Boundary Element Tearing and Interconnecting Methods in Unbounded Domains

Finite element tearing and interconnecting (FETI) methods and boundary element tearing and interconnecting (BETI) methods are special iterative substructuring methods with Lagrange multipliers. For elliptic boundary value problems on bounded domains, the condition number of these methods can be rigorously bounded by C ((1+log(H/h)), where H is the subdomain diameter and h the mesh size. The constant C is independent of H, h and possible jumps in the coefficients of the partial differential equation. In certain situations, e. g., in electromagnetic field computations, instead of imposing artificial boundary conditions one may be interested in modelling the real physical behaviour in an exterior domain with a radiation condition. In this work we analyze one-level BETI methods for such unbounded domains and show explicit condition number estimates similar to the one above. Our theoretical results are confirmed in numerical experiments.