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The Stokeslet and stresslet kernels are commonly used in boundary elementsimulations and singularity methods for slow viscous flow. Evaluating thevelocity induced by a collection of Stokeslets and stresslets by directsummation requires $O(N^2)$ operations, where $N$ is the system size. Thepresent work develops a treecode algorithm for 3D Stokeslets and stressletsthat reduces the cost to $O(N\log N)$. The particles are divided into ahierarchy of clusters, and well-separated particle-cluster interactions arecomputed by a far-field Cartesian Taylor approximation. The terms in theapproximation are contracted to promote efficient computation. Serial andparallel results display the treecode performance for several test cases. Inparticular the method has relatively simple structure and low memory usage, andthis enhances parallel efficiency for large systems.

A Treecode Algorithm for 3D Stokeslets and Stresslets