We restrict our attention in this paper to the case where the potential (or force) at a point is a sum of pairwise An algorithm is presented for the rapid evaluation of the potential and force fieldsâ€¦ (More)

Many problems in applied mathematics require the evaluation of the sum of N Gaussians at M points in space. The work required for direct evaluation grows like NM as N and M increase; this makes itâ€¦ (More)

We describe a wideband version of the Fast Multipole Method for the Helmholtz equation in three dimensions. It unifies previously existing versions of the FMM for high and low frequencies into anâ€¦ (More)

We present a systematic approach to the computation of exact nonreflecting boundary conditions for the wave equation. In both two and three dimensions, the critical step in our analysis involvesâ€¦ (More)

The nonequispaced or nonuniform fast Fourier transform (NUFFT) arises in a variety of application areas, including imaging processing and the numerical solution of partial differential equations. Inâ€¦ (More)

In this series of lectures, we describe the analytic and computational foundations of fast multipole methods, as well as some of their applications. They are most easily understood, perhaps, in theâ€¦ (More)

Many problems in applied mathematics, physics, and engineering require the solution of the heat equation in unbounded domains. Integral equation methods are particularly appropriate in this settingâ€¦ (More)

We present an adaptive fast multipole method for solving the Poisson equation in two dimensions. The algorithm is direct, assumes that the source distribution is discretized using an adaptiveâ€¦ (More)