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Volume 6, Issue 1
Convergence of the Time-Domain Perfectly Matched Layer Method for Acoustic Scattering Problems

Z. Chen

Int. J. Numer. Anal. Mod., 6 (2009), pp. 124-146.

Published online: 2009-06

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  • Abstract

In this paper we establish the stability and convergence of the time-domain perfectly matched layer (PML) method for solving the acoustic scattering problems. We first prove the well-posedness and the stability of the time-dependent acoustic scattering problem with the Dirichlet-to-Neumann boundary condition. Next we show the well-posedness of the unsplit-field PML method for the acoustic scattering problems. Then we prove the exponential convergence of the non-splitting PML method in terms of the thickness and medium property of the artificial PML layer. The proof depends on a stability result of the PML system for constant medium property and an exponential decay estimate of the modified Bessel functions.

  • Keywords

Perfectly matched layer, acoustic scattering, exponential convergence, stability.

  • AMS Subject Headings

35L50, 35B35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-6-124, author = {}, title = {Convergence of the Time-Domain Perfectly Matched Layer Method for Acoustic Scattering Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2009}, volume = {6}, number = {1}, pages = {124--146}, abstract = {

In this paper we establish the stability and convergence of the time-domain perfectly matched layer (PML) method for solving the acoustic scattering problems. We first prove the well-posedness and the stability of the time-dependent acoustic scattering problem with the Dirichlet-to-Neumann boundary condition. Next we show the well-posedness of the unsplit-field PML method for the acoustic scattering problems. Then we prove the exponential convergence of the non-splitting PML method in terms of the thickness and medium property of the artificial PML layer. The proof depends on a stability result of the PML system for constant medium property and an exponential decay estimate of the modified Bessel functions.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/759.html} }
TY - JOUR T1 - Convergence of the Time-Domain Perfectly Matched Layer Method for Acoustic Scattering Problems JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 124 EP - 146 PY - 2009 DA - 2009/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/759.html KW - Perfectly matched layer, acoustic scattering, exponential convergence, stability. AB -

In this paper we establish the stability and convergence of the time-domain perfectly matched layer (PML) method for solving the acoustic scattering problems. We first prove the well-posedness and the stability of the time-dependent acoustic scattering problem with the Dirichlet-to-Neumann boundary condition. Next we show the well-posedness of the unsplit-field PML method for the acoustic scattering problems. Then we prove the exponential convergence of the non-splitting PML method in terms of the thickness and medium property of the artificial PML layer. The proof depends on a stability result of the PML system for constant medium property and an exponential decay estimate of the modified Bessel functions.

Z. Chen. (1970). Convergence of the Time-Domain Perfectly Matched Layer Method for Acoustic Scattering Problems. International Journal of Numerical Analysis and Modeling. 6 (1). 124-146. doi:
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