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The combination of finite and boundary element methods for the numerical
solution of coupled problems has a long tradition. It has proved to be
the method of choice for several applications among which are the
acoustic-structure coupling or the soilstructure interaction. In this
work, the concept of combining these two approximation methods is
carried forward to dynamic problems by developing a coupling framework
in which the local discretization method can be chosen independently. In
fact, a Lagrange multiplier domain decomposition approach is preferred
which allows for the most flexible combination of discretization methods
within the same solution algorithm. Therefore, Dirchlet-to Neumann maps
are realized on the discrete level for the static case or at each time
step for the dynamic case. Moreover, the treatment of nonconforming
interface meshes, i.e., interface discretizations which do not have
coincident nodes or equal interpolation orders, is included easily into
this approach. The considered physical models are the acoustic wave
equation and the linear elastodynamic system together with their static
limits, Laplace equation and elastostatics.