Half-plane diffraction problems on a triangular lattice

2022/07/10 by David Kapanadze, Kapanadze, David, Ekaterina Pesetskaya +1
Engineering · Physics and Astronomy · #39A14 #39A60 #74S20 (Secondary) #78A45 (Primary) 35J05 #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2207.04386

openalex publication_date 2022/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate thin-slit diffraction problems for two-dimensional lattice waves. The peculiar structure allows us to consider the problems on the semi-infinite triangular lattice, consequently, we study Dirichlet problems for the two-dimensional discrete Helmholtz equation in a half-plane. In view of the existence and uniqueness of the solution, we provide new results for the real wave number k∈ (0,3)\backslash\2√(2)\ without passing to the complex wave number and derive an exact representation formula for the solution. For this purpose, we use the notion of the radiating solution. Finally, we propose a method for numerical calculation. The efficiency of our approach is demonstrated in an example related to the propagation of wave fronts in metamaterials through two small openings.

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