Fast Multipole Methods

``Accelerating fast multipole methods for the Helmholtz equation at low frequencies'', with L. Greengard, V. Rokhlin, and S. Wandzura, IEEE Computational Science and Engineering, 5: (3) 32-38 JUL-SEP 1998.

``A new version of the Fast Multipole Method for screened Coulomb interactions in three dimensions'' , with L. Greengard. J. Comput. Phys. 180 (2002), no. 2, 642--658.

``An Adaptive Fast Solver for the Modified Helmholtz Equation in Two Dimensions'' , with H.W. Cheng, and T. Leiterman.

Lattice Sums

``Integral representations of harmonic lattice sums'' , Journal of Mathematical Physics, 40:(10) 5240-5246, October 1999.

``Lattice sums and the two-dimensional, periodic Green's function for the Helmholtz equation'', with A. Dienstfrey and F. Hang, Proc. R. Soc. Lond. A. 457 (2005): 67-85 JAN 8 2001.

``Integral representations for elliptic functions'', with A. Dienstfrey, In Press, Corrected Proof, Available online 17 May 2005.

Krylov Deferred Correction Methods

``Accelerating the Convergence of Spectral Deferred Correction Methods'', with J. Jia, and M. Minion. Accepted by the Journal of Computational Physics.

Direct Solvers

``A Fast Direct Solver for Elliptic Differential Equations on Adaptively Refined Meshes'', with Leslie Greengard, SIAM Journal on Scientific Computing, 21: (4) 1551-1566, April 2000.

Circuit Design

``A Numerically Stable Surface Integral Formulation For the Impedance Extraction of 3D Structures'', with Zhenhai Zhu, Ben Song, and Jacob White. ICCAD-2001.

Nonlinear Shallow-Water Equation

``On a Completely Integrable Numerical Scheme for a Nonlinear Shallow-Water Wave Equation'' , with R. Camassa, and L. Lee. Journal of Nonlinear Mathematical Physics Volume 12, Supplement 1 (2005), 146–162

Preprints

``An Integral Equation Method for Epitaxial Step-Flow Growth Simulations'', with M.C. Lai, Y. Xiang.

``A Wideband Fast Multipole Method for the Helmholtz Equation in Three Dimensions'', with H. Cheng, W. Crutchfield, Z. Gimbutas, L. Greengard, F. Ethridge, V. Rokhlin, N. Yarvin, and J. Zhao.

``Remarks on the Implementation of the Wideband FMM for the Helmholtz Equation in Two Dimensions'', with W. Crutchfield, Z. Gimbutas, L. Greengard, V. Rokhlin, N. Yarvin, and J. Zhao.

``Arbitrary Order Krylov Deferred Correction Methods for Differential Algebraic Equations'', with J. Jia, and M. Minion.