Helmholtz equation in periodic media with a line defect

Julien Coatléven (1)

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation

We consider the Helmholtz equation in an unbounded periodic media perturbed by an unbounded defect whose structure is compatible with the periodicity of the underlying media. We exhibit a method coupling Dirichlet-to-Neumann maps with the Lippmann-Schwinger equation approach to solve this problem, where the Floquet-Bloch transform in the direction of the defect plays a central role. We establish full convergence estimates that makes the link between the rate of decay of a function and the good behavior of a quadrature rule to approximate the inverse Floquet-Bloch transform. Finally we exhibit a few numerical results to illustrate the efficiency of the method. © 2011 Elsevier Inc.

Domaines: Equations aux dérivées partielles [math.AP]

Julien Coatléven. Helmholtz equation in periodic media with a line defect. Journal of Computational Physics, 2012, 231 (4), pp.1675-1704. ⟨10.1016/j.jcp.2011.10.022⟩. ⟨hal-00849565⟩