The research of Shidong Jiang has mainly focused on fast numerical algorithms for PDEs and their applications to large scale problems in physics, chemistry and engineering. He has developed a fast and accurate numerical algorithm for the nonreflecting boundary conditions for the Schrodinger equation. He also developed a stable second integral equation formulation for scattering by open surfaces in two dimensions. When the SKIE formulation is combined with a Fast Multipole Method and iterative solver, a fast and stable numerical algorithm has been developed for large scale open surface problems arising in biology and antenna and radar design. Recently, he has derived analytical solutions for the hyperpolarizabilities for the one dimensional infinite single electron periodic systems which showed that the overall symmetry in nonlinear optics is actually broken.
PhD, Mathematics, Courant Institute of Mathematical Sciences, New York University, Sept. 1998- Sept. 2001
MS, Physics, New York University, Sept. 1995- Aug. 1998
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 (2008), no. 2, 261--288. (pdf)
S. Jiang and F. Hang, Generalized Poincare-Bertrand Formula on a Regular Surface in Three Dimensions, CAMS Report 0506-13, Department of Mathematical Sciences, NJIT, 2006. To be submitted.
S. Jiang and M. Xu, Size dependence of second-order hyperpolarizability of finite periodic chains under Su-Schrieffer-Heeger model, Europhys. Letter 76 (2006), no. 4, 670-676. (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 (2006) 8987-8993. (pdf)
S. Jiang, Jump Relations of the Quadruple Layer Potential on a Regular Surface in Three Dimensions, Appl. Comput. Harmon. Anal. 21 (2006) 395-403. (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. (2005) 123, 064902 (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. (2005) 123, 064901. (pdf)
S. Jiang and L. Greengard, Fast Evaluation of Nonreflecting Boundary Conditions for the Schrodinger Equation in One Dimension, Comput. Math. Appl. (2004) 47/6-7, 955-966. (pdf)
S. Jiang and V. Rokhlin, Second Kind Integral Equations for the Classical Potential Theory on Open Surfaces II, J. Comput. Phys. (2004) 195, 1-16. (pdf)
S. Jiang and V. Rokhlin, Second Kind Integral Equations for the Classical Potential Theory on Open Surfaces I: Analytical Apparatus, J. Comput. Phys. (2003) 191, 40-74. (pdf)
P. Kolm, S. Jiang, and V. Rokhlin, Quadruple and Octuple Layer Potentials in Two Dimensions I: Analytical Apparatus, Appl. Comput. Harmon. Anal. (2003) 14, 47-74. (pdf)
Fast Evaluation of Nonreflecting Boundary Conditions for the Schrodinger Equation (Thesis Adviser: Leslie Greengard) (pdf)