Stability and convergence of the method of fundamental solutions for Helmholtz problems on analytic domains. - Alex H. Barnett; Timo Betcke (J. Comput. Phys., 2008)

Perturbative Analysis of the Method of Particular Solutions for Improved Inclusion of High-Lying Dirichlet Eigenvalues. - Alex H. Barnett (SIAM J. Numer. Anal., 2009)

A new integral representation for quasi-periodic fields and its application to two-dimensional band structure calculations. - Alexander H. Barnett; Leslie Greengard (J. Comput. Phys., 2010)

An Exponentially Convergent Nonpolynomial Finite Element Method for Time-Harmonic Scattering from Polygons. - Alex H. Barnett; Timo Betcke (SIAM J. Sci. Comput., 2010)

Boundary Quasi-Orthogonality and Sharp Inclusion Bounds for Large Dirichlet Eigenvalues. - Alex H. Barnett; Andrew Hassell (SIAM J. Numer. Anal., 2011)

A fast direct solver for quasi-periodic scattering problems. - Adrianna Gillman; Alex H. Barnett (J. Comput. Phys., 2013)

Quadrature by expansion: A new method for the evaluation of layer potentials. - Andreas Klöckner; Alexander H. Barnett; Leslie Greengard; Michael O'Neil (J. Comput. Phys., 2013)

High-order accurate methods for Nyström discretization of integral equations on smooth curves in the plane. - Sijia Hao; Alex H. Barnett; Per-Gunnar Martinsson; P. Young (Adv. Comput. Math., 2014)

Evaluation of Layer Potentials Close to the Boundary for Laplace and Helmholtz Problems on Analytic Planar Domains. - Alex H. Barnett (SIAM J. Sci. Comput., 2014)

Validation of neural spike sorting algorithms without ground-truth information. - Alex H. Barnett; Jeremy F. Magland; Leslie Greengard (CoRR, 2015)

High-order boundary integral equation solution of high frequency wave scattering from obstacles in an unbounded linearly stratified medium. - Alex H. Barnett; Bradley J. Nelson; J. Matthew Mahoney (J. Comput. Phys., 2015)

A fast and robust solver for the scattering from a layered periodic structure containing multi-particle inclusions. - Jun Lai; Motoki Kobayashi; Alex H. Barnett (J. Comput. Phys., 2015)

Robust and Efficient Solution of the Drum Problem via Nyström Approximation of the Fredholm Determinant. - Lin Zhao; Alex H. Barnett (SIAM J. Numer. Anal., 2015)

Spectrally Accurate Quadratures for Evaluation of Layer Potentials Close to the Boundary for the 2D Stokes and Laplace Equations. - Alex H. Barnett; Bowei Wu; Shravan K. Veerapaneni (SIAM J. Sci. Comput., 2015)

Efficient numerical solution of acoustic scattering from doubly-periodic arrays of axisymmetric objects. - Yuxiang Liu; Alex H. Barnett (J. Comput. Phys., 2016)

A Fast Algorithm for Simulating Multiphase Flows Through Periodic Geometries of Arbitrary Shape. - Gary R. Marple; Alex H. Barnett; Adrianna Gillman; Shravan K. Veerapaneni (SIAM J. Sci. Comput., 2016)

Rapid Solution of the Cryo-EM Reconstruction Problem by Frequency Marching. - Alex H. Barnett; Leslie Greengard; Andras Pataki; Marina Spivak (SIAM J. Imaging Sci., 2017)

A parallel non-uniform fast Fourier transform library based on an "exponential of semicircle" kernel. - Alex H. Barnett; Jeremy F. Magland; Ludvig af Klinteberg (CoRR, 2018)

Accurate quadrature of nearly singular line integrals in two and three dimensions by singularity swapping. - Ludvig af Klinteberg; Alex H. Barnett (CoRR, 2019)

A Parallel Nonuniform Fast Fourier Transform Library Based on an "Exponential of Semicircle" Kernel. - Alex H. Barnett; Jeremy F. Magland; Ludvig af Klinteberg (SIAM J. Sci. Comput., 2019)

A high-order integral equation-based solver for the time-dependent Schrodinger equation. - Jason Kaye; Alex H. Barnett; Leslie Greengard (CoRR, 2020)

Aliasing error of the exp(β√(1-z2)) kernel in the nonuniform fast Fourier transform. - Alex H. Barnett (CoRR, 2020)

Efficient high-order accurate Fresnel diffraction via areal quadrature and the nonuniform FFT. - Alex H. Barnett (CoRR, 2020)

High-order discretization of a stable time-domain integral equation for 3D acoustic scattering. - Alex H. Barnett; Leslie Greengard; Thomas M. Hagstrom (J. Comput. Phys., 2020)

Solution of Stokes flow in complex nonsmooth 2D geometries via a linear-scaling high-order adaptive integral equation scheme. - Bowei Wu; Hai Zhu; Alex H. Barnett; Shravan K. Veerapaneni (J. Comput. Phys., 2020)

cuFINUFFT: a load-balanced GPU library for general-purpose nonuniform FFTs. - Yu-Hsuan Shih; Garrett Wright; Joakim Andén; Johannes P. Blaschke; Alex H. Barnett (IPDPS Workshops, 2021)

An integral equation method for the simulation of doubly-periodic suspensions of rigid bodies in a shearing viscous flow. - Jun Wang 082; Ehssan Nazockdast; Alex H. Barnett (J. Comput. Phys., 2021)

Recovering Missing Data in Coherent Diffraction Imaging. - David A. Barmherzig; Alex H. Barnett; Charles L. Epstein; Leslie F. Greengard; Jeremy F. Magland; Manas Rachh (SIAM J. Imaging Sci., 2021)

Quadrature by fundamental solutions: kernel-independent layer potential evaluation for large collections of simple objects. - David B. Stein; Alex H. Barnett (Adv. Comput. Math., 2022)

Eliminating artificial boundary conditions in time-dependent density functional theory using Fourier contour deformation. - Jason Kaye; Alex H. Barnett; Leslie Greengard; Umberto De Giovannini; Angel Rubio (CoRR, 2022)

Automatic, high-order, and adaptive algorithms for Brillouin zone integration. - Jason Kaye; Sophie Beck; Alex H. Barnett; Lorenzo Van Muñoz; Olivier Parcollet (CoRR, 2022)

How Exponentially Ill-Conditioned Are Contiguous Submatrices of the Fourier Matrix? - Alex H. Barnett (SIAM Rev., 2022)

Uniform approximation of common Gaussian process kernels using equispaced Fourier grids. - Alex H. Barnett; Philip Greengard; Manas Rachh (CoRR, 2023)

riccati: an adaptive, spectral solver for oscillatory ODEs. - Fruzsina Julia Agocs; Alex H. Barnett (J. Open Source Softw., 2023)

A superfast direct inversion method for the nonuniform discrete Fourier transform. - Heather Wilber; Ethan N. Epperly; Alex H. Barnett (CoRR, 2024)

A Method of Fundamental Solutions for Large-Scale 3D Elastance and Mobility Problems. - Anna Broms; Alex H. Barnett; Anna-Karin Tornberg (CoRR, 2024)

Trapped acoustic waves and raindrops: High-order accurate integral equation method for localized excitation of a periodic staircase. - Fruzsina Julia Agocs; Alex H. Barnett (J. Comput. Phys., 2024)

An Adaptive Spectral Method for Oscillatory Second-Order Linear ODEs with Frequency-Independent Cost. - Fruzsina Julia Agocs; Alex H. Barnett (SIAM J. Numer. Anal., 2024)

Accurate close interactions of Stokes spheres using lubrication-adapted image systems. - Anna Broms; Alex H. Barnett; Anna-Karin Tornberg (J. Comput. Phys., 2025)

Equispaced Fourier Representations for Efficient Gaussian Process Regression from a Billion Data Points. - Philip Greengard; Manas Rachh; Alex H. Barnett (SIAM/ASA J. Uncertain. Quantification, 2025)

Superfast Direct Inversion of the Nonuniform Discrete Fourier Transform via Hierarchically Semiseparable Least Squares. - Heather Wilber; Ethan N. Epperly; Alex H. Barnett (SIAM J. Sci. Comput., 2025)

A fully adaptive, high-order, fast Poisson solver for complex two-dimensional geometries. - Daniel Fortunato; David B. Stein; Alex H. Barnett (CoRR, 2025)

Accelerating Fast Ewald Summation with Prolates for Molecular Dynamics Simulations. - Jiuyang Liang; Libin Lu; Alex H. Barnett; Leslie Greengard; Shidong Jiang (CoRR, 2025)

A fast algorithm for the wave equation using time-windowed Fourier projection. - Nour G. Al Hassanieh; Alex H. Barnett; Leslie Greengard (CoRR, 2025)