Jinjie Liu, Ph.D.

Jinjie Liu

Associate Professor, Department of Mathematical Sciences

Campus Address: ETV 103

Email: jliu [at] desu.edu
(302) 857-7041
(302) 857- 7054 (fax)

Education

B.S., University of Science and Technology of China, 2001
M.S., Stony Brook University, 2003
Ph.D., Stony Brook University, 2006
Postdoctoral training: Mathematics, Arizona State University, 2006 - 2007; Mathematics, The University of Arizona, 2007 - 2009

Research Interests

Dr. Jinjie Liu’s research focuses on numerical methods and computer simulations for computational fluid dynamics, computational electrodynamics, and nonlinear optics.

Research Expertise

Applied Mathematics
Numerical Methods
Mathematical Modeling
Computer Simulation
Optics

Selected Research Projects

Transformation object
Transformation Optics Based Local Mesh Refinement

Subpixel Smoothing FDTD Method

FDTD
FDTD on Non-orthogonal Grids

Invisibility cloaking simulation

shg from metametals
SHG from metamaterials

The Front Tracking Method

selected Publications

Journal Publications

P. Xu, J. Liu, Iteration-Based Temporal Subgridding Method for the Finite-Difference Time-Domain Algorithm. Mathematics, 12(2), 302, 2024.
J. Liu, S. Appiah-Adjei, and M. Brio, Iterated Crank-Nicolson Method for Peridynamic Models, Dynamics, 2024, Accepted.
Q. Tran, J. Liu, Modified iterated Crank-Nicolson method with improved accuracy for advection equations. Numerical Algorithms, 1-22, 2023.
J. Liu, J. Cornelius, and M. Brio, “FDTD Method with Explicit Non-iterative and Second Order Treatment for Kerr Nonlinearities”, IEEE Journal on Multiscale and Multiphysics Computational Techniques, 7, 195-199, 2022.
M. Brio, J.-G. Caputo, K. Gwirtz, J. Liu, and A. Maimistov. Scattering of a short electromagnetic pulse from a Lorentz-Duffing film: Theoretical and numerical analysis. Wave Motion, 89, 43-56, 2019.
J. Nehls, C. Dineen, J. Liu, C. Poole, M. Brio, and J.V. Moloney, Stable 3D FDTD method for arbitrary fully electric and magnetic anisotropic Maxwell’s equations. International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 32(2), e2521, 2019.
Y. Zhao and J. Liu, FDTD for Hydrodynamic Electron Fluid Maxwell Equations, Photonics, 2 (2), 459-467, 2015.
J. Cornelius, J. Liu, and M. Brio, Finite-difference time-domain simulation of spacetime cloak, Optics Express, 22 (10), 12087-12095, 2014.
J. Liu, M. Brio, and J. V. Moloney, Transformation optics based local mesh refinement for solving Maxwell’s equations, Journal of computational Physics, 258, 359-370, 2014.
J. Liu, M. Brio, and J. V. Moloney, An Overlapping Yee FDTD method for Material Interfaces between Anisotropic Dielectrics and General Dispersive or PEC Media, International Journal of Numerical Modelling: Electronic Networks, Devices and Fields. 27, 22-33, 2014.
A. Marcano, I. Basaldua, A. Villette, R. Edziah, J. Liu, O. Ziane, and N. Melikechi, Photothermal lens spectrometry measurements in highly turbid samples, Applied Spectroscopy, 67, 1013-1018, 2013.
J. Liu, M. Brio, and J. V. Moloney, Subpixel smoothing Finite-Difference Time-Domain method for material interface between dielectric and dispersive media. Optics Letters, 37, 4802-4804, 2012.
J. Liu, M. Brio, and J. V. Moloney, Computation of optical force on nanoparticles using locally non-orthogonal overlapping Yee FDTD method, Journal of Electromagnetic Analysis and Applications, 4, 452-456, 2012.
Y. Zeng, J. Liu, and D. Werner, General Properties of Two-dimensional Conformal Transformations in Electrostatics, Optics Express, 19 (21), 20035-20047, 2011.
J. Liu, M. Brio, Y. Zeng, A. Zakharian, W. Hoyer, S. W. Koch, J. V. Moloney, Generalization of the FDTD algorithm for simulations of hydrodynamic nonlinear Drude model, J. Comput. Phys., 229 (17), 5921-5932, 2010.
J. Liu, M. Brio, J. V. Moloney, A Diagonal Split-cell Model for the Overlapping Yee FDTD Method, Acta Mathematica Scientia, 29 B (6):1670-1676, 2009.
Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, J. V. Moloney, Classical theory for second-harmonic generation from metallic nanoparticles, Phys. Rev. B, 79, 235109, 2009.
J. Liu, M. Brio, J. V. Moloney, Overlapping Yee FDTD Method on Nonorthogonal Grids, J. Sci. Comput., 39 (1), 129-143, 2009.
N. Feth, S. Linden, M.W. Klein, M. Decker, F.B.P. Niesler, Y. Zeng, W. Hoyer, J. Liu, S.W. Koch, J.V. Moloney, M. Wegener, Second-harmonic generation from complementary split-ring resonators, Opt. Lett., 33, 1975-1977, 2008.
S. Chen, W. Zang, A. Schülzgen, J. Liu, L. Han, Y. Zeng, J. Tian, F. Song, J. V. Moloney, N. Peyghambarian, Implicit high-order unconditionally stable complex envelope algorithm for solving the time-dependent Maxwell’s equations, Opt. Lett., 33, 2755-2757, 2008.
J. Liu, H. Lim, J. Glimm, X. Li, A Conservative Front Tracking Method in N-dimensions, J. Sci. Comput., 31, 213-236, 2007.
J. Jiang, J. Liu, On uniqueness of limit cycle for the equation x” + f(x) \phi(x’) x’ + g(x) = 0, J. Math. Anal. Appl., 284 (1), 1-8, 2003.

Conference Proceedings

J. Liu, M. Brio, Transformation Optics based moving window Finite-Difference Time-Domain method, Proceedings of the 2014 International Conference on Electromagnetics in advanced applications, Palm Beach, Aruba, August 2014.
D. Pokrajac, P. Sivakumar, Y. Markushin, D. Milovic, M. Rana, G. Holness, J. Liu, N. Melikechi, Towards Optimal CLassifier of Spectroscopy Data, Proceedings of the 1st International Conference on Electrical, Electronic and Computing Engineering (icETRAN), Vrnjacka Banja, Serbia, June 2014.
Z. Zeng, J. Liu, F. Liu, Simulation of GPR in multi-scale heterogeneity medium by overlapping Yee FDTD method, the 4rd International Conference on Environmental and Engineering Geophysics, Chengdu, China, 587-593, 2010.
Y. Zeng, W. Hoyer, J. Liu, S. W. Koch, and J. Moloney, A Classical Study of Second-Harmonic Generation from Metallic Nanoparticles, Nonlinear Optics: Materials, Fundamentals and Applications, p. NWB1. Optical Society of America, 2009.
J. Glimm, B. Fix, X. Li, J. Liu, X. Liu, T. Lu, R. Samulyak, Z. Xu, Front Tracking under TSTT, Proceedings of the IGPP-CalSpace Conference, Astronomical Society of the Pacific, 359, 15, 2007.
J. Liu, J. Glimm, X. Li, A Conservative Front Tracking Method, Proceedings of the Tenth International Conference on Hyperbolic Problems: Theory, Numerics, and Applications, Yokohama Publishers, Osaka, Japan, 57-62, 2006.

News

Oct. 28, 2013: Our paper “Transformation Optics based Local Mesh Refinement for solving Maxwell’s equations” has been accepted for publication in Journal of Computational Physics.
Sept. 26, 2013: Dr. Jinjie Liu received the DSU Vice President’s Choice Awards for research. Photo.
December, 2012: Our paper ”Subpixel smoothing FDTD method for material interface between dielectric and dispersive media”, published in Optics Letters, has been highlighted in“Spotlight on Optics”.