Seminar in Numerical Analysis: Stéphane Lanteri (Inria Sophia Antipolis)
We present a discontinuous finite element (discontinuous Galerkin) time-domain solver for the numerical simulation of the interaction of light with nanometer scale structures. The method relies on a compact stencil high order interpolation of the electromagnetic field components within each cell of an unstructured tetrahedral mesh. This piecewise polynomial numerical approximation is allowed to be discontinuous from one mesh cell to another, and the consistency of the global approximation is obtained thanks to the definition of appropriate numerical traces of the fields on a face shared by two neighboring cells. Time integration is achieved using an explicit scheme and no global mass matrix inversion is required to advance the solution at each time step. Moreover, the resulting time-domain solver is particularly well adapted to parallel computing. The proposed method is an extension of the method that we initially proposed in  for the simulation of electromagnetic wave propagation innondispersive heterogeneous media at microwave frequencies.
This is a joint work with Claire Scheid and Jonathan Viquerat.
 Fezoui, L., S. Lanteri, S. Lohrengel, and S. Piperno. Convergenceand stability of a discontinuous Galerkin time-domain method for the3D heterogeneous Maxwell equations on unstructured meshes. ESAIM:Math. Model. Numer. Anal., Vol. 39, No. 6, 1149-1176, 2005.
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