Efficient Evaluation of the Solution for the Planar Wave Diffraction in a 2D Sector

Abstract

We consider the diffraction of a planar acoustic wave in a 2D sector with the central angle \({{2\pi } \mathord{\left/ {\vphantom {{2\pi } n}} \right. \kern-0em} n}\), \(n \in \mathbb{N}\). If \(n\) is even, then the solution of this problem is straightforward by the reflection method. For odd \(n\), we present an efficient algorithm to evaluate the time-domain solution of this problem. We use this solution with \(n = 1\) and \(n = 3\) to study the accuracy of the discontinuous Galerkin method applied to the acoustical system in a domain with corners.