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Journal Articles SIAM Journal on Scientific Computing Year : 2021

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

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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Dates and versions

hal-02462264 , version 1 (31-01-2020)
hal-02462264 , version 2 (31-07-2020)
hal-02462264 , version 3 (03-08-2020)

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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, 2021, ⟨10.1137/20M1362334⟩. ⟨hal-02462264v3⟩
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