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A Kernel-Independent Treecode Based on Barycentric Lagrange Interpolation

A Kernel-Independent Treecode Based on Barycentric Lagrange Interpolation
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Year:    2020

Author:    Lei Wang, Robert Krasny, Svetlana Tlupova

Communications in Computational Physics, Vol. 28 (2020), Iss. 4 : pp. 1415–1436

Abstract

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 $\mathcal{O}$($N$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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2019-0177

Communications in Computational Physics, Vol. 28 (2020), Iss. 4 : pp. 1415–1436

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    22

Keywords:    Treecode barycentric Lagrange interpolation scale-invariance Chebyshev points regularized Stokeslets.

Author Details

Lei Wang

Robert Krasny

Svetlana Tlupova

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