A kernel-independent treecode based on barycentric Lagrange interpolation

6 Feb 2019  ·  Lei Wang, Robert Krasny, Svetlana Tlupova ·

A kernel-independent treecode (KITC) is presented for fast summation of pairwise particle interactions. In general, treecodes replace the particle-particle interactions by particle-cluster interactions, and here we utilize barycentric Lagrange interpolation at Chebyshev points to compute well-separated particle-cluster interactions. The scheme requires only kernel evaluations and is suitable for non-oscillatory kernels. For a given level of accuracy, the treecode reduces the operation count for pairwise interactions from $O(N^2)$ to $O(N \log N)$, where $N$ is the number of particles in the system. The algorithm is demonstrated in serial and parallel simulations for systems of regularized Stokeslets and rotlets in 3D, and numerical results show the treecode performance in terms of error, CPU time, and memory overhead. The KITC is a relatively simple algorithm with low memory overhead, and this enables a straightforward efficient parallelization.

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