En poursuivant votre navigation sur ce site, vous acceptez l'utilisation d'un simple cookie d'identification. Aucune autre exploitation n'est faite de ce cookie. OK
1

Transparent boundary conditions for wave propagation in fractal trees

Sélection Signaler une erreur
Multi angle
Auteurs : Kachanovska, Maryna (Auteur de la Conférence)
CIRM (Editeur )

Loading the player...

Résumé : In collaboration with Patrick Joly (Poems, Cnrs, Inria, Ensta Paris) and Adrien Semin (Technische Universität Darmstadt).
We consider the problem of a numerical resolution of a weighted wave equation on a fractal tree, which originates from an asymptotic modelling of sound propagation in lungs. Performing numerical simulations for this model relies on truncation of the computational domain to a finite tree. This is done by imposing a Dirichlet-to-Neumann (DtN) boundary condition at the ends of the truncated tree. The symbols of the DtN operators are Herglotz-Nevanlinna functions, and their Herglotz-Nevanlinna property is intimately related to the stability of the problem. Because in practical simulations we have to approximate the DtN operators, the stability of the approximated problem can be ensured if the approximated symbols of the DtNs are Herglotz-Nevanlinna functions as well. One such approximation is given by truncating to finitely many terms the meromorphic series representing the symbol of the DtN. We present the convergence analysis of this method, which relies on the estimates on the counting function for the weighted Laplacian and on the normal traces of the eigenfunctions. We finish the discussion with numerical experiments.

Codes MSC :

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 20/06/2022
    Date de captation : 25/05/2022
    Sous collection : Research talks
    arXiv category : Analysis of PDEs ; Mathematical Physics
    Domaine : PDE ; Mathematical Physics ; Mathematics in Science & Technology
    Format : MP4 (.mp4) - HD
    Durée : 00:28:55
    Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2022-05-25_Kachanovska.mp4

Informations sur la Rencontre

Nom de la rencontre : Herglotz-Nevanlinna Functions and their Applications to Dispersive Systems and Composite Materials / Fonctions de Herglotz-Nevanlinna et leurs applications aux systèmes dispersifs et aux matériaux composites
Organisateurs de la rencontre : Bonnet-Ben Dhia, Anne-Sophie ; Cassier, Maxence ; Gralak, Boris ; Luger, Annemarie ; Milton, Graeme
Dates : 23/05/2022 - 27/05/2022
Année de la rencontre : 2022
URL Congrès : https://conferences.cirm-math.fr/2225.html

Données de citation

DOI : 10.24350/CIRM.V.19920103
Citer cette vidéo: Kachanovska, Maryna (2022). Transparent boundary conditions for wave propagation in fractal trees. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19920103
URI : http://dx.doi.org/10.24350/CIRM.V.19920103

Voir aussi

Bibliographie



Imagette Video

Sélection Signaler une erreur