TY - JOUR
T1 - A Kernel-Independent Treecode Based on Barycentric Lagrange Interpolation
AU - Wang , Lei
AU - Krasny , Robert
AU - Tlupova , Svetlana
JO - Communications in Computational Physics
VL - 4
SP - 1415
EP - 1436
PY - 2020
DA - 2020/08
SN - 28
DO - http://doi.org/10.4208/cicp.OA-2019-0177
UR - https://global-sci.org/intro/article_detail/cicp/18106.html
KW - Treecode, barycentric Lagrange interpolation, scale-invariance, Chebyshev points, regularized Stokeslets.
AB - <p style="text-align: justify;">A kernel-independent treecode (KITC) is presented for fast summation of
particle interactions. The method employs barycentric Lagrange interpolation at
Chebyshev points to approximate well-separated particle-cluster interactions. The
KITC requires only kernel evaluations, is suitable for non-oscillatory kernels, and relies on the scale-invariance property of barycentric Lagrange interpolation. For a given
level of accuracy, the treecode reduces the operation count for pairwise interactions
from $\mathcal{O}$($N^2$) to <span style="text-align: justify;">$\mathcal{O}$</span>($N$log$N$), where $N$ is the number of particles in the system. The algorithm is demonstrated for systems of regularized Stokeslets and rotlets in 3D, and
numerical results show the treecode performance in terms of error, CPU time, and
memory consumption. The KITC is a relatively simple algorithm with low memory
consumption, and this enables a straightforward OpenMP parallelization.</p>