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On the Bloch decomposition based spectral method for wave propagation in periodic media
- Source :
-
Wave Motion . Jan2009, Vol. 46 Issue 1, p15-28. 14p. - Publication Year :
- 2009
-
Abstract
- Abstract: 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. [Copyright &y& Elsevier]
- Subjects :
- *MATHEMATICS
*MATHEMATICAL analysis
*QUANTUM theory
*NUMERICAL analysis
Subjects
Details
- Language :
- English
- ISSN :
- 01652125
- Volume :
- 46
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Wave Motion
- Publication Type :
- Periodical
- Accession number :
- 35502174
- Full Text :
- https://doi.org/10.1016/j.wavemoti.2008.07.001