Long time stability of regularized PML wave equations

Dojin Kim, Yonghyeon Jeon, Philsu Kim

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we consider two dimensional acoustic wave equations in an unbounded domain and introduce a modified model of the classical perfectly matched layer (PML). In the classical PML model, an unexpected and exponential increase in energy is observed in the long-time simulation after the solution reaches a quiescent state. To address such an instability, we provide a regularization technique to a lower order regularity term employed in the auxiliary variable in the classical PML model. The well-posedness of the regularized system is analyzed with the standard Galerkin method based on the energy analysis, and the numerical stability of staggered finite difference method for its discretization is provided by using von Neumann stability analysis. To support the theoretical results, under various thickness and damping values, we demonstrate a long-time stability of acoustic waves in the computational domain.

Original languageEnglish
Pages (from-to)269-273
Number of pages5
JournalInternational Journal of Circuits, Systems and Signal Processing
Volume11
StatePublished - 2017

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