You are in the College of Science and Liberal ArtsCollege of Science and Liberal Arts

Department of Mathematical Sciences

Jiang, Shidong

Contact Info
Title: Associate Professor
Email: shidong.jiang@njit.edu
Office: CULM 610
Hours: Tuesday and Thursday 2:30-4:00pm for Spring 2011
Phone: 973-596-3141
Dept: Mathematical Sciences
Webpage: http://web.njit.edu/~jiang

About Me

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.

Education

  • PhD, Mathematics, Courant Institute of Mathematical Sciences, New York University, Sept. 1998- Sept. 2001
  • MS, Physics, New York University, Sept. 1995- Aug. 1998
  • BS, Applied Physics & Applied Mathematics, Shanghai Jiaotong University, Shanghai, China, Sept. 1990- July 1994

Courses I Teach

Not teaching any courses this semester

Current Classes

Classes Taught

  • Spring 2008: Math 614-002 Numerical Methods I
  • Spring 2008: Math 337 Linear Algebra (Coordinator)
  • Fall 2007: Math 707-001 Special Topics: Fast Numerical Algorithms
  • Fall 2007: Math 337 Linear Algebra (Coordinator)
  • Spring 2007: Math 222 Differential Equations
  • Spring 2007: Math 337 Linear Algebra (Coordinator)
  • Fall 2006: Math 222 Differential Equations
  • Fall 2006: Math 337 Linear Algebra (Coordinator)
  • Spring 2006: Math 222 Differential Equations (Co-coordinator)
  • Spring 2006: Math 614 Numerical Methods I
  • Fall 2005: Math 222 Differential Equations (Co-coordinator)
  • Spring 2005: Math 340 Applied Numerical Methods
  • Fall 2004: Math 337 Linear Algebra

Publications

  • 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)

PhD Thesis

  • Fast Evaluation of Nonreflecting Boundary Conditions for the Schrodinger Equation (Thesis Adviser: Leslie Greengard) (pdf)