Overlapping Schwarz methods for Maxwell's equations in three dimensions

A two-level overlapping Schwarz method is considered for a Nedelec finite element approximation of 3D Maxwell's equations. For a tired relative overlap, the condition number of the method is bounded, independently of the mesh size of the triangulation and the number of subregions. Our results are obtained with the assumption that the coarse triangulation is quasi-uniform and, for the Dirichlet problem, that the domain is convex. Our work generalizes well-known results for conforming finite elements for second order elliptic scalar equations. Numerical results: for one and two-level algorithms are also presented.