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

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