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

Abstract

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