時(shí)間：2021年12月7日 星期二 20:00-21:00
地點(diǎn)： 騰訊會(huì)議室 174 686 030
報(bào)告題目： Fast Algorithms for Maxwell’s Equations for 3D Photonic Crystal
報(bào)告人簡(jiǎn)介：李鐵香，東南大學(xué)教授，博士研究生導(dǎo)師，東南大學(xué)丘成桐中心主任助理，南京應(yīng)用數(shù)學(xué)中心主任助理。主要研究方向?yàn)榇笠?guī)模矩陣計(jì)算及其應(yīng)用、三維計(jì)算共形幾何及應(yīng)用等。目前已經(jīng)在 SIIMS、SIMAX、JCP、Inverse Problems等學(xué)術(shù)刊物發(fā)表論文50余篇，主持3項(xiàng)國(guó)家自然科學(xué)基金項(xiàng)目、主持1項(xiàng)國(guó)防創(chuàng)新特區(qū)項(xiàng)目和1項(xiàng)裝備預(yù)研項(xiàng)目。2013年獲得江蘇省科學(xué)技術(shù)獎(jiǎng)（排名五），2014年評(píng)為江蘇省“青藍(lán)工程”中青年學(xué)術(shù)帶頭人，獲得了 2017 年和 2019 年世界華人數(shù)學(xué)家聯(lián)盟最佳論文獎(jiǎng)—“若琳獎(jiǎng)”，獲得2020年第三屆江蘇省工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)工業(yè)與應(yīng)用數(shù)學(xué)青年獎(jiǎng)。
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.
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