@Article{CiCP-20-1258,
author = {Gang Wang, Xiangyang Cui and Guangyao Li},
title = {An Element Decomposition Method for the Helmholtz Equation},
journal = {Communications in Computational Physics},
year = {2018},
volume = {20},
number = {5},
pages = {1258--1282},
abstract = {<p style="text-align: justify;">It is well-known that the traditional full integral quadrilateral element fails
to provide accurate results to the Helmholtz equation with large wave numbers due to
the &quot;pollution error&quot; caused by the numerical dispersion. To overcome this deficiency,
this paper proposed an element decomposition method (EDM) for analyzing 2D acoustic
problems by using quadrilateral element. In the present EDM, the quadrilateral
element is first subdivided into four sub-triangles, and the local acoustic gradient in
each sub-triangle is obtained using linear interpolation function. The acoustic gradient
field of the whole quadrilateral is then formulated through a weighted averaging
operation, which means only one integration point is adopted to construct the system
matrix. To cure the numerical instability of one-point integration, a variation gradient
item is complemented by variance of the local gradients. The discretized system
equations are derived using the generalized Galerkin weak form. Numerical examples
demonstrate that the EDM can achieves better accuracy and higher computational efficiency.
Besides, as no mapping or coordinate transformation is involved, restrictions
on the shape elements can be easily removed, which makes the EDM works well even
for severely distorted meshes.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.110415.240316a},
url = {http://global-sci.org/intro/article_detail/cicp/11189.html}
}