Exterior diffraction problems for a triangular lattice

Exterior Dirichlet problems for two-dimensional (2D) lattice waves on the infinite triangular lattice are considered. Namely, we study Dirichlet problems for the 2D discrete Helmholtz equation in a plane with a hole. New results are obtained for the existence and uniqueness of the solution in the case of the real wave number [Formula: see text] without passing to a complex wave number. Besides, Green’s representation formula for the solution is derived with the help of difference potentials. To demonstrate the results, we propose a method for numerical calculation.