Arti cial Boundary Conditions of Absolute Transparencyfor 2 D and 3 D External Time - Dependent

For an external problem in IR d (d = 2; 3) such that the unknown function satisses the wave equation outside a nite domain, we generate artiicial boundary conditions transparent to outgoing waves. These conditions permit an equivalent replacement of the original external problem by the problem inside the artiicial boundary which is a circle (d = 2) or a sphere (d = 3): The questions of numerical implementation of the obtained conditions that are non-local in both space and time are considered. The special attention is paid to reduction of necessary computational resources, in particular, a way of incorporating these conditions into numerical methods which makes the computational formulae local in time is suggested. The aspects of treating artiicial boundaries of a non-spherical shape are discussed. Numerical examples of 2D and 3D scattering problems demonstrate the accuracy of proposed artiicial boundary conditions.