Gregory Beylkin

About

Gregory Beylkin is a researcher whose work spans various areas in applied mathematics, computational harmonic analysis, and scientific computation. His research includes the development of algorithms for numerical analysis in high dimensions, fast methods for solving partial differential equations, and the representation and approximation of functions and operators, particularly in the context of quantum chemistry, wave propagation, and electronic structure calculations. Beylkin has contributed to the advancement of multiresolution methods, multiwavelet bases, and bandlimited function bases, with applications in fields such as satellite data analysis, tomographic reconstructions, and molecular simulations. His work also encompasses the design of efficient algorithms for Green's functions, rational approximations, and the inversion of Fourier transforms, among other topics. Beylkin's research has led to significant developments in the fast evaluation of oscillatory integrals, the representation of wavefunctions, and the solution of boundary value problems. His contributions are characterized by a focus on creating accurate, efficient computational techniques for complex scientific problems, often employing multiscale and multiresolution approaches.

Research topics

• Computer Science
• Mathematics
• Algorithm
• Artificial Intelligence
• Physics
• Mathematical analysis

Selected publications

• Fast Exchange with Gaussian Basis Set Using Robust Pseudospectral Method

  Journal of Chemical Theory and Computation · 2022 · 17 citations

  Senior authorCorresponding

  ) fast Fourier transform (FFT). Here, we introduce an algorithm that retains the cubic scaling but reduces the prefactor significantly by eliminating the need to do FFTs during each exchange build. This is accomplished by representing the products of Gaussian basis function using a linear combination of an auxiliary basis the number of which scales linearly with the size of the system. We store the potential due to these auxiliary functions in memory, which allows us to obtain the exchange matri…

  PublisherDOI

• Dirac-Fock calculations on molecules in an adaptive multiwavelet basis

  The Journal of Chemical Physics · 2019-12-18 · 17 citations

  articleSenior author

  We report the first fully numerical approach for relativistic quantum chemical calculations applicable to molecules. The approach uses an adaptive basis of multiwavelet functions to solve the full four-component Dirac-Coulomb equation to a user-specified accuracy. The accuracy of the code is demonstrated by comparison with ground state energy calculations of atoms performed in GRASP, and the applicability to molecules is shown via ground state calculations of some simple molecules, including wat…

  PublisherDOI

• Efficient Fourier basis particle simulation

  Journal of Computational Physics · 2019-07-15 · 16 citations

  articleOpen access
  PublisherOA PDFDOI

• On computing distributions of products of non-negative independent random variables

  Applied and Computational Harmonic Analysis · 2018-02-06 · 13 citations

  articleOpen access1st authorCorresponding
  PublisherOA PDFDOI

• On wavelet-based algorithms for solving differential equations

  CRC Press eBooks · 2021 · 11 citations

  1st authorCorresponding

  We describe an order N method for computing the Green’s function of the two-point boundary value problem for elliptic differential operators in the wavelet “system of coordinates.” For simplicity, we consider the ordinary O(h2) finite-difference scheme, and use wavelets only to perform the “linear algebra.” Our main tool is the diagonal preconditioning available for the periodized differential operators in the wavelet bases.

  PublisherDOI

Recent grants

• Nonlinear Approximations for Inverse Problems

  NSF · $301k · 2010–2013

• Novel Algorithms for Separated Representations in Functional Form for the Adaptive Solution of Quantum Chemistry Problems and Other Applications

  NSF · $330k · 2013–2016

• Fast Multiresolution Methods and Nonlinear Approximations for Multidimensional Problems

  NSF · $318k · 2006–2010

Frequent coauthors

• Yukina Yokoi

  Argonne National Laboratory

  44 shared

• Álvaro Vázquez‐Mayagoitia

  Argonne National Laboratory

  44 shared

• Jakob S. Kottmann

  University of Augsburg

  40 shared

• Nichols A. Romero

  36 shared

• George I. Fann

  Oak Ridge National Laboratory

  33 shared

• Rebecca Hartman–Baker

  Lawrence Berkeley National Laboratory

  29 shared

• Lucas Monzón

  University of Colorado Boulder

  29 shared

• Judith Hill

  Lawrence Livermore National Laboratory

  28 shared

Labs

• Gregory Beylkin's LabPI

  Research in applied mathematics, computational physics, and quantum chemistry

Education

• Ph. D., Mathematics

  New York University

  1982

Similar researchers at University of Colorado Boulder

• Mark J. Ablowitzh-86
• James Curryh-64
• Mark Hoeferh-32