Domain-Decomposition Approach to Krylov Subspace Iteration

Krylov subspace iterative techniques consist of finding the solution of a scattering problem as a linear combination of "generating vectors" obtained through successive matrix-vector multiplications. This letter extends this approach to domain-decomposition. Here, on each subdomain, a subspace is obtained by constructing the segments of each generating vector associated with the subdomain and by weighting these segments independently, which provides more degrees of freedom. The method is tested for scattering by a sphere and a rectangular plate, as well as radiation from connected arrays with strongly coupled antenna elements. It is shown that substantial computational savings can be obtained for the sphere and the array. This opens up new perspectives for faster solutions of multiscaled problems.