Numerical methods for treating unbounded media

In many important scientific areas such as geophysics, non-destructive testing, mine detection, etc., we deal with waves propagating in unbounded media. When using finite differences or finite element methods for simulating wave propagation phenomena as they appear in such applications we need to employ a special treatment on the boundaries of the necessarily truncated computational domain. Note that such treatement is not necessary for boundary integral methods because the behaviour of the solution at infinity is taken into account through the Green’s function of the problem.