Development of a hp-like discontinuous Galerkin time-domain method on non-conforming simplicial meshes for electromagnetic wave propagation

Hassan Fahs (1)

1 NACHOS - Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media

This work is concerned with the design of a hp-like discontinuous Galerkin (DG) method for solving the two-dimensional time-domain Maxwell equations on non-conforming locally refined triangular meshes. The proposed DG method allows non-conforming meshes with arbitrary-level hanging nodes. This method combines a centered approximation for the evaluation of fluxes at the interface between neighboring elements of the mesh, with a leap-frog time integration scheme. It is an extension of the DG formulation recently studied in [13]. Several numerical results are presented to illustrate the efficiency and the accuracy of the method, but also to discuss its limitations, through a set of 2D propagation problems in homogeneous and heterogeneous media.

Mots clés: Maxwell's equations; discontinuous Galerkin method; non-conforming triangular mesh; computational electromagnetism; hp-like method

Domaines: Physique mathématique [math-ph]; Analyse numérique [math.NA]; Electromagnétisme

Hassan Fahs. Development of a hp-like discontinuous Galerkin time-domain method on non-conforming simplicial meshes for electromagnetic wave propagation. International Journal of Numerical Analysis and Modeling, 2009, 6 (2), pp.193 - 216. ⟨hal-00600469⟩