Helmholtz equation in periodic media with a line defect

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• 作者：Julien Coatlé ; ven ^{julien.coatleven@inria.fr}
• 关键词：Exact-boundary conditions ; Helmholtz equation ; Unbounded media ; Unbounded defects ; Line defects
• 刊名：Journal of Computational Physics
• 出版年：2012
• 出版时间：20 February 2012
• 年：2012
• 卷：231
• 期：4
• 页码：1675-1704
• 全文大小：2105 K

文摘

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.