Volume 12, Issue 1
Perfectly Matched Layer Method for Acoustic Scattering Problem by a Locally Perturbed Line with Impedance Boundary Condition

Xue Jiang & Xujing Li

Adv. Appl. Math. Mech., 12 (2020), pp. 101-140.

Published online: 2019-12

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  • Abstract

In this paper, we study the two-dimensional Helmholtz scattering problem by a locally perturbed line with impedance boundary condition. Different from the problem with Dirichlet boundary condition, the Green function of the Helmholtz equation with impedance boundary condition becomes very complicated and comprises surface waves along the locally perturbed line. A uniaxial perfectly matched layer (UPML) method is proposed to truncate the half plane into a bounded computational domain.  The main contribution of this paper is to prove the well-posedness of the PML problem and the exponential convergence of the approximate solution to the exact solution as either the thickness or the medium parameter of PML increases.

  • Keywords

Uniaxial perfectly matched layer, Helmholtz equation, locally perturbed half-plane, impedance condition.

  • AMS Subject Headings

65N30, 78A45, 35Q60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

jxue@lsec.cc.ac.cn (Xue Jiang)

lixujing@lsec.cc.ac.cn (Xujing Li)

  • BibTex
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  • TXT
@Article{AAMM-12-101, author = {Jiang , Xue and Li , Xujing }, title = {Perfectly Matched Layer Method for Acoustic Scattering Problem by a Locally Perturbed Line with Impedance Boundary Condition}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {12}, number = {1}, pages = {101--140}, abstract = {

In this paper, we study the two-dimensional Helmholtz scattering problem by a locally perturbed line with impedance boundary condition. Different from the problem with Dirichlet boundary condition, the Green function of the Helmholtz equation with impedance boundary condition becomes very complicated and comprises surface waves along the locally perturbed line. A uniaxial perfectly matched layer (UPML) method is proposed to truncate the half plane into a bounded computational domain.  The main contribution of this paper is to prove the well-posedness of the PML problem and the exponential convergence of the approximate solution to the exact solution as either the thickness or the medium parameter of PML increases.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0047}, url = {http://global-sci.org/intro/article_detail/aamm/13421.html} }
TY - JOUR T1 - Perfectly Matched Layer Method for Acoustic Scattering Problem by a Locally Perturbed Line with Impedance Boundary Condition AU - Jiang , Xue AU - Li , Xujing JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 101 EP - 140 PY - 2019 DA - 2019/12 SN - 12 DO - http://dor.org/10.4208/aamm.OA-2019-0047 UR - https://global-sci.org/intro/article_detail/aamm/13421.html KW - Uniaxial perfectly matched layer, Helmholtz equation, locally perturbed half-plane, impedance condition. AB -

In this paper, we study the two-dimensional Helmholtz scattering problem by a locally perturbed line with impedance boundary condition. Different from the problem with Dirichlet boundary condition, the Green function of the Helmholtz equation with impedance boundary condition becomes very complicated and comprises surface waves along the locally perturbed line. A uniaxial perfectly matched layer (UPML) method is proposed to truncate the half plane into a bounded computational domain.  The main contribution of this paper is to prove the well-posedness of the PML problem and the exponential convergence of the approximate solution to the exact solution as either the thickness or the medium parameter of PML increases.

Xue Jiang & Xujing Li. (2019). Perfectly Matched Layer Method for Acoustic Scattering Problem by a Locally Perturbed Line with Impedance Boundary Condition. Advances in Applied Mathematics and Mechanics. 12 (1). 101-140. doi:10.4208/aamm.OA-2019-0047
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