Selected Publications
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.