English

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 k(0,22)k \in (0, 2\sqrt{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.

Keywords

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