Shidong Jiang

Contact Information

• Office: 610 Cullimore Hall
• Phone: (973) 596-3141
• Fax: (973) 596-5591
• E-mail: shidong.jiang (at) njit.edu
• Address: Department of Mathematical Sciences, NJIT, University Heights, Newark, NJ 07102

Office Hours

Fall 2008

• Monday and Wednesday 2:30-3:30pm

Research Interests

• Numerical algorithms (particularly analysis-based fast numerical algorithms)
• Nonreflecting boundary conditions
• Open surface problems
• Nonlinear optics

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

Experience

• Assistant Professor, Department of Mathematical Sciences, New Jersey Institute of Technology, Sept. 2004-present
• Postdoctoral Associate, Department of Computer Science, Yale University, Oct. 2001- Aug. 2004 (Mentor: Vladimir Rokhlin)

Courses

• Fall 2008: Math 712-001 Numerical Methods II
• Fall 2008: Math 337 Linear Algebra
• 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)

Ph.D. Thesis

• Fast Evaluation of Nonreflecting Boundary Conditions for the Schrodinger Equation (Thesis Adviser: Leslie Greengard) (pdf)
• Link to the directory containing the pole approximation of the convolution kernel