213 citations · 1.1k across the 67 of their papers we have counts for
75 papers
Truncated kernel windowed Fourier projection: a fast algorithm for the 3D free-space wave equation
Nour G. Al Hassanieh, Alex H. Barnett, Leslie Greengard
We present a spectrally accurate fast algorithm for evaluating the solution to the scalar wave equation in free space driven by a large collection of point sources in a bounded dom…
Fast Multipole Method with Complex Coordinates
Tristan Goodwill, Leslie Greengard, Jeremy Hoskins +2
When solving problems of potential theory in unbounded layered media, recently developed integral equation methods rely on coordinate complexification to permit truncation of the c…
A fast algorithm for the wave equation using time-windowed Fourier projection
Nour G. Al Hassanieh, Alex H. Barnett, Leslie Greengard
We introduce a new arbitrarily high-order method for the rapid evaluation of hyperbolic potentials (space-time integrals involving the Green's function for the scalar wave equation…
Coordinate complexification for the Helmholtz equation with Dirichlet boundary conditions in a perturbed half-space
Charles L. Epstein, Leslie Greengard, Jeremy Hoskins +2
We present a new complexification scheme based on the classical double layer potential for the solution of the Helmholtz equation with Dirichlet boundary conditions in compactly pe…
On the construction of scattering matrices for irregular or elongated enclosures using Green's representation formula
Carlos Borges, Leslie Greengard, Michael O'Neil +1
Multiple scattering methods are widely used to reduce the computational complexity of acoustic or electromagnetic scattering problems when waves propagate through media containing…
A Dual-space Multilevel Kernel-splitting Framework for Discrete and Continuous Convolution
Shidong Jiang, Leslie Greengard
We introduce a new class of multilevel, adaptive, dual-space methods for computing fast convolutional transforms. These methods can be applied to a broad class of kernels, from the…
Fast adaptive high-order integral equation methods for electromagnetic scattering from smooth perfect electric conductors
Felipe Vico, Leslie Greengard, Michael O'Neil +1
Many integral equation-based methods are available for problems of time-harmonic electromagnetic scattering from perfect electric conductors. Among the many challenges that arise i…
A new version of the adaptive fast Gauss transform for discrete and continuous sources
Leslie Greengard, Shidong Jiang, Manas Rachh +1
We present a new version of the fast Gauss transform (FGT) for discrete and continuous sources. Classical Hermite expansions are avoided entirely, making use only of the plane-wave…
An FMM Accelerated Poisson Solver for Complicated Geometries in the Plane using Function Extension
Fredrik Fryklund, Leslie Greengard
We describe a new, adaptive solver for the two-dimensional Poisson equation in complicated geometries. Using classical potential theory, we represent the solution as the sum of a v…
pmwd: A Differentiable Cosmological Particle-Mesh -body Library
Yin Li, Libin Lu, Chirag Modi +7
The formation of the large-scale structure, the evolution and distribution of galaxies, quasars, and dark matter on cosmological scales, requires numerical simulations. Differentia…
Differentiable Cosmological Simulation with Adjoint Method
Yin Li, Chirag Modi, Drew Jamieson +5
Rapid advances in deep learning have brought not only myriad powerful neural networks, but also breakthroughs that benefit established scientific research. In particular, automatic…
On the robustness of inverse scattering for penetrable, homogeneous objects with complicated boundary
Carlos Borges, Manas Rachh, Leslie Greengard
The acoustic inverse obstacle scattering problem consists of determining the shape of a domain from measurements of the scattered far field due to some set of incident fields (prob…
Eliminating artificial boundary conditions in time-dependent density functional theory using Fourier contour deformation
Jason Kaye, Alex Barnett, Leslie Greengard +2
We present an efficient method for propagating the time-dependent Kohn-Sham equations in free space, based on the recently introduced Fourier contour deformation (FCD) approach. Fo…
Robust ab initio solution of the cryo-EM reconstruction problem at low resolution with small data sets
Aaditya V. Rangan, Leslie Greengard
Single particle cryo-electron microscopy has become a critical tool in structural biology over the last decade, able to achieve atomic scale resolution in three dimensional models…
FMM-LU: A fast direct solver for multiscale boundary integral equations in three dimensions
Daria Sushnikova, Leslie Greengard, Michael O'Neil +1
We present a fast direct solver for boundary integral equations on complex surfaces in three dimensions using an extension of the recently introduced recursive strong skeletonizati…
Periodic Fast Multipole Method
Ruqi Pei, Travis Askham, Leslie Greengard +1
A new scheme is presented for imposing periodic boundary conditions on unit cells with arbitrary source distributions. We restrict our attention here to the Poisson, modified Helmh…
A fast spectral method for electrostatics in doubly-periodic slit channels
Ondrej Maxian, Raul P. Peláez, Leslie Greengard +1
We develop a fast method for computing the electrostatic energy and forces for a collection of charges in doubly-periodic slabs with jumps in the dielectric permittivity at the sla…
Fast multipole methods for evaluation of layer potentials with locally-corrected quadratures
Leslie Greengard, Michael O'Neil, Manas Rachh +1
While fast multipole methods (FMMs) are in widespread use for the rapid evaluation of potential fields governed by the Laplace, Helmholtz, Maxwell or Stokes equations, their coupli…
Recovering missing data in coherent diffraction imaging
David Barmherzig, Alex B. Barnett, Charles L. Epstein +3
In coherent diffraction imaging (CDI) experiments, the intensity of the scattered wave impinging on an object is measured on an array of detectors. This signal can be interpreted a…
A high-order integral equation-based solver for the time-dependent Schrodinger equation
Jason Kaye, Alex Barnett, Leslie Greengard
We introduce a numerical method for the solution of the time-dependent Schrodinger equation with a smooth potential, based on its reformulation as a Volterra integral equation. We…
Fast integral equation methods for linear and semilinear heat equations in moving domains
Jun Wang, Leslie Greengard, Shidong Jiang +1
We present a family of integral equation-based solvers for the linear or semilinear heat equation in complicated moving (or stationary) geometries. This approach has significant ad…
A fast boundary integral method for high-order multiscale mesh generation
Felipe Vico, Leslie Greengard, Michael O'Neil +1
In this work we present an algorithm to construct an infinitely differentiable smooth surface from an input consisting of a (rectilinear) triangulation of a surface of arbitrary sh…
A fast solver for the narrow capture and narrow escape problems in the sphere
Jason Kaye, Leslie Greengard
We present an efficient method to solve the narrow capture and narrow escape problems for the sphere. The narrow capture problem models the equilibrium behavior of a Brownian parti…
High-order discretization of a stable time-domain integral equation for 3D acoustic scattering
Alex H. Barnett, Leslie Greengard, Tom Hagstrom
We develop a high-order, explicit method for acoustic scattering in three space dimensions based on a combined-field time-domain integral equation. The spatial discretization, of N…