Fast Eigensolver for 3D Photonic Crystals in Oblique Coordinate System



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:2023923日(周六)下午 16:30-17:30

地点:数学学院 A310


Abstract: In this talk, we consider studying the eigen-decomposition and developing the fast solver for 3D Maxwells equations for photonic crystals. The fast algorithm for Maxwells 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 Maxwells 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。