和 2019 年世界华人数学家联盟最佳论文奖—“若琳奖”，2020年第三届江苏省工业与应用数学青年奖。