Implementing a boundary condition for incident waves in FE calculations

An boundary condition for three dimensional scattering and diffraction problems is presented. On the exterior boundary, where a finite element mesh has to be truncated, a surface integral is introduced to incorporate the incident wave into the finite element scheme, while an absorbing boundary condition is applied to absorb the outgoing scattered wave. The boundary condition can be easily included in the finite element formulation, but some pitfalls are highlighted. Three dimensional numerical examples show the accuracy of the method.