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Volume 42, Issue 5
The Nyström Method for Elastic Wave Scattering by Unbounded Rough Surfaces

Jianliang Li, Xiaoli Liu, Bo Zhang & Haiwen Zhang

DOI: 10.4208/jcm.2304-m2022-0185

J. Comp. Math., 42 (2024), pp. 1407-1426.

Published online: 2024-07

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  • Abstract

We consider a numerical algorithm for the two-dimensional time-harmonic elastic wave scattering by unbounded rough surfaces with Dirichlet boundary condition. A Nyström method is proposed for the scattering problem based on the integral equation method. Convergence of the Nyström method is established with convergence rate depending on the smoothness of the rough surfaces. In doing so, a crucial role is played by analyzing the singularities of the kernels of the relevant boundary integral operators. Numerical experiments are presented to demonstrate the effectiveness of the method.

  • Keywords

Elastic wave scattering, Unbounded rough surface, Nyström method.

  • AMS Subject Headings

35P25, 45P05

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-42-1407, author = {Li , JianliangLiu , XiaoliZhang , Bo and Zhang , Haiwen}, title = {The Nyström Method for Elastic Wave Scattering by Unbounded Rough Surfaces}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {42}, number = {5}, pages = {1407--1426}, abstract = {

We consider a numerical algorithm for the two-dimensional time-harmonic elastic wave scattering by unbounded rough surfaces with Dirichlet boundary condition. A Nyström method is proposed for the scattering problem based on the integral equation method. Convergence of the Nyström method is established with convergence rate depending on the smoothness of the rough surfaces. In doing so, a crucial role is played by analyzing the singularities of the kernels of the relevant boundary integral operators. Numerical experiments are presented to demonstrate the effectiveness of the method.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2304-m2022-0185}, url = {http://global-sci.org/intro/article_detail/jcm/23283.html} }
TY - JOUR T1 - The Nyström Method for Elastic Wave Scattering by Unbounded Rough Surfaces AU - Li , Jianliang AU - Liu , Xiaoli AU - Zhang , Bo AU - Zhang , Haiwen JO - Journal of Computational Mathematics VL - 5 SP - 1407 EP - 1426 PY - 2024 DA - 2024/07 SN - 42 DO - http://doi.org/10.4208/jcm.2304-m2022-0185 UR - https://global-sci.org/intro/article_detail/jcm/23283.html KW - Elastic wave scattering, Unbounded rough surface, Nyström method. AB -

We consider a numerical algorithm for the two-dimensional time-harmonic elastic wave scattering by unbounded rough surfaces with Dirichlet boundary condition. A Nyström method is proposed for the scattering problem based on the integral equation method. Convergence of the Nyström method is established with convergence rate depending on the smoothness of the rough surfaces. In doing so, a crucial role is played by analyzing the singularities of the kernels of the relevant boundary integral operators. Numerical experiments are presented to demonstrate the effectiveness of the method.

Jianliang Li, Xiaoli Liu, Bo Zhang & Haiwen Zhang. (2024). The Nyström Method for Elastic Wave Scattering by Unbounded Rough Surfaces. Journal of Computational Mathematics. 42 (5). 1407-1426. doi:10.4208/jcm.2304-m2022-0185
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