A time-splitting spectral scheme for the Maxwell-Dirac system

Zhongyi Huang*, Shi Jin, Peter A. Markowich, Christof Sparber, Chunxiong Zheng

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

68 Scopus citations


We present a time-splitting spectral scheme for the Maxwell-Dirac system and similar time-splitting methods for the corresponding asymptotic problems in the semi-classical and the non-relativistic regimes. The scheme for the Maxwell-Dirac system conserves the Lorentz gauge condition is unconditionally stable and highly efficient as our numerical examples show. In particular, we focus in our examples on the creation of positronic modes in the semi-classical regime and on the electron-positron interaction in the non-relativistic regime. Furthermore, in the non-relativistic regime, our numerical method exhibits uniform convergence in the small parameter δ, which is the ratio of the characteristic speed and the speed of light.

Original languageEnglish (US)
Pages (from-to)761-789
Number of pages29
JournalJournal of Computational Physics
Issue number2
StatePublished - Sep 20 2005
Externally publishedYes


  • Maxwell-Dirac system
  • Non-relativistic limit
  • Schrödinger-Poisson system
  • Semi-classical asymptotics
  • Time-splitting spectral method
  • WKB-expansion

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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