Tree-based algorithms are popular methods for the fast summation of particle interactions, including the Barnes-Hut treecode and the Greengard-Rokhlin fast multiple method, which reduce the operation count for a given tolerance from O(N) to O(NlogN) and O(N) respectively. Since then, there have been several improvements to these algorithms to solve different problems. In this talk, we present the Kernel Independent Treecode (KITC) [1] and the Barycentric Lagrange Dual Tree Traversal (BLDTT) [2] methods, both of which take advantage of the stability properties of barycentric Lagrange polynomial interpolation which will also be discussed. Additionally, we will show how these methods are easily parallelizable using CPUs or GPUs, as well as discussing the performance with examples of problems in fluid and plasma dynamics where these methods have been used. Finally, we present plans for future implementations of these methods in modeling the solar magnetic field in the solar corona.

[1] L. Wang, R. Krasny, and S. Tlupova, “A kernel-independent treecode based on barycentric lagrange interpolation”, CiCP 28, 1415–1436 (2020).

[2] L. Wilson, N. Vaughn, and R. Krasny, “A GPU-accelerated fast multipole method based on barycentric lagrange interpolation and dual tree traversal”, Computer Physics Communications 265, 108017 (2021).