江蘇省應用數學（中國礦業大學）中心系列學術報告
題目：Fast Eigensolver for 3D Photonic Crystals in Oblique Coordinate System
報告人：李鐵香 教授 單位： 東南大學 伟德bv
時 間：2023年9月23日（周六）下午 16:30-17:30
地點：伟德bv A310
報告内容簡介：
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.
報告人簡介：李鐵香，東南大學教授，博士生導師，南京應用數學中心主任助理，東南大學丘成桐中心主任助理，江蘇省數學學會計算數學分會第二屆理事會理事，不确定性系統分析與仿真專業委員會委員，江蘇省“青藍工程”中青年學術帶頭人。主要研究方向為大規模矩陣計算及應用、電磁場高效計算、三維計算幾何等，主持多項國家級科研項目，發表五十餘篇學術論文，獲 2017 年和 2019 年世界華人數學家聯盟最佳論文獎—“若琳獎”，2020年第三屆江蘇省工業與應用數學青年獎。