In this talk, I will introduce optimized non-overlapping Schwarz domain decomposition methods for wave equations in the harmonic regime. The construction of the algorithms will be explained in details as well as their convergence properties. An important point concerning the efficiency of these methods is related to the construction of transmitting boundary conditions between the subdomains. To this end, a review of existing boundary conditions and new conditions will be proposed. Finally, numerical simulations will illustratre the behavior of the domain decomposition methods for acoustic (Helmholtz) and electromagnetic (Maxwell) equations.

Professor Xavier Antoine obtained his PhD in Applied Mathematics at the Laboratoire de Mathématiques Appliquées, Université de Pau et des Pays de l'Adour, in 1997. In 2004,  professor Xavier Antoine completed his Habilitation  at the Université de Toulouse. Form 2005, he has been a full professor in Universités at the Ecole des Mines de Nancy, and a member of the Institut Elie Cartan de Lorraine, & Sphinxs INRIA Team. Professor Xavier Antoine's current research interests are 1) modeling, mathematical analysis and numerical simulation of Maxwell and Helmholtz equations in the high-frequency spectrum and 2) numerical simulation of time-dependent linear and nonlinear Schrödinger-type equations.