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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.