Non-conforming Coupled Time Domain Boundary Element Analysis

The time domain Boundary Element Method (BEM) has been found to be well suited for modeling wave propagation phenomena in large or unbounded media. Nevertheless, material discontinuities or local non-linear effects are beyond the scope of classical BEM and require special techniques. Here, a (possibly hybrid) Domain Decomposition Method is proposed in order to circumvent these limitations and to obtain an efficient solution procedure at the same time.

In time domain analysis it is preferable to have a coupling technique which is able to couple domains with different grids. If e.g. two domains with different materials are considered, in each domain a different suitable spatial and temporal grid is necessary. In the finite element community, several methods which provide such techniques are known, for example the

Mortar

-Method (see [

1

,

2

]). Such type of method is also proposed here for a BE time domain formulation.

By means of local Dirichlet-to-Neumann maps and a weak statement of the interface conditions a condensed abstract formulation is obtained. The global problem is given in a variational principle without a specification of the discretization method (e.g., BEM or FEM). Whereas this methodology has been fully established for elliptic partial differential equations, the transfer to hyperbolic initial boundary value problems is still an open question.

Here, the formal procedure is given followed by some exemplary numerical tests.