Optimized Schwarz method for solving time-harmonic Maxwell's equations discretized by a discontinuous Galerkin method

Victorita Dolean (1, 2) , Stephane Lanteri (2, 3) , Ronan Perrussel (4)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 CAIMAN - Scientific computing, modeling and numerical analysis
3 CRISAM - Inria Sophia Antipolis - Méditerranée
4 AMPERE - Ampère

The numerical solution of the three-dimensional time-harmonic Maxwell equations using high order methods such as discontinuous Galerkin formulations require efficient solvers. A domain decomposition strategy is introduced for this purpose. This strategy is based on optimized Schwarz methods applied to the first order form of the Maxwell system and leads to the best possible convergence of these algorithms. The principles are explained for a 2D model problem and numerical simulations confirm the predicted theoretical behavior. The efficiency is further demonstrated on more realistic 3D geometries including a bioelectromagnetism application.

Mots clés: optimized interface conditions; Domain decomposition methods; discontinuous Galerkin methods; optimized interface conditions.

Domaines: Calcul parallèle, distribué et partagé [cs.DC]; Electromagnétisme

Victorita Dolean, Stephane Lanteri, Ronan Perrussel. Optimized Schwarz method for solving time-harmonic Maxwell's equations discretized by a discontinuous Galerkin method. 2007. ⟨hal-00164838v2⟩