Exterior diffraction problems for a triangular lattice
Analysis of PDEs
2023-01-20 v1 Mathematical Physics
math.MP
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 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.
Cite
@article{arxiv.2301.07888,
title = {Exterior diffraction problems for a triangular lattice},
author = {David Kapanadze and Ekaterina Pesetskaya},
journal= {arXiv preprint arXiv:2301.07888},
year = {2023}
}
Comments
7 figures. arXiv admin note: text overlap with arXiv:2207.04386