Exact Boundary Conditions for Scattering Problems

Scattering in an unbounded uniform medium when the scatterer is of finite size is considered. The scatterer can, in general, be inhomogeneous and nonlinear. Determination of the exact boundary data on the boundary of a finite computational domain G by using Kirchhoff’s formula is proposed. The integral in the formula is evaluated on a surface containing the scatterer and lying inside of G. This formula is explicit since the integrand depends only on the retarded values.