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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2014010826
pages 423-450

HOMOGENIZATION OF THE SPECTRAL EQUATION IN ONE DIMENSION

Thi Trang Nguyen
FEMTO-ST Institute, Departement Temps-Frequence, 26 Chemin de l'Epitaphe, 25000 Besancon, France
Michel Lenczner
FEMTO-ST, Departement Temps-Frequence, University of Franche-Comte, 26 Chemin de l'Epitaphe, 25030 Besancon Cedex, France
Matthieu Brassart
Laboratoire de Mathematiques de Besancon, University of Franche-Comte, France

ABSTRACT

The asymptotic behavior of a one-dimensional spectral problem with periodic coefficient is addressed for high-frequency modes by a method of Bloch wave homogenization. The analysis leads to a spectral problem including both microscopic and macroscopic eigenmodes. Numerical simulation results are provided to corroborate the theory.