  This paper presents an accelerated quadrature scheme for the evaluation of
layer potentials in three dimensions. Our scheme combines a generic, high order
quadrature method for singular kernels called Quadrature by Expansion (QBX)
with a modified version of the Fast Multipole Method (FMM). Our scheme extends
a recently developed formulation of the FMM for QBX in two dimensions, which,
in that setting, achieves mathematically rigorous error and running time
bounds. In addition to generalization to three dimensions, we highlight some
algorithmic and mathematical opportunities for improved performance and
stability. Lastly, we give numerical evidence supporting the accuracy,
performance, and scalability of the algorithm through a series of experiments
involving the Laplace and Helmholtz equations.

Numerical Analysis