Modeling Methods for Silent Boundaries in Infinite Media

In several problems of interest in computational modeling there is a media that is either infinite or semi-infinite. Some examples include: modeling the ocean when doing ship analysis, modeling the soil underneath a footing, and modeling the air around an airplane. However, every finite element model must be terminated at some finite boundary. Unfortunately, for problems involving wave propagation analysis, the usual finite boundary of the finite element model will cause the elastic waves to be reflected and superimposed with the progressing waves. Therefore, we wish to create a boundary, which is perfectly radiating to outgoing waves (no spurious reflections) and transparent to incoming waves. In addition, we would like the boundary to be as close to the finite structure as possible for computational efficiency. A simple solution to the problem is to move the boundary a great distance away from the finite structure so that the boundary does not influence the results. However, this violates the concept of computational efficiency. Hence, we need an artificial boundary condition to simulate a model without any finite boundary. Through a literature research there appears to be two basic approaches to this boundary condition. The first is to create boundary elements with special properties to absorb the outgoing waves. The second approach is to create infinite elements. This report will discuss three concepts of the boundary element approach: plane wave approximation, viscous damping boundary method, and perfectly matched layers. A brief introduction into infinite elements will be presented as well.