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In the formulation of the problem of scattering of monochromatic waves andthe numerical simulation of the solution to the Helmholtz equation, there is acomputational inconvenience: the calculation is performed on a finite grid ofdiscretization nodes of the finite scattering region, while the radiationconditions for the scattered wave are formulated at the infinitely distantboundary. Overcoming this inconvenience leads to a new type of boundarycondition: a nonlocal boundary condition (or condition of the 4th kind).

Radiation condition for the 3-dimensional Helmholtz equation on the boundary of a bounded domain