Overlapping Schwarz methods for Maxwell's equations in three dimensions

A two-level overlapping Schwarz method is considered for a Nedelec finite e lement approximation of 3D Maxwell's equations. For a tired relative overla p, the condition number of the method is bounded, independently of the mesh size of the triangulation and the number of subregions. Our results are ob tained with the assumption that the coarse triangulation is quasi-uniform a nd, for the Dirichlet problem, that the domain is convex. Our work generali zes well-known results for conforming finite elements for second order elli ptic scalar equations. Numerical results: for one and two-level algorithms are also presented.