Highly efficient GPU eigensolver for three-dimensional photonic crystal band structures with any Bravais lattice

Tsung Ming Huang, Wen Wei Lin, Hsinhan Tsai, Weichung Wang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


A null-space free method with the FFT-based matrix–vector multiplications was proposed to solve the Maxwell equations that model the three-dimensional photonic crystals. The most time-consuming parts of this method were the FFT-based matrix–vector multiplications. In this article, we propose new mathematical formulas to compute the FFT-based matrix–vector multiplications and derive highly efficient algorithms on top of the NVIDIA GPU architecture. The resulting algorithms are approximately two- to threefold faster than the previous algorithms. We have successfully used a single NVIDIA Tesla P100 GPU to solve a set of generalized eigenvalue problems of 5,184,000 dimensions in 17 to 22 seconds for each problem. Furthermore, we ported the codes to a GPU cluster and achieved near linear scalability. To our knowledge, these GPU implementations of the proposed algorithms are the fastest implementations. The schemes can be applied to simulate a three-dimensional photonic crystal with all 14 Bravais lattices. These highly efficient schemes and codes raise possibilities for large-scale and near real-time numerical simulations for novel physical discoveries and engineering applications of photonic crystals.

Original languageEnglish
Article number106841
JournalComputer Physics Communications
Publication statusPublished - 2019 Dec


  • Fast Fourier transform
  • Null-space free method
  • Parallel GPU computing
  • The Maxwell equations
  • Three-dimensional photonic crystals

ASJC Scopus subject areas

  • Hardware and Architecture
  • General Physics and Astronomy


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