In this thesis, we present a strategy based on a hybrid approach in the time domain, by coupling 3D method (FDTD) with a multi-conductors transmission line (MTL) method, in order to simulate complex large scale electromagnetic problems. This report gives the theoretical and numerical elements for coupling these approaches for two kind of problems, which are the multi domains approach and the multi scale approach. The multiple domains approach is an extension of the classical FDTD method taking into account several 3D subdomains, interconnected by a wire network, on which a 1D transmission line formalism is used. The main issues are, on one hand to have an implicit expression of the electromagnetic field in the transmission line approach, and on the other hand to be able to take into account the ground effects on the induced currents, on the transmission line parameters and on the electromagnetic field. The multi scale approach is developed to extend the capabilities of FDTD to deal with complex cables routing. We assume that the cross section of the cables are smallest than the cell size, and in these problems, the 1D transmission line problem is physically included in the 3D global computational domain. The work done in this thesis leaded to a new field to transmission line coupling based on the common mode current, and an evaluation of the transmission. line parameters based on a Laplace equation resolution in 2D. In this work, we have elaborated and proposed efficient numerical strategies for the computation of electromagnetic induced effects on large and complex sites, composed of several interconnected distant buildings. An application to lightning problems have been done.
