Wave propagation in fractal trees. Mathematical and numerical issues

Patrick Joly; Maryna Kachanovska; Adrien Semin; Patrick Joly; Maryna Kachanovska; Adrien Semin

doi:10.3934/nhm.2019010

Networks and Heterogeneous Media

2019, Volume 14, Issue 2: 205-264. doi: 10.3934/nhm.2019010

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Wave propagation in fractal trees. Mathematical and numerical issues

1.
POEMS (UMR 7231 CNRS-INRIA-ENSTA), ENSTA ParisTech, 828 Boulevard des Maréchaux, Palaiseau, F-91120, France
2.
Technische Universität Darmstadt, Fachgebiet Mathematik, AG Numerik und Wissenschaftliches Rechnen, Dolivostraße 15, Darmstadt, D-64293, Germany

Received: 01 December 2016 Revised: 01 October 2018
Primary: 35J05, 37E25, 65D15; Secondary: 35J20

We propose and analyze a mathematical model for wave propagation in infinite trees with self-similar structure at infinity. This emphasis is put on the construction and approximation of transparent boundary conditions. The performance of the constructed boundary conditions is then illustrated by numerical experiments.
- Laplace equation,
- Helmholtz equation,
- fractal,
- graph domain,
- boundary operator,
- functional approximation
Citation: Patrick Joly, Maryna Kachanovska, Adrien Semin. Wave propagation in fractal trees. Mathematical and numerical issues[J]. Networks and Heterogeneous Media, 2019, 14(2): 205-264. doi: 10.3934/nhm.2019010

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Abstract

We propose and analyze a mathematical model for wave propagation in infinite trees with self-similar structure at infinity. This emphasis is put on the construction and approximation of transparent boundary conditions. The performance of the constructed boundary conditions is then illustrated by numerical experiments.

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