Optimized Schwarz domain decomposition methods for scalar and vector Helmholtz equations

Xavier Antoine (1, 2) , Christophe Geuzaine (3)

1 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
2 IECL - Institut Élie Cartan de Lorraine
3 ACE - Applied and Computational Electromagnetics [Liège]

In this chapter we review Schwarz domain decomposition methods for scalar and vector Helmholtz equations, with a focus on the choice of the associated transmission conditions between the subdomains. The methods are analyzed in both acoustic and electromagnetic settings, and generic weak formulations directly amenable to finite element discretization are presented. An open source solver along with ready-to-use examples is freely available online for further testing.

Mots clés: electromagnetics; domain decomposition methods; Helmholtz Equation; acoustics; numerical simulation

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Xavier Antoine, Christophe Geuzaine. Optimized Schwarz domain decomposition methods for scalar and vector Helmholtz equations. D. Lahaye, J. Tang and K. Vuik. Modern Solvers for Helmholtz Problems, Springer International Publishing, pp.189-213, 2016, Lecture notes in geosystems mathematics and computing, ⟨10.1007/978-3-319-28832-1_8⟩. ⟨hal-01276808⟩