Optimized Schwarz methods for the time-harmonic Maxwell equations with damping

Mohamed El Bouajaji (1) , Victorita Dolean (2) , Martin Gander (3) , Stephane Lanteri (1)

1 NACHOS - Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media
2 JAD - Laboratoire Jean Alexandre Dieudonné
3 Section de mathématiques [Genève]

In a previous paper, two of the authors have proposed and analyzed an entire hierarchy of optimized Schwarz methods for Maxwell's equations both in the time-harmonic and time-domain case. The optimization process has been perfomed in a particular situation where the electric conductivity was neglected. Here, we take into account this physical parameter which leads to a fundamentally different analysis and a new class of algorithms for this more general case. From the mathematical point of view, the approach is different, since the algorithm does not encounter the pathological situations of the zero-conductivity case and thus the optimization problems are different. We analyze one of the algorithms in this class in detail and provide asymptotic results for the remaining ones. We illustrate our analysis with numerical results.

Domaines: Analyse numérique [math.NA]

Mohamed El Bouajaji, Victorita Dolean, Martin Gander, Stephane Lanteri. Optimized Schwarz methods for the time-harmonic Maxwell equations with damping. 2011. ⟨hal-00637822⟩