10-29【李铁香】腾讯会议 国家数学与交叉科学(合肥)中心系列报告

发布者:卢珊珊发布时间:2021-10-21浏览次数:584


题目: Fast Algorithms for Maxwell’s Equations for 3D Photonic Crystal

报告人: 李铁香,东南大学

时间: 20211029 下午 2:00-3:00

地点: 腾讯会议 ID366 395 265


摘要: 

In this work, we propose the Fast Algorithms for Maxwell's Equations (FAME) package for solving Maxwell's equations for modeling three-dimensional photonic crystals. FAME combines the null-space free method with fast Fourier transform (FFT)-based matrix-vector multiplications to solve the generalized eigenvalue problems (GEPs) arising from Yee's discretization. A GEP is transformed into a null-space free standard eigenvalue problem with a Hermitian positive-definite coefficient matrix. The computation times for FFT-based matrix-vector multiplications with $7$ million matrix dimensions are only $0.33$ and $3.6 \times 10^{-3}$ seconds using MATLAB and a single NVIDIA Tesla P100 GPU, respectively. Such multiplications significantly reduce the computational costs of the conjugate gradient (CG) method for solving linear systems. We successfully use FAME on a single P100 GPU to solve a set of GEPs with more than $19$ million dimensions in $127$ to $191$ seconds per problem. These results demonstrate the potential of our proposed package to enable large-scale numerical simulations for novel physical discoveries and engineering applications of photonic crystals.

报告人:李铁香,东南大学教授,博士研究生导师,东南大学丘成桐中心主任助理,南京应用数学中心主任助理。主要研究方向为大规模矩阵计算及其应用、电磁场高效计算、反问题计算、三维计算共形几何及应用等。目前已经在 SIIMSSIMAXCPCJDEJCPJSCInverse Problems等国际学术刊物发表学术论文40余篇,主持二项国家自然科学基金委面上项目、主持完成一项国家自然科学基金委青年项目、主持一项国防创新特区项目和一项装备预研项目、主持完成多项省部级项目和横向课题。2013年获得江苏省科学技术奖(排名五),2014年评为江苏省青蓝工程中青年学术带头人,获得了 2017 年和 2019 年世界华人数学家联盟最佳论文奖—“若琳奖,获得2020年第三届江苏省工业与应用数学学会工业与应用数学青年奖,也曾获得东南大学青年教师授课竞赛二等奖、东南大学教学一等奖等荣誉。