@article{b7b56b52996048e09db161aa816aa657,
title = "FAME: Fast Algorithms for Maxwell{\textquoteright}s Equations for Three-dimensional Photonic Crystals",
abstract = "In this article, 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. The GEPs are 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 matrices of dimension 7 million are only 0.33 and 3.6 × 10 - 3 seconds using MATLAB with an Intel Xeon CPU and CUDA C++ programming with a single NVIDIA Tesla P100 GPU, respectively. Such multiplications significantly reduce the computational costs of the conjugate gradient method for solving linear systems. We successfully use FAME on a single P100 GPU to solve a set of GEPs with matrices of dimension more than 19 million, 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. ",
author = "Lyu, {Xing Long} and Tiexiang Li and Huang, {Tsung Ming} and Lin, {Jia Wei} and Lin, {Wen Wei} and Sheng Wang",
note = "Funding Information: T. Li was supported in part by the National Natural Science Foundation of China (NSFC) 11971105. T.-M. Huang was partially supported by the Ministry of Science and Technology of Taiwan (MoST) 108-2115-M-003-012-MY2. W.-W. Lin was partially supported by MoST 106-2628-M-009-004-. This work was also partially supported by the National Centre of The-oretical Sciences (NCTS) and ST Yau Centre in Taiwan, the Shing-Tung Yau Center and the Big Data Computing Center of Southeast University. The numerical calculation of this work was partially performed on TianHe-2, thanks to the support of the National Supercomputing Center in Guangzhou (NSCC-GZ). Updated author order and affiliations: XING-LONG LYU, Southeast University; TIEXIANG LI, Southeast University and Nanjing Center for Applied Mathematics; TSUNG-MING HUANG, National Taiwan Normal University; JIA-WEI LIN, National Yang Ming Chiao Tung University; WEN-WEI LIN, National Yang Ming Chiao Tung University and Nanjing Center for Applied Mathematics; SHENG WANG, National Yang Ming Chiao Tung University. Authors{\textquoteright} addresses: X.-L. Lyu, School of Mathematics, Southeast University, Nanjing 211189, China; email: lxl_math@seu.edu.cn; T. Li (corresponding author), School of Mathematics, Southeast University, Nanjing 211189, China, Nanjing Center for Applied Mathematics, Nanjing 211135, China; email: txli@seu.edu.cn; T.-M. Huang (corresponding author), Department of Mathematics, National Taiwan Normal University, Taipei 116, Taiwan; email: min@ntnu.edu.tw; J.-W. Lin, Department of Applied Mathematics, National Yang Ming Chiao Tung University, Hsinchu 300, Taiwan; email: jiawei.am05g@g2.nctu.edu.tw; W.-W. Lin, Department of Applied Mathematics, National Yang Ming Chiao Tung University, Hsinchu 300, Taiwan, Nanjing Center for Applied Mathematics, Nanjing 211135, China; email: wwlin@math.nctu.edu.tw; S. Wang, Department of Applied Mathematics, National Yang Ming Chiao Tung University, Hsinchu 300, Taiwan; email: shengwang.am08g@nctu.edu.tw. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. {\textcopyright} 2021 Association for Computing Machinery. 0098-3500/2021/06-ART26 $15.00 https://doi.org/10.1145/3446329 Publisher Copyright: {\textcopyright} 2021 ACM.",
year = "2021",
month = jun,
doi = "10.1145/3446329",
language = "English",
volume = "47",
journal = "ACM Transactions on Mathematical Software",
issn = "0098-3500",
publisher = "Association for Computing Machinery (ACM)",
number = "3",
}