FAME swMATH ID: 41128 Software Authors: Lyu, Xing-long; Li, Tiexiang; Huang, Tsung-ming; Lin, Jia-wei; Lin, Wen-wei; Wang, Sheng Description: FAME. Fast algorithms for Maxwell’s equations for three-dimensional photonic crystals. 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 imes 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. Homepage: https://sites.google.com/g2.nctu.edu.tw/fame Related Software: JDQZ; JDQR; lobpcg.m; AFLOW; FAME; CUDA; Matlab Cited in: 2 Publications Further Publications: https://sites.google.com/g2.nctu.edu.tw/fame/publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year FAME. Fast algorithms for Maxwell’s equations for three-dimensional photonic crystals. Zbl 07467957Lyu, Xing-long; Li, Tiexiang; Huang, Tsung-ming; Lin, Jia-wei; Lin, Wen-wei; Wang, Sheng 2021 all top 5 Cited by 7 Authors 1 Huang, Tsungming 1 Li, Tiexiang 1 Lin, Jiawei 1 Lu, Zhongjie 1 Lyu, Xing-Long 1 Wang, Sheng 1 Xu, Yan Cited in 2 Serials 1 ACM Transactions on Mathematical Software 1 Journal of Scientific Computing Cited in 3 Fields 2 Numerical analysis (65-XX) 1 Optics, electromagnetic theory (78-XX) 1 Statistical mechanics, structure of matter (82-XX) Citations by Year