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Volume 30, Issue 3
An Edge-Based Smoothed Finite Element Method with TBC for the Elastic Wave Scattering by an Obstacle

Ze Wu, Junhong Yue, Ming Li, Ruiping Niu & Yufei Zhang

DOI: 10.4208/cicp.OA-2020-0095

Commun. Comput. Phys., 30 (2021), pp. 709-748.

Published online: 2021-07

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  • Abstract

Elastic wave scattering has received ever-increasing attention in military and medical fields due to its high-precision solution. In this paper, an edge-based smoothed finite element method (ES-FEM) combined with the transparent boundary condition (TBC) is proposed to solve the elastic wave scattering problem by a rigid obstacle with smooth surface, which is embedded in an isotropic and homogeneous elastic medium in two dimensions. The elastic wave scattering problem satisfies Helmholtz equations with coupled boundary conditions obtained by Helmholtz decomposition. Firstly, the TBC of the elastic wave scattering is constructed by using the analytical solution to Helmholtz equations, which can truncate the boundary value problem (BVP) in an unbounded domain into the BVP in a bounded domain. Then the formulations of ES-FEM with the TBC are derived for Helmholtz equations with coupled boundary conditions. Finally, several numerical examples illustrate that the proposed ES-FEM with the TBC (ES-FEM-TBC) can work effectively and obtain more stable and accurate solution than the standard FEM with the TBC (FEM-TBC) for the elastic wave scattering problem.

  • Keywords

Elastic wave scattering problem, edge-based smoothed finite element method, Helmholtz equations, transparent boundary condition.

  • AMS Subject Headings

35Q99, 65N99

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

woyuejunhong@163.com (Junhong Yue)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-30-709, author = {Wu , ZeYue , JunhongLi , MingNiu , Ruiping and Zhang , Yufei}, title = {An Edge-Based Smoothed Finite Element Method with TBC for the Elastic Wave Scattering by an Obstacle}, journal = {Communications in Computational Physics}, year = {2021}, volume = {30}, number = {3}, pages = {709--748}, abstract = {

Elastic wave scattering has received ever-increasing attention in military and medical fields due to its high-precision solution. In this paper, an edge-based smoothed finite element method (ES-FEM) combined with the transparent boundary condition (TBC) is proposed to solve the elastic wave scattering problem by a rigid obstacle with smooth surface, which is embedded in an isotropic and homogeneous elastic medium in two dimensions. The elastic wave scattering problem satisfies Helmholtz equations with coupled boundary conditions obtained by Helmholtz decomposition. Firstly, the TBC of the elastic wave scattering is constructed by using the analytical solution to Helmholtz equations, which can truncate the boundary value problem (BVP) in an unbounded domain into the BVP in a bounded domain. Then the formulations of ES-FEM with the TBC are derived for Helmholtz equations with coupled boundary conditions. Finally, several numerical examples illustrate that the proposed ES-FEM with the TBC (ES-FEM-TBC) can work effectively and obtain more stable and accurate solution than the standard FEM with the TBC (FEM-TBC) for the elastic wave scattering problem.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0095}, url = {http://global-sci.org/intro/article_detail/cicp/19308.html} }
TY - JOUR T1 - An Edge-Based Smoothed Finite Element Method with TBC for the Elastic Wave Scattering by an Obstacle AU - Wu , Ze AU - Yue , Junhong AU - Li , Ming AU - Niu , Ruiping AU - Zhang , Yufei JO - Communications in Computational Physics VL - 3 SP - 709 EP - 748 PY - 2021 DA - 2021/07 SN - 30 DO - http://doi.org/10.4208/cicp.OA-2020-0095 UR - https://global-sci.org/intro/article_detail/cicp/19308.html KW - Elastic wave scattering problem, edge-based smoothed finite element method, Helmholtz equations, transparent boundary condition. AB -

Elastic wave scattering has received ever-increasing attention in military and medical fields due to its high-precision solution. In this paper, an edge-based smoothed finite element method (ES-FEM) combined with the transparent boundary condition (TBC) is proposed to solve the elastic wave scattering problem by a rigid obstacle with smooth surface, which is embedded in an isotropic and homogeneous elastic medium in two dimensions. The elastic wave scattering problem satisfies Helmholtz equations with coupled boundary conditions obtained by Helmholtz decomposition. Firstly, the TBC of the elastic wave scattering is constructed by using the analytical solution to Helmholtz equations, which can truncate the boundary value problem (BVP) in an unbounded domain into the BVP in a bounded domain. Then the formulations of ES-FEM with the TBC are derived for Helmholtz equations with coupled boundary conditions. Finally, several numerical examples illustrate that the proposed ES-FEM with the TBC (ES-FEM-TBC) can work effectively and obtain more stable and accurate solution than the standard FEM with the TBC (FEM-TBC) for the elastic wave scattering problem.

Wu , ZeYue , JunhongLi , MingNiu , Ruiping and Zhang , Yufei. (2021). An Edge-Based Smoothed Finite Element Method with TBC for the Elastic Wave Scattering by an Obstacle. Communications in Computational Physics. 30 (3). 709-748. doi:10.4208/cicp.OA-2020-0095
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