The <i>k</i>‐space formulation of the scattering problem in the time domain

The arbitrary direct scattering problem is solved numerically in closed form in the time domain and spatial Fourier transform space. This solution consists of casting the general basic global laws (i.e., the second‐order partial differential wave equation or its integral representation) as a local algebraic equation in the spatial Fourier transform space, and leaving the specific local constitutive equations (i.e., the algebraic boundary conditions, which specify a given structure, which are conventionally imposed on the differential or integral representation of the general basic global wave equation) as a local algebraic equation in real space, thereby reducing the scattering problem to a statement of two simultaneous local algebraic equations in two unknowns (the fields and the induced sources) in two spaces connected by the spatial Fourier transform. A temporally local representation in both spaces is obtained with the aid of an introduced auxilliary field and two propagators. By virtue of causality, ...