Leslie Greengard 

Phones

Email

Mail Address

Teaching Links

Research Interests

Click for more information on the following projects:

• DOE Courant Math and Computing Laboratory (CMCL)
• NSF Research and Training Group in Scientific Computing
• Fast solvers
• Protein Design
• Nonuniform FFTs and medical imaging

Selected Publications

• A Fast Algorithm for Particle Simulations
  (with V. Rokhlin).  J. Comput. Phys. 73, 325 (1987).
• A Fast Adaptive Multipole Algorithm for Particle Simulations [pdf: 1,922 Kb]
  (with J. Carrier and V. Rokhlin).   SIAM J. Sci. Stat. Comput. 9, 669 (1988).
• Potential Flow in Channels [pdf: 1,827 Kb]
    SIAM J. Sci. Stat. Comput. 11, 603 (1990).
• A Fast Algorithm for the Evaluation of Heat Potentials [Preprint, pdf: 170 Kb]
  (with J. Strain ).   published version: Comm. Pure Appl. Math. 43, 949-963 (1990).
• Spectral Integration and Two-Point Boundary Value Problems [pdf: 898 Kb]
  
• The Fast Gauss Transform [pdf: 1,372 Kb]
  (with J. Strain).   SIAM J. Sci. Stat. Comput. 12, 79 (1991).
• Spectral Integration and Two-Point Boundary Value Problems [pdf: 898 Kb]
    SIAM J. Numer. Anal. 28, 1071 (1991).
• Laplace's Equation and the Dirichlet-Neumann Map in Multiply-Connected Domains
  (with A. Greenbaum, G. B. McFadden).  J. Comput. Phys. 105, 267 (1993).
• A Renormalization Method for the Evaluation of Lattice Sums
  (with C. L. Berman).  J. Math. Phys. 35, 6036 (1994).
• A Fast Poisson Solver for Complex Geometries
  (with A. McKenney, A. Mayo).  J. Comput. Phys. 118, 348 (1995).
• A Direct Adaptive Poisson Solver of Arbitrary Order Accuracy
  (with J.-Y. Lee).  J. Comput. Phys. 125, 415 (1996).
• A Fast Adpative Numerical Method for Stiff Two-Point Boundary Value Problems [pdf: 1,039 Kb]
  (with J. Y. Lee).   SIAM J. Sci. Comput. 18, 403 (1997).
• A Method of Images for the Evaluation of Electrostatic Fields in Systems of Closely Spaced Conducting Cylinders [pdf: 1,130 Kb]
  (with H. Cheng).   SIAM J. Appl. Math. 58, 122 (1998).
• An Integral Equation Approach to the Incompressible Navier-Stokes Equations in Two Dimensions [pdf: 1,039 Kb]
  (with M. C. Kropinski).   SIAM J. Sci. Comput. 20, 318 (1998).
• On the Numerical Evaluation of Elastostatic Fields in Locally Isotropic Two-Dimensional Composites
  (with J. Helsing ).  J. Mech. Phys. Solids 46, 1441 (1998).
• A Fast Adaptive Multipole Algorithm in Three Dimensions
  (with H. Cheng, V. Rokhlin).  J. Comput. Phys. 155, 468 (1999).
• An Integral Evolution Formula for the Wave Equation
  (with B. Alpert, T. Hagstrom).  J. Comput. Phys. 162, 536 (2000).
• Spectral Approximation of the Free-Space Heat Kernel [pdf: 158 Kb]
  (with P. Lin).  Appl. Comput. Harmonic Anal. 9, 83 (2000).
• Coulomb Interactions on Planar Structures: Inverting the Square Root of the Laplacian [pdf: 509 Kb]
  (with Z. Gimbutas, M. Minion).   SIAM J. Sci. Comput. 22, 6 (2001).
• A New Fast-Multipole Accelerated Poisson Solver inTwo Dimensions[pdf: 2926 Kb]
  (with F. Ethridge).   SIAM J. Sci. Comput. 23, 741 (2001).
• Nonreflecting Boundary Conditions for the Time-Dependent Wave Equation
  (with B. Alpert, T. Hagstrom).  J. Comput. Phys. 180, 270 (2002).
• A New Version of the Fast Multipole Method for Screened Coulomb Interactions in Three Dimensions
  (with J. Huang ).  J. Comput. Phys. 180, 642 (2002).
• Accelerating the Nonuniform Fast Fourier Transform [pdf: 582 Kb]
  (with J.-Y. Lee).   SIAM Review 46, 443 (2004).
• High-order Marching Schemes for the Wave Equation in Complex Gemoetry
  (with J.-R. Li).  J. Comput. Phys. 198, 295 (2004).
• Fast Evaluation of Nonreflecting Boundary Conditions for the Schrodinger Equation in One Dimension
  (with S. Jiang).  Comput. Math. with Appl. 47, 955 (2004).
• Electrostatics and Heat Conduction in High Contrast Composite Materials
  (with J.-Y. Lee).  J. Comput. Phys. 211, 64 (2006).
• Plasmon-Assisted Chemical Vapor Deposition
  (with D. Boyd, M. Brongersma, M. Y. El-Naggar, D. Goodwin).  Nano Letters 6, 2592 (2006).
• A Mathematical Tool for Exploring the Dynamics of Biological Networks
  (with P. Barbano, M. Spivak, M. Flajolet, A.C. Nairn, P. Greengard).  PNAS 104, 19169 (2007).
• A Fast Multipole Method for the Three Dimensional Stokes Equations
  (with A. K. Tornberg).  J. Comput. Phys. 227, 1613 (2008).
• Fast Direct Solvers for Integral Equations in Complex Three Dimensional Domains
  (with D. Gueyffier, P.-G. Martinsson, V. Rokhlin).  Acta Numerica, 243 (2009).
• High Order Accurate Methods for the Evaluation of Layer Heat Potentials[pdf: 238 Kb]
  (with J.-R. Li).   SIAM J. Sci. Comput. 31, 3847 (2009).
• Debye Sources and the Numerical Solution of the Time Harmonic Maxwell Equations
  (with C. Epstein).  Comm. Pure Appl. Math. 63, 413 (2009).
• A New Integral Representation for Quasi-Periodic Fields and its Application to Two-dimensional Band Structure Calculations
  (with A. Barnett).  J. Comput. Phys. 229, 6898 (2010).