Papers submitted for Publication
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Shidong Jiang.
A fast Gauss transform in one dimension using sum-of-exponentials approximations.
(arXiv version)
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Jun Wang, Leslie Greengard, Shidong Jiang, Shravan Veerapaneni.
Fast integral equation methods for linear and semilinear heat equations in moving domains.
(arXiv version)
Journal Publications
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Yong Zhang, Chijie Zhuang, Shidong Jiang.
Fast one-dimensional convolution for general kernels using
sum-of-exponentials approximation.
Commun. Comput. Phys., accepted.
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Bo Wang, Zhiguo Yang, Li-Lian Wang, and Shidong Jiang. On time-domain NRBC for Maxwell's
equations and its application in accurate simulation of electromagnetic invisibility cloaks. J. Sci.
Comput., accepted.
(arXiv version)
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Leslie Greengard, Shidong Jiang, and Jun Wang.
On the accurate evaluation of unsteady Stokes layer potentials in moving two-dimensional geometries.
Adv. Comput. Math., 46:17, 2020.
(arXiv version)
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Xiaoyu Wei, Shidong Jiang, Andreas Kloeckner, Xiao-Ping Wang.
An Integral Equation Method for the Cahn-Hilliard Equation in the Wetting
Problem. J. Comput. Phys., 419:109521, 2020.
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Zydrunas Gimbutas, Shidong Jiang, Li-Shi Luo.
Evaluation of Abramowitz functions in the right half of the complex
plane. J. Comput. Phys., 405:109169, 2020
(arXiv version)
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Szu-Pei P. Fu, Rolf J. Ryham, Andreas Klöckner, Matt Wala, Shidong Jiang, and Yuan-Nan Young.
Multiscale Hydrophobic Lipid Dynamics Simulated by Efficient Integral Equation Methods.
SIAM J. Multiscale Model. Simul., 18(1):79 - 103, 2020
(arXiv version)
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Dong Wang, Shidong Jiang, Xiao-Ping Wang.
An Efficient Boundary Integral Scheme for the Threshold Dynamics Method
II: Applications to Wetting Dynamics. Journal of Scientific Computing 81(3), 1860-1881, 2019.
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Alex Barnett, Charles Epstein, Leslie Greengard, Shidong Jiang, Jun Wang.
Explicit unconditionally stable methods for the heat equation via
potential theory.
Pure and Applied Analysis 1, no. 4, 709-742, 2019.
(arXiv version)
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Zecheng Gan, Ziwei Wang, Shidong Jiang, Zhenli Xu, and Erik Luijten.
Efficient dynamic simulations of charged dielectric colloids through a
novel hybrid method. Journal of Chemical Physics, 151, 024112, 2019.
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Leslie Greengard and Shidong Jiang.
A new mixed potential representation for the equations of unsteady, incompressible flow.
SIAM Review 61, no. 4, 733-755, 2019.
(arXiv version)
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S. Wang, S. Jiang, and J. Wang.
Fast High-Order Integral Equation Methods for Solving
Boundary Value Problems of Two Dimensional Heat
Equation in Complex Geometry.
J. Sci. Comput. 79(2), 787-808, May 2019.
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Rami Ben-Zvi, Shidong Jiang, Harvey Scher, and Brian Berkowitz.
Finite-Element Method Solution of Non-Fickian
Transport in Porous Media: The CTRW-FEM
Package.
Groundwater 57(3), 479-484, May-June 2019.
(pdf)
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L. Greengard, S. Jiang, and Y. Zhang.
The anisotropic truncated kernel method for convolution with free-space Green's functions.
SIAM J. Sci. Comput. 40(6), A3733-A3754, 2018.
(pdf)
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J. Helsing and S. Jiang.
On Integral Equation Methods for the First Dirichlet Problem of the Biharmonic and Modified Biharmonic
Equations in NonSmooth Domains.
SIAM J. Sci. Comput. 40(4), A2609--A2630, 2018.
(pdf)
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J. Lai and S. Jiang.
Second Kind Integral Equation Formulation for the Mode Calculation of Optical Waveguide.
Applied and Computational Harmonic Analysis 44, Issue 3, 645-664, May 2018.
(pdf)
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S. Jiang, D. Wang, and X. P. Wang,
An Efficient Boundary Integral Scheme for the MBO
Threshold Dynamics Method via NUFFT, Journal of Scientific Computing 74, Pages 474-490, 2018.
(pdf)
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Q. Zhang, J. Zhang, S. Jiang, and Z. Zhang.
Numerical solution to a linearized time fractional KdV equation on unbounded domains.
Mathematics of Computation,
Vol. 87, No. 310, Pages 693-719, March 2018.
(pdf)
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S. Jiang, J. Zhang, Q. Zhang, and Z. Zhang.
An Efficient Algorithm for Solving Fractional Diffusion Equations.
Communications in Computational Physics, Vol. 21, No. 3, pp. 650-678, 2017.
(pdf)
(Matlab code for the SOE approximation of
power functions)
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S. Jiang, M. Rachh, and Y. Xiang.
An efficient high order method for dislocation climb in two dimensions.
SIAM Journal on Multiscale Modeling and Simulation, Vol. 15, No. 1, pp. 235-253, 2017.
(pdf)
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S. Jiang and J. Lai.
A Quantitative Study of the Effect of Cladding Thickness on Modal Confinement Loss in Photonic Waveguides.
Optics Express 24(22), 24872-24882, October 2016.
(pdf)
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Z. Gan, S. Jiang, E. Luijten, and Z. Xu.
A Hybrid Method for Systems of Closely Spaced Dielectric Spheres and Ions.
SIAM Journal on Scientific Computing 38(3), B375-B395, 2016.
(pdf)
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S. Jiang and L. Luo.
Analysis and Solutions of the Integral Equation Derived from the
Linearized BGKW Equation for the Steady Couette Flow.
Journal of Computational Physics 316, 416-434, July 2016.
(pdf)
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R. Ben-Zvi, H. Scher, S. Jiang, and B. Berkowitz.
One-dimensional Finite Element Method Solution of a Class of Integro-Differential equations:
Application to non-Fickian transport in Disordered Media.
Transport in Porous Media, 2016. DOI: 10.1007/s11242-016-0712-0
(pdf)
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L. Greengard, T. Hagstrom, and S. Jiang.
Extension of the Debye-Mie-Lorenz Formalism to the Time Domain.
Journal of Computational Physics 299(15), 98-105, 2015.
(pdf)
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S.-P. Fu, Y.-N. Young, S. Jiang,
Efficient Brownian Dynamics Simulation of DNA molecules with Hydrodynamic Interactions,
Physical Review E 91, 063008, 2015.
(pdf)
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W. Bao, S. Jiang, Q. Tang, and Y. Zhang,
Computing the Ground State and Dynamics of the Schrodinger-Poisson Equation via Nonuniform FFT,
Journal of Computational Physics 291(1), 72-89, 2015.
(pdf)
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S. Jiang, L. Greengard, and S. Wang,
Efficient sum-of-exponentials approximations for the heat kernel and their applications,
Advances in Computational Mathematics 41(3), 529-551, 2015.
(pdf)
(Matlab code for kernel approximation)
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S. Jiang, L. Greengard, and W. Bao,
Fast and accurate evaluation of nonlocal Coulomb and dipole-dipole interactions via the nonuniform FFT,
SIAM Journal on Scientific Computing 36(5), B777-B794, 2014.
(pdf)
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L. Greengard, T. Hagstrom, and S. Jiang,
The solution of the scalar wave equation in the exterior of a sphere,
Journal of Computational Physics 274, 191-207, 2014.
(pdf)
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S. Jiang, M. C. A. Kropinski, and B. Quaife,
Second Kind Integral Equation Formulation for the Modified Biharmonic
Equation and its Applications, J. Comput. Phys. 249, 113-126, Sept. 2013.
(pdf)
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S. Jiang, Z. Liang, and J. Huang,
A fast algorithm for Brownian dynamics simulation with hydrodynamic interactions,
Math Comput. 82, 1631-1645, July 2013.
(pdf)
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K. Xu and S. Jiang,
A Bootstrap Method for Sum-of-Poles Approximations,
J. Sci. Comput. 55, 16-39, April 2013.
(pdf)
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Z. Liang, Z. Gimbutas, L. Greengard, J. Huang, and S. Jiang,
A fast multipole method for the
Rotne-Prager-Yamakawa tensor and its
applications, J. Comput. Phys. 234, 133-139, February 2013.
(pdf)
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S. Jiang, S. Veerapaneni, and L. Greengard,
Integral Equation Methods for Unsteady Stokes Flow in Two Dimensions,
SIAM J. Sci. Comput. 34, no. 4, A2197-A2219, August 2012.
(pdf)
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S. Jiang, B. Ren, P. Tsuji, and L. Ying, Second
kind integral equations for the first kind Dirichlet problem of the
biharmonic equation in three dimensions,
J. Comput. Phys. 230, no. 19, 7488-7501, 2011
(pdf)
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M. F. Causley, P. G. Petropoulos, and S. Jiang,
Incorporating the Havriliak-Negami Dielectric Model in Numerical
Solutions of the Time-Domain Maxwell Equations,
J. Comput. Phys. 230, no. 10, 3884-3899, 2011.
(pdf)
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F. Hang and S. Jiang,
Generalized Poincare-Bertrand Formula on a hypersurface,
Applied and Computational Harmonic Analysis 27, no. 1, 100-116, 2009.
(pdf)
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S. Jiang and L. Greengard,
Efficient Representation of Nonreflecting Boundary Conditions for
the Time-Dependent Schrodinger Equation in Two Dimensions,
Comm. Pure & Appl. Math., 61, no. 2, 261--288, 2008.
(pdf)
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S. Jiang and M. Xu,
Size dependence of second-order hyperpolarizability of finite periodic chains
under Su-Schrieffer-Heeger model, Europhys. Letter 76, no. 4,
670-676, 2006.
(pdf)
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M. Xu and S. Jiang,
Breaking of the Overall Permutation Symmetry in Nonlinear Optical
Susceptibilities of One-Dimensional Periodic Dimerized Hueckel Model,
J. Phys.: Condens. Matter 18, 8987-8993, 2006.
(pdf)
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S. Jiang,
Jump Relations of the Quadruple Layer Potential on a Regular Surface
in Three Dimensions,
Appl. Comput. Harmon. Anal. 21, 395-403, 2006.
(pdf)
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M. Xu and S. Jiang,
Hyperpolarizabilities for the One-Dimensional Infinite
Single-Electron Periodic Systems
II. Dipole-Dipole versus Current-Current Correlations,
J. Chem. Phys. 123, 064902, 2005.
(pdf)
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S. Jiang and M. Xu,
Hyperpolarizabilities for the One-Dimensional Infinite Single-Electron
Periodic Systems I. Analytical Solutions under Dipole-Dipole Correlations,
J. Chem. Phys. 123, 064901, 2005.
(pdf)
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S. Jiang and L. Greengard,
Fast Evaluation of Nonreflecting Boundary Conditions for the Schrodinger Equation
in One Dimension,
Comput. Math. Appl. 47/6-7, 955-966, 2004.
(pdf)
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S. Jiang and V. Rokhlin,
Second Kind Integral Equations for the Classical Potential Theory on
Open Surfaces II,
J. Comput. Phys. 195, 1-16, 2004.
(pdf)
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S. Jiang and V. Rokhlin,
Second Kind Integral Equations for the Classical Potential Theory on
Open Surfaces
I: Analytical Apparatus,
J. Comput. Phys. 191, 40-74, 2003.
(pdf)
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P. Kolm, S. Jiang, and V. Rokhlin,
Quadruple and Octuple Layer Potentials in Two Dimensions I: Analytical Apparatus,
Appl. Comput. Harmon. Anal. 14, 47-74, 2003.
(pdf)
Refereed Conference Proceedings
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S. Jiang and S. Wang,
An Efficient High-Order Integral Equation Method for
Solving the Heat Equation with Complex Geometries in
Three Dimensions, Proceedings of the Seventh International
Congress of Chinese Mathematicians (ICCM), 2016.
Nonrefereed Technical Reports
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S. Jiang,
Potential Theory for Initial-boundary Value Problems of Unsteady Stokes Flow in Two Dimensions,
NJIT CAMS report 1112-8, 2011.
(pdf)
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S. Jiang, An efficient algorithm for the evaluation of certain
convolution integrals with singular kernels, NJIT CAMS report
0910-4, 2009.
(pdf)
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S. Jiang and F. Hang, Generalized Poincare-Bertrand Formula on a
regular surface in three dimensions,
NJIT CAMS report
0506-13, 2006.
(pdf)
Ph.D. Thesis
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Fast Evaluation of Nonreflecting Boundary Conditions for the
Schrodinger Equation.