Boundary Element Tearing and Interconnecting Methods for Acoustic and Electromagnetic Scattering

Tearing and interconnecting methods are well known domain decomposition methods used for an approximate solution of various physical problems. The theory of this method is mainly based on partial differential equations, which imply elliptic bilinear forms. Since the acoustic and electromagnetic wave equations do not fulfill this requirement, the theory has to be modified. In this work, we establish a rigorous theory for the BETI method applied to the scattering problems. A main part is dedicated to the treatment of the local subproblems, since they are not necessary well posed if the standard approach is directly carried over to scattering problems. Further a new combined field integral equation approach is established for exterior scattering problems. This approach differs from others, and it can easily be incorporated in the presented domain decomposition approach. Therefore bounded and unbounded domains can be treated in a unified way. In addition we discuss a preconditioning approach for the BETI method in the acoustic case. This approach is carried over from the FETI-H method. Finally, numerical examples are given which confirm the theoretical results.