Solving Composite Problems with Interface Relaxation

This paper deals with a solution approach suitable for (:omposite PDEs with interface conditions. We present a general framework based on interface relaxation which provides a uniform platform for building problem solving environmen\.s t1lrough efficient softwaIe integration and for implementing various relaxation schemes. Mathematically, this framework contains many existing domain decomposition methods and also allows the extension to a variety of new relaxers. In particular, we describe a class of relaxers whicb are suitable for very general and complicated interface conditions. Interface relaxation is morc general than the traditional domain decomposition methods in tha.t it allows unrelated PDE problems on different subdomains. Convergence analysis, error estimates and preconditioning strategies are presented which show that these relaxers are competitive with e:cisting domain decomposition methods {or model problems involving a single PDE. We present experimental results which demonstrate the wide applicabilit.y of this approach. Differences between this approach and other domain decomposition methods are also discussed.