Comptes Rendus
Partial Differential Equations
Mathematical and numerical modeling of wave propagation in fractal trees
Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1047-1051.

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

Nous proposons et analysons un modèle mathématique pour la propagation dʼondes dans des arbres infinis qui sont auto-similaires à lʼinfini. Lʼaccent est mis sur la construction et lʼapproximation de conditions aux limites transparentes.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2011.09.008

Patrick Joly 1; Adrien Semin 2

1 POEMS, UMR 7231, CNRS-ENSTA-INRIA, INRIA, domaine de Voluceau, 78153 Le Chesnay cedex, France
2 Applied Mathematics, University of Crete and IACM/FORTH, 71409 Heraklion, Greece
@article{CRMATH_2011__349_19-20_1047_0,
     author = {Patrick Joly and Adrien Semin},
     title = {Mathematical and numerical modeling of wave propagation in fractal trees},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1047--1051},
     publisher = {Elsevier},
     volume = {349},
     number = {19-20},
     year = {2011},
     doi = {10.1016/j.crma.2011.09.008},
     language = {en},
}
TY  - JOUR
AU  - Patrick Joly
AU  - Adrien Semin
TI  - Mathematical and numerical modeling of wave propagation in fractal trees
JO  - Comptes Rendus. Mathématique
PY  - 2011
SP  - 1047
EP  - 1051
VL  - 349
IS  - 19-20
PB  - Elsevier
DO  - 10.1016/j.crma.2011.09.008
LA  - en
ID  - CRMATH_2011__349_19-20_1047_0
ER  - 
%0 Journal Article
%A Patrick Joly
%A Adrien Semin
%T Mathematical and numerical modeling of wave propagation in fractal trees
%J Comptes Rendus. Mathématique
%D 2011
%P 1047-1051
%V 349
%N 19-20
%I Elsevier
%R 10.1016/j.crma.2011.09.008
%G en
%F CRMATH_2011__349_19-20_1047_0
Patrick Joly; Adrien Semin. Mathematical and numerical modeling of wave propagation in fractal trees. Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1047-1051. doi : 10.1016/j.crma.2011.09.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.09.008/

[1] Y. Achdou; C. Sabot; N. Tchou Transparent boundary conditions for the Helmholtz equation in some ramified domains with a fractal boundary, J. Comput. Phys., Volume 220 (2007) no. 2, pp. 712-739

[2] P. Joly; A. Semin Construction and analysis of improved Kirchoff conditions for acoustic wave propagation in a junction of thin slots, ESAIM Proc., Volume 25 (2008), pp. 44-67

[3] P. Kuchment Graph models for waves in thin structures, Waves Random Media, Volume 12 (2002) no. 4, p. R1-R24

[4] B. Maury; D. Salort; C. Vannier Trace theorems for trees, application for the human lung, Netw. Heterog. Media, Volume 4 (2009) no. 3, pp. 469-500

[5] E.R. Wiebel Morphometry of the Human Lung, Springer Verlag/Academic Press, Berlin/New York, 1963

Cited by Sources:

Comments - Policy