Volume 11, Issue 4
A Treecode Algorithm for 3D Stokeslets and Stresslets

Adv. Appl. Math. Mech., 11 (2019), pp. 737-756.

Published online: 2019-06

[An open-access article; the PDF is free to any online user.]

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• 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.

• Keywords

Stokeslet, stresslet, fast summation, treecode, Taylor approximation.

65D99, 76D07

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@Article{AAMM-11-737, author = {Wang , LeiTlupova , Svetlana and Krasny , Robert}, title = {A Treecode Algorithm for 3D Stokeslets and Stresslets}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {11}, number = {4}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0187}, url = {http://global-sci.org/intro/article_detail/aamm/13188.html} }
TY - JOUR T1 - A Treecode Algorithm for 3D Stokeslets and Stresslets AU - Wang , Lei AU - Tlupova , Svetlana AU - Krasny , Robert JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 737 EP - 756 PY - 2019 DA - 2019/06 SN - 11 DO - http://doi.org/10.4208/aamm.OA-2018-0187 UR - https://global-sci.org/intro/article_detail/aamm/13188.html KW - Stokeslet, stresslet, fast summation, treecode, Taylor approximation. AB -

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.

Lei Wang, Svetlana Tlupova & Robert Krasny. (2019). A Treecode Algorithm for 3D Stokeslets and Stresslets. Advances in Applied Mathematics and Mechanics. 11 (4). 737-756. doi:10.4208/aamm.OA-2018-0187
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