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This work introduces the kernel-independent multi-level algorithm "skelFMM"for evaluating all pairwise interactions between $N$ points connected through akernel such as the fundamental solution of the Laplace or the Helmholtzequations. The method is based on linear algebraic tools such as randomized lowrank approximation and "skeleton representations" of far-field interactions.The work is related to previously proposed linear algebraic reformulations ofthe fast multipole method (FMM), but is distinguished by relying on simplerdata structures. In particular, skelFMM does not require an "interaction list",as it relies instead on algebraically-modified kernel interactions betweennear-neighbors at every level. Like other kernel independent algorithms, itonly requires evaluation of the kernel function, allowing the methodology toeasily be extended to a range of different kernels in 2D and 3D. The simplicityof the algorithm makes it particularly amenable to parallel implementation onheterogeneous hardware architectures.  The performance of the algorithm is demonstrated through numericalexperiments conducted on uniform and non-uniform point distributions in 2D and3D, involving Laplace and (low frequency) Helmholtz kernels. The algorithmrelies on a precomputation stage that constructs a tailored representation fora given geometry of points. Once the precomputation has completed, thematrix-vector multiplication attains high speed through GPU acceleration thatleverages batched linear algebra.

SkelFMM: A Simplified Fast Multipole Method Based on Recursive Skeletonization