In this dissertation we have applied Trefethen and Gopal's Lightning Method to solve the Helmholtz equation in the exterior of two dimensional piecewise smooth domains. The background theory motivating the method is presented, and we explore the optimal method implementation for the unit square, which is subsequently used to give a guide on parameter selection for a general region. The behaviour of the computed solutions is verified to act in accordance with our intuition and current understanding of wave propagation, and we show that the wave decays to approximately 0 in the shadow region.

翻译：本论文将 Trefethen 和 Gopal 的 Lightning 方法应用于求解二维分段光滑域外部的 Helmholtz 方程。首先阐述了该方法背后的理论依据，然后探讨了针对单位正方形的最优方法实现，并以此为基础给出了通用区域参数选择的指导原则。计算解的行为被验证与我们对波传播的直觉及当前理解相一致，且结果表明波在阴影区域衰减至近似为零。