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Shidong Jiang

Jiang, Shidong
Professor, Mathematical Sciences
CULM 610
About Me

My main research interests lie in the field of numerical analysis and scientific computing with particular emphasis on fast numerical algorithms and integral equation methods for solving initial/boundary value problems for various partial differential equations. I have constructed well-conditioned second kind integral equation formulations for the open-surface problems, fourth order biharmonic and modified biharmonic equations, and mode calculation of optical waveguides. I have studied sum-of-exponentials and sum-of-poles approximations and their applications to nonreflecting boundary conditions for the Schrodinger equation, the Havriliak-Negami dielectric model, the fractional derivative, layer potentials for the heat equation, and the continuous time random walk transport equation. I have also developed fast algorithms for nonlocal interactions, Brownian dynamics and molecular dynamics simulations.

  • PhD, Mathematics, Courant Institute of Mathematical Sciences, New York University, 2001
  • MSc, Physics, New York University, 1998
  • Bsc, Applied Physics and Applied Mathematics, Shanghai Jiao Tong University, 1994
Research Interests

Shidong Jiang's research lies on numerical analysis, scientific computing, and applied math in general. His interests include:

  • Fast algorithms
  • Integral equation methods
  • Computational fluid dynamics
  • Computational electromagnetics
​​Current Research

I am currently working on efficient algorithms for dislocation dynamics, interface problem, integrated photonics, and nonequilibrium gas dynamics.

  • 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, 2016.
  • 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, 2016.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.​