Year: 2025
Type: article
Abstract: We are interested in the Helmholtz equation in a junction of two periodic half-spaces. When the overall medium is periodic in the direction of the interface, Fliss and Joly (2019) proposed a method which consists in applying a partial Floquet-Bloch transform along the interface, to obtain a family of waveguide problems parameterized by the Floquet variable. In this paper, we consider two model configurations where the medium is no longer periodic in the direction of the interface. Inspired by the works of Gérard-Varet and Masmoudi (2011, 2012), and Blanc, Le Bris, and Lions (2015), we use the fact that the overall medium has a so-called quasiperiodic structure, in the sense that it is the restriction of a higher dimensional periodic medium. Accordingly, the Helmholtz equation is lifted onto a higher dimensional problem with coefficients that are periodic along the interface. This periodicity property allows us to adapt the tools previously developed for periodic media. However, the augmented PDE is elliptically degenerate (in the sense of the principal part of its differential operator) and thus more delicate to analyse.
Source: Pure and Applied Analysis
Authors: Pierre Amenoagbadji, Sonia Fliss, Patrick Joly
Institutions: Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, École Nationale Supérieure de Techniques Avancées, Institut Polytechnique de Paris, POEMS: Propagation des Ondes : Etude Mathématique et Simulationan, École Nationale Supérieure de Techniques Avancées Paris, Columbia University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394591280