ABSTRACT: We consider domain decomposition preconditioners for the linear algebraic equations which result from finite element discretization of problems involving the bilinear form $\alpha(\cdot,\cdot)+(\curl\cdot,\curl\cdot)$ defined on a non-convex domain $\Omega$. Here $(\cdot,\cdot)$ denotes the inner product in $(L^2(\Omega))^3$ and $\alpha$ is a positive number. We use Nedelec's curl-conforming finite elements to discretize the problem. Both additive and multiplicative overlapping Schwarz preconditioners are studied. Our results are uniform with respect to the mesh size and $\alpha$ under standard assumptions concerning the overlapping subdomains.
ACKNOWLEGEMENTS: This work was supported in part by the National Science Foundation through grant number DMS-9973328.