论文标题
三角晶格上的半平面衍射问题
Half-plane diffraction problems on a triangular lattice
论文作者
论文摘要
我们研究了二维晶格波的薄条衍射问题。特殊的结构使我们能够考虑半侵入三角晶格上的问题，因此，我们研究了半平面中二维离散的Helmholtz方程的差异问题。鉴于解决方案的存在和唯一性，我们为真实的波数$ k \ in（0,3）\ backslash \ {2 \ sqrt {2} \} $提供了新的结果，而无需传递复杂的波数并导致解决方案的精确表示。为此，我们使用辐射解决方案的概念。最后，我们提出了一种数值计算的方法。在与两个小开口在超材料中的波沿相关的示例中，证明了我们方法的效率。
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 $k\in (0,3)\backslash\{2\sqrt{2}\}$ 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.
