時間：2021年12月7日 星期二 20:00-21:00
地點： 騰訊會議室 174 686 030
報告題目： Fast Algorithms for Maxwell’s Equations for 3D Photonic Crystal
報告人簡介：李鐵香，東南大學教授，博士研究生導師，東南大學丘成桐中心主任助理，南京應(yīng)用數(shù)學中心主任助理。主要研究方向為大規(guī)模矩陣計算及其應(yīng)用、三維計算共形幾何及應(yīng)用等。目前已經(jīng)在 SIIMS、SIMAX、JCP、Inverse Problems等學術(shù)刊物發(fā)表論文50余篇，主持3項國家自然科學基金項目、主持1項國防創(chuàng)新特區(qū)項目和1項裝備預(yù)研項目。2013年獲得江蘇省科學技術(shù)獎（排名五），2014年評為江蘇省“青藍工程”中青年學術(shù)帶頭人，獲得了 2017 年和 2019 年世界華人數(shù)學家聯(lián)盟最佳論文獎—“若琳獎”，獲得2020年第三屆江蘇省工業(yè)與應(yīng)用數(shù)學學會工業(yè)與應(yīng)用數(shù)學青年獎。
內(nèi)容提要： 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.
歡迎老師、同學們參加！
