Modeling large almost periodic structures using a non-overlapping domain decomposition method

Domain decomposition is a tool that is introduced artificially to ease large scale computation or that is natural in some situations. Domain decomposition methods are a very natural way to exploit the possibilities of multiprocessor computers, but such algorithms are very useful even when used on single process PC environment. The idea is to decompose the computational domain into smaller subdomains. The equations are solved on each subdomain. We first describe a domain decomposition method, a non-overlapping Schwarz algorithm, for solving large almost periodic electromagnetic problems. For large almost periodic structures, when using domain decomposition approach, the FEM matrix only needs to be evaluated once for all domains that are of the same building block. The solving process of domain decomposition is iterative and can become prohibitively slow. We describe a procedure that results in superior speed-up of the solving process.