Hybrid domain decomposition method and boundary element method for the solution of large array problems

The non-overlapping domain decomposition method (DDM) has emerged as a powerful and attractive technique for numerically-rigorous solution of Maxwell's equations due to its inherent parallelism and its beauty as an efficient and effective preconditioner. DDM is based on a divide-and-conquer philosophy. Instead of tackling a large and complex problem directly as a whole, the original problem is partitioned into smaller, possibly repetitive, and easier to solve sub-domains. Some suitable boundary conditions called transmission conditions are prescribed at the interfaces between adjacent sub-domains to enforce the continuity of electromagnetic fields. However in the existing approaches, the radiation condition is approximated by the first order absorbing boundary condition (ABC), producing the unwanted spurious reflection from the truncation boundary. In order to minimize such unphysical reflection, the truncation boundary must be placed sufficiently far away from the object, resulting a large number of sub-domains. In this paper, the unbounded exterior space will be treated as an additional domain. This domain is formulated by a boundary element method (BEM) which incorporates the radiation condition through its Green's function.