Selected Publications

Fast Fourier transforms of piecewise polynomials,
J. Comput. Phys. 373, 346-369 (2018): DOI.
Convergence of an efficient local least-squares fitting method for bases with compact support (with S Govindjee, T J Mitchell and R L Taylor),
Comp. Meth. Appl. Mech. Engng. 213-216, 84-92 (2012): PDF.
On the order of deferred correction (with A C Hansen),
Applied Numerical Mathematics 61, 961-973 (2011): PDF.
A geometric non-uniform fast Fourier transform (with I Sammis),
J. Comput. Phys. 228, 7086--7108 (2009): PDF.
Piecewise-polynomial discretization and Krylov-accelerated multigrid for elliptic interface problems (with T Chen),
J. Comput. Phys. 227, 7503--7542 (2008): PDF.
Locally-corrected semi-Lagrangian methods for Stokes flow with elastic moving interfaces (with J Thomas Beale),
J. Comput. Phys., 227, 3896--3920 (2008): PDF.
Locally-corrected spectral methods and overdetermined elliptic systems,
J. Comput. Phys., 224, 1243--1254 (2007): PDF
A semi-Lagrangian contouring method for fluid simulation (with A Bargteil, T G Goktekin and J F O'Brien),
ACM Transactions on Graphics, January 2006, Vol. 25, No. 1: PDF, code and videos.
A semi-Lagrangian contouring method for fluid simulation (with A Bargteil, T G Goktekin and J F O'Brien),
Computer generated animation, in Visual Proceedings of ACM SIGGRAPH 2005. PDF, code and videos.
High-order fractional step methods for index-1 differential-algebraic equations (with P Vijalapura and S Govindjee )
J. Comput. Phys., 203, 305-320 (2005): PDF.
Growth of the zeta function for a quadratic map and the dimension of the Julia set (with M Zworski )
Nonlinearity, 17 (2004), 1607-1622: PDF.
A fast semi-Lagrangian contouring method for moving interfaces
J. Comput. Phys., 169 (2001), 1-22: PDF.
A Fast Modular Semi-Lagrangian Method for Moving Interfaces
J. Comput. Phys. 161 (2000), 512--536: PDF.
Fast Tree-based Redistancing for Level Set Computations
J. Comput. Phys. 152 (1999), 648-666. PDF.
Tree Methods for Moving Interfaces
J. Comput. Phys. 151 (1999), 616-648. PDF.
Semi-Lagrangian Methods for Level Set Equations
J. Comput. Phys. 151 (1999), 498-533. PDF.
Fast Adaptive 2D Vortex Methods
J. Comput. Phys. 132 (1997), 108-122. PDF.
2D Vortex Methods and Singular Quadrature Rules
J. Comput. Phys. 124 (1996), 1-23. PDF.
Fast Vortex Methods
Proceedings of the 1996 ASME Fluids Engineering Division Summer Meeting, San Diego, California, July 1996. PDF.
Locally-corrected Multidimensional Quadrature Rules for Singular Functions
SIAM J. Sci. Comp. 16 (1995), 992-1017. PDF.
Spectral Methods for Nonlinear Parabolic Systems
J. Comput. Phys. 122 (1995), 1-12. PDF.
Fast Triangulated Vortex Methods for the 2-D Euler Equations (with G Russo)
J. Comput. Phys. 111 (1994), 291-323. PDF.
Fast Spectrally-Accurate Methods for Variable-Coefficient Elliptic Problems
Proc. of the AMS. 122 (1994), 843-850. PDF.
Computing the Weak Limit of KdV (with D W McLaughlin)
Comm. Pure Appl. Math. XLVII (1994), 1319-1364. PDF.
Fast Adaptive Methods for the Free-Space Heat Equation
SIAM J. Sci. Comput. 15 (1994), 185-206. PDF.
Fast Potential Theory II: Layer Potentials and Discrete Sums
J. Comput. Phys. 99 (1992), 251-270. PDF.
A Fast Laplace Transform based on Laguerre Functions
Math. Comp. 58 (1992), 275-284. PDF.
Crystal Growth and Dendritic Solidification (with J A Sethian)
J. Comput. Phys. 98 (1992), 231-253.
The Fast Gauss Transform with Variable Scales
SIAM J. Sci. Stat. Comput. 12 (1991), 1131-1139. PDF.
The Fast Gauss Transform (with L Greengard)
SIAM J. Sci. Stat. Comput. 12 (1991), 79-94. PDF.
A Fast Algorithm for Evaluating Heat Potentials (with L Greengard)
Comm. Pure Appl. Math. XLIII (1990), 949-963. PDF.
Velocity Effects in Unstable Solidification
SIAM J. Appl. Math. 50 (1990), 1-15.
A Boundary Integral Approach to Unstable Solidification
J. Comput. Phys. 85 (1989), 342-389.
Linear Stability of Planar Solidification Fronts
Physica 30D (1988), 297-320.

Preprints

Fast Fourier transforms of piecewise polynomials PDF.
Fast stable deferred correction methods for two-point boundary value problems PDF.

Talks

First-order overdetermined systems for elliptic problems .
A butterfly algorithm for the geometric nonuniform FFT .
ADI iterations for general elliptic problems .
Boundary integral methods for general elliptic problems .

Movies

SLC.mov.
slc-et-web.mov.

Disclaimer

This material is based upon work supported by the National Science Foundation under grant number DMS-0913695, and by the Air Force Office of Scientific Research, Air Force Materiel Command, USAF, under grant number FA9550-08-1-0131. Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF), the Air Force Office of Scientific Research, or the U.S.\ Government. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon.