Towards scalable solvers for the time-harmonic Maxwell equations in complex media

par Ari Rappaport (LJLL, Sorbonne Université)

mardi 20 oct. 2026, 14:00 → 15:00 Europe/Paris

GI041 (UTC - GI)

Computing electromagnetic waves in heterogeneous and anisotropic materials requires solving large, challenging linear systems. This talk presents two-level overlapping Schwarz methods for the time-harmonic Maxwell equations, combining parallel local solves with a global coarse correction.

I will discuss quantitative GMRES convergence estimates that make explicit the dependence on frequency, material contrast, absorption, and the domain decomposition parameters. These estimates give sufficient conditions on the subdomain and coarse mesh sizes for effective preconditioning. Numerical experiments explore these predictions, showing how coarse refinement can compensate for material contrast and where the theoretical conditions are conservative. A parallel absorbing-coating simulation with over seven million unknowns in 3D illustrates the method's performance beyond the analytical setting.

Joint work with Marcella Bonazzoli, Patrick Ciarlet, and Axel Modave.