Papers submitted for Publication

  1. Shidong Jiang. A fast Gauss transform in one dimension using sum-of-exponentials approximations. (arXiv version)
  2. 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

  1. Yong Zhang, Chijie Zhuang, Shidong Jiang. Fast one-dimensional convolution for general kernels using sum-of-exponentials approximation. Commun. Comput. Phys., accepted.
  2. 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)
  3. 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)
  4. 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.
  5. 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)
  6. 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)
  7. 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.
  8. 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)
  9. 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.
  10. 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)
  11. 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.
  12. 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)
  13. 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)
  14. 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)
  15. 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)
  16. 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)
  17. 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)
  18. 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)
  19. 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)
  20. 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)
  21. 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)
  22. 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)
  23. 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)
  24. 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)
  25. 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)
  26. 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)
  27. 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)
  28. 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)
  29. 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)
  30. 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)
  31. 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)
  32. K. Xu and S. Jiang, A Bootstrap Method for Sum-of-Poles Approximations, J. Sci. Comput. 55, 16-39, April 2013. (pdf)
  33. 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)
  34. 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)
  35. 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)
  36. 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)
  37. F. Hang and S. Jiang, Generalized Poincare-Bertrand Formula on a hypersurface, Applied and Computational Harmonic Analysis 27, no. 1, 100-116, 2009. (pdf)
  38. 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)
  39. 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)
  40. 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)
  41. 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)
  42. 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)
  43. 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)
  44. 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)
  45. 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)
  46. 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)
  47. 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

  1. 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

  1. S. Jiang, Potential Theory for Initial-boundary Value Problems of Unsteady Stokes Flow in Two Dimensions, NJIT CAMS report 1112-8, 2011. (pdf)
  2. S. Jiang, An efficient algorithm for the evaluation of certain convolution integrals with singular kernels, NJIT CAMS report 0910-4, 2009. (pdf)
  3. 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