Mercredi 3 Juin

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Mercredi 3 Juin
Heure: 15:00 - 16:00
Lieu: Salle B405, bâtiment B, LAGA, Institut Galilée, Université Paris 13
Résumé: Modélisation et Calcul Scientifique - Construction of transparent boundary conditions for wave propagation in fractal trees. -
Description: Maryna Kachanovska
The principal difficulty for the numerical resolution of the problem is the 'infiniteness' of the geometry. To deal with this issue, we present transparent boundary conditions, used to truncate the computational domain to a finite subtree. The construction of such transparent conditions relies on the approximation of the Dirichlet-to-Neumann (DtN) operator, whose symbol is a meromorphic function that satisfies a certain non-linear functional equation. We present one approach to approximate the DtN in the time domain, inspired by the Engquist-Majda ABCs (cf. [Engquist, Majda 1977]). This approach consists in approximating the DtN by local operators, obtained from the truncation of the meromorphic series which represents the symbol of the DtN. The respective error analysis relies on the Weyl estimates for the eigenvalues of the weighted Laplacian on the fractal tree and on the estimates on the respective eigenfunctions. This is a joint work with Patrick Joly (INRIA, France) and Adrien Semin (TU Darmstadt, Germany).