FAME: Fast Algorithms for Maxwell’s Equations for Three-dimensional Photonic Crystals

Xing Long Lyu, Tiexiang Li*, Tsung Ming Huang, Jia Wei Lin, Wen Wei Lin, Sheng Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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.

Original languageEnglish
Article number26
JournalACM Transactions on Mathematical Software
Issue number3
Publication statusPublished - 2021 Jun

ASJC Scopus subject areas

  • Software
  • Applied Mathematics


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