Wave propagation in fractal trees. Mathematical and Numerical Issues

Patrick Joly (1) , Maryna Kachanovska (1) , Adrien Semin (2)

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
2 TU Darmstadt - Technische Universität Darmstadt - Technical University of Darmstadt

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.

Mots clés: Laplace equation; Helmholtz equation; fractal; graph domain; boundary operator; functional approximation

Domaines: Analyse numérique [math.NA]

Patrick Joly, Maryna Kachanovska, Adrien Semin. Wave propagation in fractal trees. Mathematical and Numerical Issues. Networks and Heterogeneous Media, 2019, 14 (2), ⟨10.3934/nhm.2019010⟩. ⟨hal-01801394v2⟩