A Treecode Algorithm for 3D Stokeslets and Stresslets

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.