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 - <p style="text-align: justify;">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.</p>