Optimized Schwarz Methods for Maxwell's Equations with Non-Zero Electric Conductivity

Victorita Dolean (1, 2) , Mohamed El Bouajaji (1) , 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]

The first ideas for optimized Schwarz methods for Maxwell's equations came from the analysis of optimized Schwarz methods for the Helmholtz equation, see [3, 4, 2, 11]. For the case of the rot-rot formulation of the Maxwell equations, optimized Schwarz methods were developed in [1]. The systematic study of Schwarz methods for Maxwell's equations in their general formulation was started in [9, 10], and an entire hierarchy of families of optimized Schwarz methods was analyzed in [8], see also [5] for discontinuous Galerkin discretizations and large scale experiments. We present in this paper a first analysis of optimized Schwarz methods for Maxwell's equations with non-zero electric conductivity. We illustrate our analysis with numerical experiments.

Domaines: Analyse numérique [math.NA]

Victorita Dolean, Mohamed El Bouajaji, Martin Gander, Stephane Lanteri. Optimized Schwarz Methods for Maxwell's Equations with Non-Zero Electric Conductivity. 2010. ⟨hal-00487520⟩