An iterative substructuring method for Maxwell's equations in two dimensions

Iterative substructuring methods, also known as Schur complement methods, f orm an important family of domain decomposition algorithms. They are precon ditioned conjugate gradient methods where solvers on local subregions and a solver on a coarse mesh are used to construct the preconditioner. For conf orming finite element approximations of H-1, it is known that the number of conjugate gradient steps required to reduce the residual norm by a fixed f actor is independent of the number of substructures, and that it grows only as the logarithm of the dimension of the local problem associated with an individual substructure. In this paper, the same result is established for similar iterative methods for low-order Nedelec finite elements, which appr oximate H (curl; Omega) in two dimensions. Results of numerical experiments are also provided.