Geodesic
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.

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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.

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 
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     title = {Mathematical and numerical modeling of wave propagation in fractal trees},
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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://geodesic.mathdoc.fr/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

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