|Hours:||On sabbatical leave for the academic year 2018-2019.|
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
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
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.