The geometry of the problem is depicted. The cross-section of an infinite plate which has a small defected region is shown below.
A wave is incident from the left and the aim is to find the scattering that occurs due to the defected region. One way to solve this problem is to use a full FE discretization throughout the whole domain. The problem with such an approach is that the computation power required for the solution increases with the size of the undefected region. We, on the other hand, have used FE for the small region in the center whereas the outside region is solved semi-analytically. The two solutions are joined on the boundaries to get the scattered field. The semi-analytical (Global) solution comes from the SAFE (semi analytical FE) which has the advantage over analytical solution in being much more versatile.
In the example shown below, scattering due to two different kinds of notches in an aluminum plate are compared. An So mode is incident from the left some part of which gets mode converted to Ao. The total energy from the scattering equals the incident energy at all frequencies which provides confidence to the analysis. The plot below also shows how this method can be used to choose the inspection frequencies for a particular defect.
The figure below shows a similar analysis for a more complex of a composite plate made of several layers of carbon reinforced laminae. This kind of analysis is neither possible by analytical techniques nor by some numerical schemes like the transfer matrix method. Using SAFE provides the hybrid method with the capability of applying it to highly complex structures.