Embedding techniques for directivities in acoustics and elasticity

例如，在评估结构的安全性或评估飞机的雷达剖面时，通常需要一个绕射系数。该系数描述了远离目标的信号的特征；随着参数的改变，这些参数可能很难评估和重新评估。嵌入提供了彻底改变这些计算方式的可能性，基本上解决了一个主问题，一个人评估了它的方向性。一个人真正想要的方向性是通过操纵来找到的，关键是主问题涉及的变量更少，所以你只需要评估这个方向性几次。因此，人们可能只需进行几次计算，就可以对轨道裂缝的散射进行建模，并对改变输入波场的效果进行建模，而无需再次解决问题。

It is often required, during say the evaluation of the safety of a structure or evaluating the radar profile of an aircraft, that one needs a diffraction coefficient. This coefficient characterizes the signal seen far from the object; these can be awkward to evaluate and re-evaluate as a parameter changes.Embedding offers the possibility of revolutionizing how these are calculated, basically one instead solves a master problem and one evaluates its directivity. The directivity one actually wants to have is found from this by manipulations, the key point is that less variables are involved in the master problem so you evaluate this directivity only a few times. Hence one could potentially model, say, scattering by a crack in a rail track by doing just a few calculations and model the effect of altering the incoming wavefield without ever having solve the problem again.