Abstract : We present in this work a time-domain discontinuous Galerkin finite element method (DGTD) applied and adapted to the time domain numerical characterization of antennas, in association with a fictitious domain approach.
First, a Discontinuous Galerkin method is presented, which is based on centered numerical fluxes and a second order explicit leap-frog time scheme. The scheme obtained is non-diffusive, stable, with low dispersion and perfectly adapted for the use of nonconforming locally refined meshes. To deal efficiently with unbounded problems, we used an unsplitted version of Perfectly Matched layers (UPML). Then, we used the DGTD method to calculate impedances, S parameters and VSWR of various planar structures. The comparison between simulation and measurement of theses structures shows the good behaviour of the method.
Next, a fictitious domain approach based on the Discontinuous Galerkin Time-Domain (DGTD) method is developped in order to take into account obstacles with complex geometries. The fictitious domain method uses two independent meshes : a cartesian grid, for the electromagnetic field propagation, and a surfacic mesh which takes into account the obstacle geometry. In the general case, the convergence of the method is linked to obtaining an uniform inf-sup condition, leading to a compatibility condition between the boundary mesh and the volumic mesh, i.e. the volumic space step is linked to the smallest triangle of the surfacic mesh. Thus the constraint can be severe for surfacic meshes with small details, in particular for methods which do not cope easily with locally refined grids (like the FDTD method). A DGTD method is perfectly adapted to the use of local subgridding and allows the control of the volumic meshes dimension.