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Local transparent boundary conditions for wave propagation in fractal trees (I). Method and numerical implementation

Patrick Joly 1 Maryna Kachanovska 1 
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : This work is dedicated to the construction and analysis of high-order transparentboundary conditions for the weighted wave equation on a fractal tree, which models sound propaga-tion inside human lungs. This article follows the works [9, 6], aimed at the analysis and numerical treatment of the model, as well as the construction of low-order and exact discrete boundary conditions. The method suggested in the present work is based on the truncation of the meromorphicseries that represents the symbol of the Dirichlet-to-Neumann operator, in the spirit of the absorbingboundary conditions of B. Engquist and A. Majda. We analyze its stability and convergence, as wellas present computational aspects of the method. Numerical results confirm theoretical findings
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Submitted on : Monday, August 3, 2020 - 6:53:59 PM
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Patrick Joly, Maryna Kachanovska. Local transparent boundary conditions for wave propagation in fractal trees (I). Method and numerical implementation. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, In press, ⟨10.1137/20M1362334⟩. ⟨hal-02462264v3⟩

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