A stable decoupled perfectly matched layer for the 3D wave equation using the nodal discontinuous Galerkin method

TL;DR

The paper documents elsarticle.cls, a LaTeX document class designed for Elsevier journal submissions. It preserves the LaTeX kernel interface to minimize package clashes and ensures compatibility with common tools such as natbib, geometry, and amsmath. It contrasts elsarticle.cls with the older elsart.cls by emphasizing a base on article.cls, default preprint formatting, and streamlined handling of lists and theorem environments, plus final-model formats. Installation guidance and distribution channels (Elsevier author resources and CTAN) are provided, including steps to generate the class from dtx/ins sources and integrate it into the TEXMF tree. Overall, the work offers a robust, flexible class that simplifies manuscript formatting and submission for Elsevier journals.

Abstract

In outdoor acoustics, the calculations of sound propagating in air can be computationally heavy if the domain is chosen large enough to fulfil the Sommerfeld radiation condition. By strategically truncating the computational domain with a efficient boundary treatment, the computational cost is lowered. One commonly used boundary treatment is the perfectly matched layer (PML) that dampens outgoing waves without polluting the computed solution in the inner domain. The purpose of this study is to propose and assess a new perfectly matched layer formulation for the 3D acoustic wave equation, using the nodal discontinuous Galerkin finite element method. The formulation is based on an efficient PML formulation that can be decoupled to further increase the computational efficiency and guarantee stability without sacrificing accuracy. This decoupled PML formulation is demonstrated to be long-time stable and an optimization procedure of the damping functions is proposed to enhance the performance of the formulation.