@Article{CiCP-36-1378,
author = {Chen , GengjianMa , Yuheng and Zhang , Jiwei},
title = {Efficient Implementation of 3D FEM for Nonlocal Poisson Problem with Different Ball Approximation Strategies},
journal = {Communications in Computational Physics},
year = {2024},
volume = {36},
number = {5},
pages = {1378--1410},
abstract = {<p style="text-align: justify;">Nonlocality brings many challenges to the implementation of finite element
methods (FEM) for nonlocal problems, such as a large number of neighborhood query
operations being invoked on the meshes. Besides, the interactions are usually limited
to Euclidean balls, so direct numerical integrals often introduce numerical errors. The
issues of interactions between the ball and finite elements have to be carefully dealt
with, such as using ball approximation strategies. In this paper, an efficient representation and construction methods for approximate balls are presented based on the
combinatorial map, and an efficient parallel algorithm is also designed for the assembly of nonlocal linear systems. Specifically, a new ball approximation method based on
Monte Carlo integrals, i.e., the fullcaps method, is also proposed to compute numerical
integrals over the intersection region of an element with the ball.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0210},
url = {http://global-sci.org/intro/article_detail/cicp/23612.html}
}