213 citations · 1.1k across the 67 of their papers we have counts for
6 papers · 1 filter
Fast and Accurate Evaluation of Nonlocal Coulomb and Dipole-Dipole Interactions via the Nonuniform FFT
Shidong Jiang, Leslie Greengard, Weizhu Bao
We present a fast and accurate algorithm for the evaluation of nonlocal (long-range) Coulomb and dipole-dipole interactions in free space. The governing potential is simply the con…
Debye Sources, Beltrami Fields, and a Complex Structure on Maxwell Fields
Charles L. Epstein, Leslie Greengard, Michael O'Neil
The Debye source representation for solutions to the time harmonic Maxwell equations is extended to bounded domains with finitely many smooth boundary components. A strong uniquene…
Efficient sum-of-exponentials approximations for the heat kernel and their applications
Shidong Jiang, Leslie Greengard, Shaobo Wang
In this paper, we show that efficient separated sum-of-exponentials approximations can be constructed for the heat kernel in any dimension. In one space dimension, the heat kernel…
The solution of the scalar wave equation in the exterior of a sphere
Leslie Greengard, Thomas Hagstrom, Shidong Jiang
We derive new, explicit representations for the solution to the scalar wave equation in the exterior of a sphere, subject to either Dirichlet or Robin boundary conditions. Our form…
A fast direct solver for scattering from periodic structures with multiple material interfaces in two dimensions
Leslie Greengard, Kenneth L. Ho, June-Yub Lee
We present a new integral equation method for the calculation of two-dimensional scattering from periodic structures involving triple-points (multiple materials meeting at a single…
Norm-preserving discretization of integral equations for elliptic PDEs with internal layers I: the one-dimensional case
Travis Askham, Leslie Greengard
We investigate the behavior of integral formulations of variable coefficient elliptic partial differential equations (PDEs) in the presence of steep internal layers. In one dimensi…