Differential and finite-difference problems of active shielding

The paper presents the solution of a very important problem, which can be used for active noise shielding and vibration control. The problem of active shielding is related with shielding one domain from the influence of another one via a distribution of additional sources outside of the first domain. The general solution of the problem of active shielding in the differential form is obtained. The solution only requires the knowledge of the total field on the boundary of the shielded area. It does not need any additional information about the characteristics of the undesirable sources or the surrounding medium. The knowledge of the Green's function is not required either. The active shielding source terms in acoustics are obtained in the form of the potential of a simple layer. We show a correspondence between the active shielding solutions obtained in the analytical and finite-difference formulations. We also suggest an estimate of a space step in the finite-difference formulation.