@Article{IJNAM-10-815,
author = {H. Tian, H. Wang and W. Wang},
title = {An Efficient Collocation Method for a Non-Local Diffusion Model},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2013},
volume = {10},
number = {4},
pages = {815--825},
abstract = {<p style="text-align: justify;">The non-local diffusion model provides an appropriate description of the deformation of a continuous body involving discontinuities or other singularities, which cannot be described
properly by classical theory of solid mechanics. However, because the non-local nature of the
non-local diffusion operator, the numerical methods for non-local diffusion model generate dense
or even full stiffness matrices. A direct solver typically requires $O(N^3)$ of operations and $O(N^2)$ of memory where $N$ is the number of unknowns. We develop a fast collocation method for the
non-local diffusion model which has the following features: (i) It reduces the computational cost
from $O(N^3)$ to $O(N log^2 N)$ and memory requirement from $O(N^2)$ to $O(N)$. (ii) It requires only
one-fold integration in the evaluation of the stiffness matrix. Numerical experiments show the
utility of the method.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/597.html}
}