Title: A kernel-independent fast multipole algorithm 

(NYU-CS-TR839)

Authors: George Biros, Lexing Ying, and Denis Zorin 

Abstract:
We present a new fast multipole method for particle simulations.
The main feature of our algorithm is that is kernel independent, in
the sense that no analytic expansions are used to represent the far
field.  Instead we use equivalent densities, which we compute by
solving small Dirichlet-type boundary value problems. The
translations from the sources to the induced potentials are
accelerated by singular value decomposition in 2D and fast Fourier
transforms in 3D. We have tested the new method on the single and
double layer operators for the Laplacian, the modified Laplacian,
the Stokes, the modified Stokes, the Navier, and the modified Navier
operators in two and three dimensions. Our numerical results
indicate that our method compares very well with the best known
implementations of the analytic FMM method for both the Laplacian
and modified Laplacian kernels. Its advantage is the (relative)
simplicity of the implementation and its immediate extension to more
general kernels.