Calculation of the operator of transparent boundary conditions on a three-dimensional plane boundary for a homogeneous in the normal direction medium

The transparent boundary conditions (TBC) on the artificial boundaries of the computational domain for 3D problems on the propagation of waves in an elastic medium are developed in the case when the properties of the medium vary along the boundary of the computational domain, but are constant in the direction perpendicular to it. The auxiliary elliptic problems in the normal to the boundary direction are solved by the collocation method. Numerical examples are given that indicate that the developed boundary conditions are stable and sufficiently accurate.