no. 19-20
Partial Differential Equations
Mathematical and numerical modeling of wave propagation in fractal trees
[Modélisation mathématique et numérique de la propagation dʼondes dans des arbres fractals]

Présenté par : the Editorial Board

Joly, Patrick1 ; Semin, Adrien2
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
Comptes Rendus. Mathématique, Tome 349 (2011) no. 19-20, pp. 1047-1051.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.09.008
Joly, Patrick 1 ; Semin, Adrien 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 = {Joly, Patrick and Semin, Adrien},
     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},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2011.09.008/}
}
TY  - JOUR
AU  - Joly, Patrick
AU  - Semin, Adrien
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
UR  - http://www.numdam.org/articles/10.1016/j.crma.2011.09.008/
DO  - 10.1016/j.crma.2011.09.008
LA  - en
ID  - CRMATH_2011__349_19-20_1047_0
ER  - 
%0 Journal Article
%A Joly, Patrick
%A Semin, Adrien
%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
%U http://www.numdam.org/articles/10.1016/j.crma.2011.09.008/
%R 10.1016/j.crma.2011.09.008
%G en
%F CRMATH_2011__349_19-20_1047_0
Joly, Patrick; Semin, Adrien. Mathematical and numerical modeling of wave propagation in fractal trees. Comptes Rendus. Mathématique, Tome 349 (2011) no. 19-20, pp. 1047-1051. doi : 10.1016/j.crma.2011.09.008. http://www.numdam.org/articles/10.1016/j.crma.2011.09.008/

[1] Achdou, Y.; Sabot, C.; Tchou, N. 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] Joly, P.; Semin, A. 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] Kuchment, P. Graph models for waves in thin structures, Waves Random Media, Volume 12 (2002) no. 4, p. R1-R24

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

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

Cité par Sources :