Overlapping Schwarz methods for Maxwell's equations in three dimensions

Two-level overlapping Schwarz methods are considered for nite element problems of 3D Maxwell's equations. N ed elec elements built on tetrahedra and hexahedra are considered. Once the relative overlap is xed, the condition number of the additive Schwarz method is bounded, independently of the diameter of the triangulation and the number of subregions. A similar result is obtained for a multiplicative method. These bounds are obtained for quasi-uniform triangulations. In addition, for the Dirichlet problem, the convexity of the domain has to be assumed. Our work generalizes well-known results for conforming nite elements for second order elliptic scalar equations.