The Construction of Preconditioners for Elliptic Problems by Substructuring. II

We give a method for constructing preconditioners for the discrete systems arising in the approximation of solutions of elliptic boundary value problems. These preconditioners are based on domain decomposition techniques and lead to algorithms which are well suited for parallel computing environments. The method presented in this paper leads to a preconditioned system with condition number proportional to $d/h$ where d is the subdomain size and h is the mesh size. These techniques are applied to singularly perturbed problems and problems in three dimensions. The results of numerical experiments illustrating the performance of the method on problems in two and three dimensions are given.