Two-level DDM preconditioners for positive Maxwell equations

In this paper we develop and analyse domain decomposition methods for linear systems of equations arising from conforming finite element discretisations of positive Maxwell-type equations. Convergence of domain decomposition methods rely heavily on the efficiency of the coarse space used in the second level. We design adaptive coarse spaces that complement the near-kernel space made of the gradient of scalar functions. This extends the results in [2] to the variable coefficient case and non-convex domains at the expense of a larger coarse space.