Wave propagation in fractal trees. Mathematical and numerical issues

Patrick Joly; Maryna Kachanovska; Adrien Semin

doi:10.3934/nhm.2019010

Wave propagation in fractal trees. Mathematical and numerical issues

Patrick Joly, Maryna Kachanovska, Adrien Semin

Fachgebiet Mathematik, AG Numerik und Wissenschaftliches Rechnen Dolivostraße

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	205-264
Number of pages	60
Journal	Networks and Heterogeneous Media
Volume	14
Issue number	2
DOIs	https://doi.org/10.3934/nhm.2019010
Publication status	Published - 1 Jan 2019

Keywords

Boundary operator
Fractal
Functional approximation
Graph domain
Helmholtz equation
Laplace equation

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title = "Wave propagation in fractal trees. Mathematical and numerical issues",

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.",

keywords = "Boundary operator, Fractal, Functional approximation, Graph domain, Helmholtz equation, Laplace equation",

author = "Patrick Joly and Maryna Kachanovska and Adrien Semin",

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year = "2019",

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AU - Kachanovska, Maryna

AU - Semin, Adrien

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PY - 2019/1/1

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N2 - 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.

AB - 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.

KW - Boundary operator

KW - Fractal

KW - Functional approximation

KW - Graph domain

KW - Helmholtz equation

KW - Laplace equation

U2 - 10.3934/nhm.2019010

DO - 10.3934/nhm.2019010

M3 - Article

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VL - 14

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JO - Networks and Heterogeneous Media

JF - Networks and Heterogeneous Media

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ER -

Wave propagation in fractal trees. Mathematical and numerical issues

Abstract

Keywords

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