@Article{AAMM-15-6,
author = {Yue, Junhong and Yu, Wang and Yan, Li and Ming, Li},
title = {A Node-Based Smoothed Finite Element Method with Linear Gradient Fields for Elastic Obstacle Scattering Problems},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2023},
volume = {15},
number = {6},
pages = {1562--1601},
abstract = {<p style="text-align: justify;">In this paper, a node-based smoothed finite element method (NS-FEM) with
linear gradient fields (NS-FEM-L) is presented to solve elastic wave scattering by a
rigid obstacle. By using Helmholtz decomposition, the problem is transformed into a
boundary value problem with coupled boundary conditions. In numerical analysis,
the perfectly matched layer (PML) and transparent boundary condition (TBC) are introduced to truncate the unbounded domain. Then, a linear gradient is constructed
in a node-based smoothing domain (N-SD) by using a complete order of polynomial.
The unknown coefficients of the smoothed linear gradient function can be solved by
three linearly independent weight functions. Further, based on the weakened weak
formulation, a system of linear equation with the smoothed gradient is established for
NS-FEM-L with PML or TBC. Some numerical examples also demonstrate that the presented method possesses more stability and high accuracy. It turns out that the modified gradient makes the NS-FEM-L-PML and NS-FEM-L-TBC possess an ideal stiffness
matrix, which effectively overcomes the instability of original NS-FEM. Moreover, the
convergence rates of $L^2$ and $H^1$ semi-norm errors for the two NS-FEM-L models are
also higher.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2021-0270},
url = {https://global-sci.com/article/72884/a-node-based-smoothed-finite-element-method-with-linear-gradient-fields-for-elastic-obstacle-scattering-problems}
}