A Kernel-Independent Treecode for General Rotne-Prager-Yamakawa Tensor

Abstract

A particle-cluster treecode based on barycentric Lagrange interpolation is presented for fast summation of hydrodynamic interactions through general Rotne-Prager-Yamakawa tensor in 3D. The interpolation nodes are taken to be Chebyshev points of the 2nd kind in each cluster. The barycentric Lagrange interpolation is scale-invariant that promotes the treecode's efficiency. Numerical results show that the treecode CPU time scales like $\mathcal{O}(N \log N)$, where $N$ is the number of beads in the system. The kernel-independent treecode is a relatively simple algorithm with low memory consumption, and this enables a straightforward OpenMP parallelization.