Publications


2014


  • L. Greengard, T. Hagstrom and S. Jiang, The solution of the scalar wave equation in the exterior of a sphere, J. Comput. Phys., 274, 191-207 (2014).
  • A. J. Ilotta, S. Chandrashekar, A. Kloeckner, H. J. Chang, N. M. Trease, C. P. Grey, L. Greengard, A. Jerschow, Visualizing skin effects in conductors with MRI: 7-Li MRI experiments and calculations, J. Magnetic Resonance, 245, 143-149 (2014).
  • J. Lai, M. Kobayashi, and L. Greengard, A fast solver for multi-particle scattering in a layered medium, Optics Express, 22, 20481–20499 (2014).
  • L. Greengard, K. L. Ho and J.-Y. Lee, A fast direct solver for scattering from periodic structures with multiple material interfaces in two dimensions, J. Comput. Phys., 258, 738-751 (2014).
  • L. Greengard, M. O'Neil, and A. Pataki, On the efficient representation of the half-space impedance Green's function for the Helmholtz equation, Wave Motion, 51, 1-13 (2014).
  • K. L. Ho and L. Greengard, A fast direct least squares algorithm for hierarchically structured block separable matrices, J. Comput. Phys., 258, 738-751 (2014).
  • F. Vico, L. Greengard, and Z. Gimbutas, Boundary integral equation analysis on the sphere, Numer. Math., to appear.
  • S. Jiang and L. Greengard and S. Wang, Efficient sum-of-exponentials approximations for the heat kernel and their applications, Adv. Comput. Math., to appear.
  • T. Askham and L. Greengard, Norm-preserving discretization of integral equations for elliptic PDEs with internal layers I: the one-dimensional case, SIAM Review, to appear.
  • S. Jiang, L. Greengard, and W. Bao, Fast and accurate evaluation of nonlocal Coulomb and dipole-dipole interactions via the nonuniform FFT, SIAM J. Sci. Comput., to appear.
  • C. Epstein, L. Greengard and M. O'Neil, Debye sources, Beltrami fields and a complex structure on Maxwell fields, Comm. Pure Appl. Math., to appear.
  • J. Lai, S. Ambikasaran, and L. Greengard, A fast direct solver for high frequency scattering from a large cavity in two dimensions, arXiv:1404.3451, SIAM J. Sci. Comput., to appear.
  • J.Sifuentes, Z. Gimbutas, and L. Greengard, Randomized methods for rank-deficient linear systems, arXiv:1401.3068, submitted.
  • S. Ambikasaran, D. Foreman-Mackey, L. Greengard, D. W. Hogg, and M. O’Neil, Fast direct methods for Gaussian processes and the analysis of NASA Kepler mission data, arXiv:1403.6015, submitted.
  • Z. Gimbutas and L. Greengard, A fast multipole method for the evaluation of elastostatic fields in a half-space with zero normal stress, arXiv:1404.0036, submitted.
  • F. Vico, L. Greengard, Z. Gimbutas, and M. Ferrando, The decoupled potential integral equation for time-harmonic electromagnetic scattering, arXiv:1404.0749, submitted.
  • C. Borges and L. Greengard, Inverse obstacle scattering in two dimensions with multiple frequency data and multiple angles of incidence, arXiv:1408.5436, submitted.

    • 2013


  • C. L. Epstein, A. Kloeckner, and L. Greengard, On the convergence of local expansions of layer potentials, SIAM J. Numer. Anal., 51, 2660-2679 (2013).
  • A. Kloeckner, A. Barnett, L. Greengard, and M. O'Neil, Quadrature by expansion: a new method for the evaluation of layer potentials, J. Comput. Phys., 252, 332-349 (2013).
  • M. O'Neil, A. Pataki, A. J. Cerfon, J. P. Freidberg, and L. Greengard, A fast, high-order solver for the Grad-Shafranov equation, submitted, J. Comput. Phys., 243, 28-45 (2013).
  • F. Vico, Z. Gimbutas, L. Greengard and M. Ferrando-Bataller, Overcoming low-frequency breakdown of the magnetic field integral equation, IEEE Trans. Antennas and Propagation, 61, 1285-1290 (2013).
  • Z. Liang, Z. Gimbutas, L. Greengard, J. Huang, and S. Jiang, A fast multipole method for the Rotne-Prager-Yamakawa tensor and its applications, J. Comput. Phys., 234, 133-139 (2013).
  • C. L. Epstein, Z. Gimbutas, L. Greengard, A. Kloeckner, and M. O'Neil, A consistency condition for the vector potential in multiply-connected domains, IEEE Trans. Magnetics, 49, 1072-1076 (2013).
  • C. Epstein, L. Greengard and M. O'Neil, Debye sources and the numerical solution of the time harmonic Maxwell equations II, Comm. Pure Appl. Math., 66, 753-789 (2013).
  • Z. Gimbutas and L. Greengard, Fast multi-particle scattering: a hybrid solver for the Maxwell equations in microstructured materials, J. Comput. Phys., 232, 22-32 (2013).

    • 2012


  • L. Greengard and J.-Y. Lee, Stable and accurate integral equation methods for scattering problems with multiple material interfaces in two dimensions, J. Comput. Phys., 231, 2389-2395 (2012).
  • K. L. Ho and L. Greengard, A Fast Direct Solver for Structured Linear Systems by Recursive Skeletonization, SIAM J. Sci. Comput., 35, A2507-A2532 (2012).

    • 2011


  • F. Valdes, F. Andriulli, K. Cools, and E. Michielssen, A Calderon-preconditioned single source combined field integral equation for analyzing scattering from homogeneous penetrable objects, IEEE Trans. Antennas and Propagation, 59, 2315-2328 (2011).