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Symmetry 2019, 11(2), 177; https://doi.org/10.3390/sym11020177

A Modified PML Acoustic Wave Equation

Department of Mathematics, Pusan National University, Busan 46241, Korea
Received: 3 January 2019 / Revised: 26 January 2019 / Accepted: 30 January 2019 / Published: 2 February 2019
(This article belongs to the Special Issue Current Trends in Symmetric Polynomials with their Applications)
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Abstract

In this paper, we consider a two-dimensional acoustic wave equation in an unbounded domain and introduce a modified model of the classical un-split perfectly matched layer (PML). We apply a regularization technique to a lower order regularity term employed in the auxiliary variable in the classical PML model. In addition, we propose a staggered finite difference method for discretizing the regularized system. The regularized system and numerical solution are analyzed in terms of the well-posedness and stability with the standard Galerkin method and von Neumann stability analysis, respectively. In particular, the existence and uniqueness of the solution for the regularized system are proved and the Courant-Friedrichs-Lewy (CFL) condition of the staggered finite difference method is determined. To support the theoretical results, we demonstrate a non-reflection property of acoustic waves in the layers. View Full-Text
Keywords: well-posedness; stability; acoustic wave equation; perfectly matched layer well-posedness; stability; acoustic wave equation; perfectly matched layer
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Kim, D. A Modified PML Acoustic Wave Equation. Symmetry 2019, 11, 177.

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