On the Bloch decomposition based spectral method for wave propagation in periodic media

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We extend the Bloch-decomposition based time-splitting spectral method introduced in an earlier paper [Z. Huang, S. Jin, P. Markowich, C. Sparber, A Bloch decomposition based split-step pseudo spectral method for quantum dynamics with periodic potentials, SIAM J. Sci. Comput. 29 (2007) 515-538] to the case of (non-)linear Klein-Gordon equations. This provides us with an unconditionally stable numerical method which achieves spectral convergence in space, even in the case where the periodic coefficients are highly oscillatory and/or discontinuous. A comparison to a traditional pseudo-spectral method and to a finite difference/volume scheme shows the superiority of our method. We further estimate the stability of our scheme in the presence of random perturbations and give numerical evidence for the well-known phenomenon of Anderson's localization.

Original languageEnglish (US)
Pages (from-to)15-28
Number of pages14
JournalWave Motion
Issue number1
StatePublished - Jan 2009
Externally publishedYes


  • Anderson localization
  • Bloch decomposition
  • Klein-Gordon equation
  • Periodic structure
  • Time-splitting spectral method
  • Wave propagation

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics
  • General Physics and Astronomy
  • Modeling and Simulation


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