Teaching Links
Numerical Methods II (Spring 2021)
Research Interests
Scientific computing, fast algorithms, adaptive methods, integral equations, potential theory, electromagnetics, computational chemistry, computational biology.
Click for more information on the following projects:
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, 949963 (1990).
 The Fast Gauss Transform [pdf: 1,372 Kb]
(with J. Strain).
SIAM J. Sci. Stat. Comput. 12, 79 (1991).
 Spectral Integration and TwoPoint Boundary Value Problems [pdf: 898 Kb]
SIAM J. Numer. Anal. 28, 1071 (1991).
 Laplace's Equation and the DirichletNeumann Map in MultiplyConnected 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 TwoPoint 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 NavierStokes 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 TwoDimensional 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 FreeSpace 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 FastMultipole Accelerated Poisson Solver inTwo Dimensions[pdf: 2926 Kb]
(with F. Ethridge).
SIAM J. Sci. Comput. 23, 741 (2001).
 Nonreflecting Boundary Conditions for the TimeDependent 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).
 Highorder 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).
 PlasmonAssisted Chemical Vapor Deposition
(with D. Boyd, M. Brongersma, M. Y. ElNaggar, 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 QuasiPeriodic Fields
and its Application to Twodimensional Band Structure Calculations
(with A. Barnett).
J. Comput. Phys. 229, 6898 (2010).
 A New Integral Representation for QuasiPeriodic Scattering
Problems in Two Dimensions
(with A. Barnett).
BIT 51, 898 (2011).
 A Fast Direct Solver for Structured Linear Systems by
Recursive Skeletonization
(with K. L. Ho).
SIAM J. Sci. Comput. 35, A25077 (2012).
 Fast Multiparticle Scattering: a Hybrid Solver for the
Maxwell equations in Microstructured Materials
(with Z. Gimbutas).
J. Comput. Phys. 232, 22 (2013).
 A Consistency Condition for the Vector Potential in
MultiplyConnected Domains
(with C. L. Epstein, Z. Gimbutas, A. Kloeckner, and
M. O'Neil).
IEEE Trans. Magnetics 49, 1072 (2013).
 A Fast Direct Solver for Scattering from Periodic Structures with
Multiple Material Interfaces in Two Dimensions
(with K. L. Ho and J.Y. Lee).
J. Comput. Phys. 258, 738 (2014).
 Visualizing Skin Effects in Conductors with MRI: Li7 MRI Experiments
and Calculations
(with A. J. Ilotta, S. Chandrashekar, A. Kloeckner, H. J. Chang, N. M. Trease,
C. P. Grey, A. Jerschow).
J. Magnetic. Resonance. 245, 143 (2014).
 Normpreserving Discretization of Integral Equations for Elliptic PDEs
with Internal Layers I: the Onedimensional Case
(with T. Askham).
SIAM Rev. 56, 625 (2014).
 Simple and Efficient Representations for the Fundamental Solutions
of Stokes Flow in a Halfspace
(with Z. Gimbutas, S. Veerapaneni).
J. Fluid Mech. 776, R1 (2015).
 Fast Direct Methods for Gaussian Processes
(with S. Ambikasaran, D. ForemanMackey,
D. W. Hogg, and M. O’Neil).
IEEE Trans. Pattern Anal. Mach. Intell. 38, 252 (2016).
 On the Stability of Timedomain Integral Equations for
Acoustic Wave Propagation
(with C. L. Epstein, T. Hagstrom).
Disc. Cont. Dyn. Sys. 36, 4367 (2016).
 Validation of Neural Spike Sorting Algorithms Without
Groundtruth Information
(with A. H. Barnett, J. F. Magland).
J. Neurosci. Methods 264, 65 (2016).
 Integral Equation Methods for Elastance and Mobility Problems
in Two Dimensions
(with M. Rachh).
SIAM J. Num. Anal. 54, 2889 (2016).
 High Resolution Inverse Scattering in Two Dimensions using
Recursive Linearization
(with C. Borges, A. Gillman).
SIAM J. Imaging Sci. 10, 641 (2017).
 A Fully Automatic Approach to Spike Sorting
(with J. E. Chung, J. F. Magland, A. H. Barnett, V. M. Tolosa,
A. C. Tooker, K. Y. Lee, K. G. Shah, S. H. Felix, L. M. Frank).
Neuron 95, 1381 (2017).
 An Adaptive Fast Gauss Transform in Two Dimensions
(with J. Wang).
SIAM J. Sci. Comput. 40, A1274 (2018).
 Cathleen Morawetz and the Scattering of Acoustic Waves
(with T. SanchezVizuet).
Notices Amer. Math. Soc. 65, 770 (2018).
A Short Course on Fast Multipole Methods
Software
A number of open source software packages are available.
