Exterior diffraction problems for a triangular lattice

2023/01/19 by David Kapanadze, Kapanadze, David, Ekaterina Pesetskaya +1
Computer Science · Mathematics · #39A14 #39A60 #74S20 (Secondary) #78A45 (Primary) 35J05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2301.07888

openalex publication_date 2023/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Exterior Dirichlet problems for two-dimensional lattice waves on the semi-infinite triangular lattice are considered. Namely, we study Dirichlet problems for the two-dimensional 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 k ∈ (0, 2√(2)) 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.

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