Selected Publications

"American Option Pricing Model as an Obstacle Problem,"
working paper, 2008.
"Serial Persistence and Holding Period Dependence of Real Estate Risk,"
(with Cheng, et. al.), Real Estate Economics, to be submitted, 2008.
"Convergence of Free Boundaries in Discrete Obstacle Problems,"
Numerische Mathematik (2007) 106:157-164.
"Numerical Evaluation of Impact of Laser Preheat on Interface Structure and Instability,"
(with Drake, et. al.), Physics of Plasma, 14,062703, 2007.
"A Multiscale Front Tracking method for Compressible Free Surface Flows,"
(with Xu, et. al.), Chemical Engineering Science Journal, 62 (13): 3538-3548, 2007.
"Interface Tracking for Reactive Flows with Application to Type Ia Supernova,"
(with Li, et. al.), preprint, 2006.
"Monotone Convergence of Finite Element Approximation of Obstacle Problems"
Applied Mathematics Letters, 20, 445-449, 2007.
"Error Estimates for the Numerical Approximation of Time-dependent Flow of Bingham Fluid in Cylindrical Pipes by the Regularization Method,"
Numerische Mathematik, Vol 96, No. 1, 153-184, 2003.
"Multilevel Projection Algorithm for Obstacle Problems,"
Computers and Mathematics with Applications, 41 (2001) 1505-1513.
"Numerical Solution of Variational Inequalities,"
Ph.D thesis, University of Chicago, 1997.
"A Monotonicity Principle and $L^{\infty}$-Error Bound for a Discrete Obstacle Problem"
Technical Report (TR-96-21), University of Chicago, 1996.
"A Posterior Error Analysis of a Two-level Scheme for Solving the Obstacle Problem,"
INFORMATION, Vol. 3, No. 4, 469-477, October 2000.
"Numerical Calculation of Rayleigh-Taylor and Richtmyer-Meshkov Instabilities for Three Dimensional Axisymmetric flows in Cylindrical and Spherical Geometries,"
(with J. Glimm, J. Grove) Los Alamos Laboratory, Report# LA-UR99-6796, 1999.
"Three Dimensional Axisymmetric Simulations of Fluid Instabilities in Curved Geometry,"
(with J. Glimm, J. Grove) In M. Rahman and C. A. Brebbia, editors, Advances in Fluid Mechanics III, 643-652, WIT press, Southampton, UK, 2000.
"Interface Tracking for Axisymmetric Flows,"
SIAM J. Sci. Comp., Vol 24, No. 1, 208-236, 2002.
"Numerical Study of Axisymmetric Richtmyer-Meshkov Instability and Azimuthal Effect on Spherical Mixing,"
(with J. Glimm, J. Grove, S. Dutta), J. Stat. Physics, Vol. 107, nos 112, 241-260, 2002.
"Experiments to produce a hydrodynamically unstable spherically diverging system of relevance to instabilities in supernovae,"
Astrophysical Journal, Vol. 564, 2, 896-908, 2002.
"A Two Pressure Numerical Model of Two Fluid Mixtures,"
(with Glimm et al) SIAM J. Multiscale Modeling and Simulation, 1:458-484, 2003.
"A Fast Algorithm for Moving Interface Problems,"
(with Dutta et al),In V. Kumar et al, editors, Computational Science and Its Applications, ICCSA 2003, LNCS 2668, 782--790, Springer-Verlag, Berlin Heidelberg, 2003.
"Front Tracking for Multiphase Fluid Mixing,"
In A. A. Mammoli and C. A. Brebbia, editors, Computational Methods in Multiphase Flow II, pp. 13-22, WIT Press, Southampton, UK, 2004.
"Error Comparison in Tracked and Untracked Spherical Simulations,"
(with Dutta et al), Computers & Mathematics with Applications, 48, 1733-1747, 2004.
"Spherical Richtmyer-Meshkov instability for axisymmetric flow,"
(with Dutta et al), Mathematics and Computers in Simulation, 65 (2004) 417-430.
"Shock Wave Interactions in Spherical and Perturbed Spherical Geometries,"
(with Dutta et al), Nonlinear Analysis, 63/5-7, pp. 644-652, 2005.
"Radiation Coupled Front Tracking Simulations for Laser Driven Shock Experiments,"
(with Drake et al), Nonlinear Analysis, 63/5-7, pp. e1635-e1644, 2005.
"Tracked Flame Simulation for Type Ia Supernova,"
(with Glimm, and Dutta), In Computational Fluid and Solid Mechanics, K. J. Bathe, editor, 950-953, Elsever 2005.
"LES Simulations of Turbulent Combustion in a Type Ia Supernova"
(with Dutta, and Glimm), Submitted to Astrophysical Journal, 2005.