Interface connections in domain decomposition methods

Parallel computers are increasingly used in scientific computing. They enable one to perform large scale computations. New algorithms which are well suited to such architectures have to be designed. Domain decomposition methods are a very natural way to exploit the possibilities of multiprocessor computers, but such algorithms are very useful when used on monoprocessor computers as well. The idea is to decompose the computational domain into smaller subdomains. The equations are solved on each subdomain. In order to enforce the matching of the local solutions, interface conditions have to be written on the boundary between subdomains. These conditions are imposed iteratively. The convergence rate is very sensitive to these interface conditions. Theoretical and numerical results are given.