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

Fachgebiet Mathematik, AG Numerik und Wissenschaftliches Rechnen Dolivostraße

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

10 Citations (Scopus)

Résumé

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.

langue originale	Anglais
Pages (de - à)	205-264
Nombre de pages	60
journal	Networks and Heterogeneous Media
Volume	14
Numéro de publication	2
Les DOIs	https://doi.org/10.3934/nhm.2019010
état	Publié - 1 janv. 2019

Accès au document

10.3934/nhm.2019010

Contient cette citation

@article{935d8072cf5c4e6988027fba4f4baa1c,

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",

note = "Publisher Copyright: {\textcopyright} American Institute of Mathematical Sciences.",

year = "2019",

month = jan,

day = "1",

doi = "10.3934/nhm.2019010",

language = "English",

volume = "14",

pages = "205--264",

journal = "Networks and Heterogeneous Media",

issn = "1556-1801",

publisher = "American Institute of Mathematical Sciences",

number = "2",

}

TY - JOUR

T1 - Wave propagation in fractal trees. Mathematical and numerical issues

AU - Joly, Patrick

AU - Kachanovska, Maryna

AU - Semin, Adrien

N1 - Publisher Copyright: © American Institute of Mathematical Sciences.

PY - 2019/1/1

Y1 - 2019/1/1

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

AN - SCOPUS:85064208011

SN - 1556-1801

VL - 14

SP - 205

EP - 264

JO - Networks and Heterogeneous Media

JF - Networks and Heterogeneous Media

IS - 2

ER -

Wave propagation in fractal trees. Mathematical and numerical issues

Résumé

Accès au document

Empreinte digitale

Contient cette citation