  Fast multipole methods (FMM) were originally developed for accelerating
$N$-body problems for particle-based methods. FMM is more than an $N$-body
solver, however. Recent efforts to view the FMM as an elliptic Partial
Differential Equation (PDE) solver have opened the possibility to use it as a
preconditioner for a broader range of applications. FMM can solve Helmholtz
problems with optimal $\mathcal{O}(N \log N)$ complexity, has compute-bound
inner kernels, and highly asynchronous communication patterns. The combination
of these features makes FMM an interesting candidate as a preconditioner for
sparse solvers on architectures of the future. The use of FMM as a
preconditioner allows us to use lower order multipole expansions than would be
required as a solver because individual solves need not be accurate. This
reduces the amount of computation and communication significantly and makes the
time-to-solution competitive with state-of-the-art preconditioners.
Furthermore, the high asynchronicity of FMM allows it to scale to much larger
core counts than factorization-based and multilevel methods. We describe our
tests in reproducible details with freely available codes.
