Papers submitted for Publication

• S. Jiang and S. Wang, An Efficient High-Order Integral Equation Method for Solving the Heat Equation with Complex Geometries in Three Dimensions, submitted, 2017.

Journal Publications

• J. Lai and S. Jiang. Second Kind Integral Equation Formulation for the Mode Calculation of Optical Waveguide. Applied and Computational Harmonic Analysis, Volume 44, Issue 3, Pages 645-664, May 2018. (pdf)
• 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, Vol. 74, Pages 474-490, 2018.
• 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)
• 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)
• 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)
• 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)
• 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)
• 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)
• 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)
• 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)
• 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)
• 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)
• 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)
• 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)
• 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)
• 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)
• 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)
• K. Xu and S. Jiang, A Bootstrap Method for Sum-of-Poles Approximations, J. Sci. Comput. 55, 16-39, April 2013. (pdf)
• 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)
• 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)
• 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)
• 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)
• F. Hang and S. Jiang, Generalized Poincare-Bertrand Formula on a hypersurface, Applied and Computational Harmonic Analysis 27, no. 1, 100-116, 2009. (pdf)
• 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)
• 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)
• 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)
• 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)
• 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)
• 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)
• 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)
• 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)
• 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)
• 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)

Nonrefereed Technical Reports

• S. Jiang, Potential Theory for Initial-boundary Value Problems of Unsteady Stokes Flow in Two Dimensions, NJIT CAMS report 1112-8, 2011. (pdf)
• S. Jiang, An efficient algorithm for the evaluation of certain convolution integrals with singular kernels, NJIT CAMS report 0910-4, 2009. (pdf)
• 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

• Fast Evaluation of Nonreflecting Boundary Conditions for the Schrodinger Equation.