TY - JOUR
T1 - Long time stability of regularized PML wave equations
AU - Kim, Dojin
AU - Jeon, Yonghyeon
AU - Kim, Philsu
N1 - Publisher Copyright:
© 2017, North Atlantic University Union. All rights reserved.
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85034947590&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:85034947590
SN - 1998-4464
VL - 11
SP - 269
EP - 273
JO - International Journal of Circuits, Systems and Signal Processing
JF - International Journal of Circuits, Systems and Signal Processing
ER -