@Article{NMTMA-17-2,
author = {Siqing, Li and Ling, Leevan and Xin, Liu and Pankaj, Mishra, K. and Sen, Mrinal, K. and Zhang, Jing},
title = {Enhancing RBF-FD Efficiency for Highly Non-Uniform Node Distributions via Adaptivity},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2024},
volume = {17},
number = {2},
pages = {331--350},
abstract = {<p style="text-align: justify;">Radial basis function generated finite-difference (RBF-FD) methods have
recently gained popularity due to their flexibility with irregular node distributions.
However, the convergence theories in the literature, when applied to nonuniform
node distributions, require shrinking fill distance and do not take advantage of areas
with high data density. Non-adaptive approach using same stencil size and degree
of appended polynomial will have higher local accuracy at high density region, but
has no effect on the overall order of convergence and could be a waste of computational power. This work proposes an adaptive RBF-FD method that utilizes the
local data density to achieve a desirable order accuracy. By performing polynomial
refinement and using adaptive stencil size based on data density, the adaptive RBF-FD method yields differentiation matrices with higher sparsity while achieving the
same user-specified convergence order for nonuniform point distributions. This allows the method to better leverage regions with higher node density, maintaining
both accuracy and efficiency compared to standard non-adaptive RBF-FD methods.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2023-0095},
url = {https://global-sci.com/article/91262/enhancing-rbf-fd-efficiency-for-highly-non-uniform-node-distributions-via-adaptivity}
}