204 citations · 422 across the 26 of their papers we have counts for
32 papers
Linear-cost Polyharmonic Spline Interpolation of Arbitrary Degree
Christopher J. Geoga, Michael O'Neil
We introduce a simple and performant approach for rapidly and accurately performing polyharmonic spline (PHS) interpolation using a combination of the fast multipole method (FMM) f…
A Butterfly-Accelerated Manifold Harmonic Transform
Paul G. Beckman, Samuel F. Potter, Michael O'Neil
The eigenfunctions of the Laplacian are a natural basis of functions for many tasks in computational mathematics. On the circle and sphere, the eigenfunctions are given by complex…
Fast Direct Solvers
Per-Gunnar Martinsson, Michael O'Neil
This survey describes a class of methods known as "fast direct solvers". These algorithms address the problem of solving a system of linear equations $\boldsymbol{Ax}=\boldsymbol{b…
A Nonuniform Fast Hankel Transform
Paul G. Beckman, Michael O'Neil
We describe a fast algorithm for computing discrete Hankel transforms of moderate orders from nonuniform points to nonuniform frequencies in operati…
A parametrix method for elliptic surface PDEs
Tristan Goodwill, Michael O'Neil
Elliptic problems along smooth surfaces embedded in three dimensions occur in thin-membrane mechanics, electromagnetics (harmonic vector fields), and computational geometry. In thi…
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…
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…
FMM-accelerated solvers for the Laplace-Beltrami problem on complex surfaces in three dimensions
Dhwanit Agarwal, Michael O'Neil, Manas Rachh
The Laplace-Beltrami problem on closed surfaces embedded in three dimensions arises in many areas of physics, including molecular dynamics (surface diffusion), electromagnetics (ha…
An interface formulation of the Laplace-Beltrami problem on piecewise smooth surfaces
Tristan Goodwill, Michael O'Neil
The Laplace-Beltrami problem on closed surfaces embedded in three dimensions arises in many areas of physics, including molecular dynamics (surface diffusion), electromagnetics (ha…
Efficient reduced-rank methods for Gaussian processes with eigenfunction expansions
Philip Greengard, Michael O'Neil
In this work we introduce a reduced-rank algorithm for Gaussian process regression. Our numerical scheme converts a Gaussian process on a user-specified interval to its Karhunen-Lo…
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…
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…
Efficient high-order singular quadrature schemes in magnetic fusion
Dhairya Malhotra, Antoine J. Cerfon, Michael O'Neil +1
Several problems in magnetically confined fusion, such as the computation of exterior vacuum fields or the decomposition of the total magnetic field into separate contributions fro…
Taylor States in Stellarators: A Fast High-order Boundary Integral Solver
Dhairya Malhotra, Antoine Cerfon, Lise-Marie Imbert-Gérard +1
We present a boundary integral equation solver for computing Taylor relaxed states in non-axisymmetric solid and shell-like toroidal geometries. The computation of Taylor states in…
An FFT-accelerated direct solver for electromagnetic scattering from penetrable axisymmetric objects
Jun Lai, Michael O'Neil
Fast, high-order accurate algorithms for electromagnetic scattering from axisymmetric objects are of great importance when modeling physical phenomena in optics, materials science…
A high-order wideband direct solver for electromagnetic scattering from bodies of revolution
Charles L. Epstein, Leslie Greengard, Michael O'Neil
The generalized Debye source representation of time-harmonic electromagnetic fields yields well-conditioned second-kind integral equations for a variety of boundary value problems,…
Second-kind integral equations for the Laplace-Beltrami problem on surfaces in three dimensions
Michael O'Neil
The Laplace-Beltrami problem has several applications in mathematical physics, differential geometry, machine learning, and topology. In this work, we present novel secon…
An integral equation-based numerical solver for Taylor states in toroidal geometries
Michael O'Neil, Antoine J. Cerfon
We develop an algorithm for the numerical calculation of Taylor states in toroidal and toroidal shell geometries using an analytical framework developed for the solution to the tim…
Accurate and efficient numerical calculation of stable densities via optimized quadrature and asymptotics
Sebastian Ament, Michael O'Neil
Stable distributions are an important class of infinitely-divisible probability distributions, of which two special cases are the Cauchy distribution and the normal distribution. A…
Robust integral formulations for electromagnetic scattering from three-dimensional cavities
Jun Lai, Leslie Greengard, Michael O'Neil
Scattering from large, open cavity structures is of importance in a variety of electromagnetic applications. In this paper, we propose a new well conditioned integral equation for…
Fast algorithms for Quadrature by Expansion I: Globally valid expansions
Manas Rachh, Andreas Klöckner, Michael O'Neil
The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer poten…
A new hybrid integral representation for frequency domain scattering in layered media
Jun Lai, Leslie Greengard, Michael O'Neil
A variety of problems in acoustic and electromagnetic scattering require the evaluation of impedance or layered media Green's functions. Given a point source located in an unbounde…
Smoothed corners and scattered waves
Charles L. Epstein, Michael O'Neil
We introduce an arbitrary order, computationally efficient method to smooth corners on curves in the plane, as well as edges and vertices on surfaces in . The method i…
Exact axisymmetric Taylor states for shaped plasmas
Antoine J. Cerfon, Michael O'Neil
We present a general construction for exact analytic Taylor states in axisymmetric toroidal geometries. In this construction, the Taylor equilibria are fully determined by specifyi…