Abstract

The talk is dedicated to unifying the framework used to derive the Wiener–Hopf equations arising in both discrete and continuous wave diffraction problems. The main tools are the discrete Green’s identity and the appropriate notion of a discrete normal derivative. The resulting formal analogy between the Wiener–Hopf equations makes it possible to move effortlessly between the discrete and continuous formulations. The validity of this novel analogy is illustrated through several well-known two-dimensional canonical diffraction problems and extended to three-dimensional problems. Using the analogy, embedding formulae for diffraction problems on square lattices are introduced and verified numerically with the method of boundary algebraic equations. Finally, we briefly discuss the continuum limit of discrete diffraction problems and indicate a way to recover the continuous solution from the lattice one.