Truncated transparent boundary conditions for second order hyperbolic systems

In [22] we announced equations for yielding differential operators of transparent boundary conditions (TBCs) for a certain class of second order hyperbolic systems. Here we present the full derivation of these equations and consider ways of their solving. The solutions represent local parts of TBCs, and they can be used as approximate nonreflecting boundary conditions. We give examples of computing such conditions called 'truncated TBCs' for 3D elasticity and Biot poroelasticity