Year: 2019
Author: Lei Wang, Svetlana Tlupova, Robert Krasny
Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 4 : pp. 737–756
Abstract
The Stokeslet and stresslet kernels are commonly used in boundary element simulations and singularity methods for slow viscous flow. Evaluating the velocity induced by a collection of Stokeslets and stresslets by direct summation requires $\mathcal{O}(N^2)$ operations, where $N$ is the system size. The present work develops a treecode algorithm for 3D Stokeslets and stresslets that reduces the cost to $\mathcal{O}(N\log N)$. The particles are divided into a hierarchy of clusters and well-separated particle-cluster interactions are computed by a far-field Cartesian Taylor approximation. The terms in the approximation are contracted to promote efficient computation. Serial and parallel results display the performance of the treecode for several test cases. In particular, the method has relatively simple structure and low memory usage and this enhances parallel efficiency for large systems.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2018-0187
Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 4 : pp. 737–756
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Stokeslet stresslet fast summation treecode Taylor approximation.