My research is in the area of computational and applied mathematics with a main focus on analysis, development and implementation of numerical methods for multiple unstable solutions (i.e., saddle points) to nonlinear partial differential equations (PDEs) and differential systems arising in physics (e.g., condensed matter physics, nonlinear optics), biology (e.g., pattern formation), etc. We aim to develop and establish some computational theory and methods for multiple solution problems in nonlinear PDEs. In particular, we investigate those unstable solutions in three aspects: characterizations, instability analysis and numerical computations. A little more detail of my research can be found here. Recently, we found some solutions to the Liouville-Gelfand problem using a local min-orthogonal method developed.
Ph.D. Mathematics, Texas
A&M University (TAMU), College Station, TX
1999, M.S. Applied Math., Huazhong University of Science and Technology(HUST), Wuhan, P.R. China
1997, B.S. Mathematics, Huazhong University of Science and Technology, Wuhan, P.R. China
methods for multiple (unstable) solution problems
Nonlinear Schrodinger systems
Nonlinear elliptic systems
Scientific computing and computer simulation
theory and methods for solving multiple solution problems",
sponsored by US National Science Foundation, #DMS-0311905. Advisor: Jianxin Zhou.
"Modeling and 3-D computer simulations of leaking oxygen in sealed chambers"
(with professor Huan Qi), 1999-2001
"An optimization-based decision support system for ship scheduling and computer simu-
lations of operation of permanent sluices in Three-Gorge Dam"
(with professor Huan Qi and other team members), 1998-2000
"Simulations and optimal design of Floating Raft Isolation Systems"
(with professor Huan Qi), 1998-1999
numerical method for finding multiple co-existing solutions to
systems" (with J. Zhou and X. Yao), Applied Numerical Mathematics, pdf
"On homotopy continuation method for computing multiple solutions to the Henon
equation" (with J. Zhou), Num. Meth. PDEs, pdf
"Estimates of Morse index via a local min-orthogonal method" (with J. Zhou), preprint
Min-Max-Orthogonal method for multiple solutions of noncooperative
elliptic systems" (with J. Zhou), to appear on Math. Comp.
numerical simulation on gas leakage and dispersion" (with H. Qi
and C. Wu),
Computer Simulation, Vol. 20, 2(2003), 24-27.
"3-D simulation of oxygen's leak and diffusion in a sealed chamber" (with H. Qi and
C. Wu), Computer Simulation, Vol. 19, 6(2002), 15-18
"Optimal design of a two-stage mounting isolation system by maximum entropy approach"
(with H. Qi and C. Wu), Journal of Sound & Vibration, U.K., Vol. 243, 4(2001), 591-599
"System simulation on Three Gorges permanent shiplock’s running" (with F. Lu
and H. Qi), Proceedings of Chinese Control and Decision Conference 2000, P.R. China, 709-712
"Fuzzy random analysis of reliability of communication network" (with S.H. Zhang and
M. Chen), J. of Huazhong Univ. of Sci. & Tech., Vol. 28, 10(2000), 83-84
"A state-space approach for simulating a floating raft isolation system"
(with H. Qi and C. Wu), Noise and Vibration Control, 1(1999), 15-18
”A numerical method and its demo on finding multiple unstable
to nonlinear variational systems”,
Seventh Mississippi State-UAB Conference on Differential
Equations & Computational Simulations, Birmingham, AL November 1-3, 2007
”A local min-max-orthogonal method and its convergence”,
Variational and Topological Methods: Theory, Applications, Numerical Simulations, and
Open Problems, Northern Arizona University, Flagstaff, AZ, May 23-26, 2007
”Saddle point characterization and computation for strongly indefinite functionals”,
AMS Session on PDEs, Joint Mathematics Meetings, New Orleans, LA, January 5-8, 2007
”On characterization of multiple solutions to two classes of nonlinear elliptic systems”,
Special Session on Nonlinear Elliptic and Parabolic Equations,
AMS Sectional Meeting, Storrs, CT, October 28-29, 2006
min-max-orthogonal method for finding multiple solutions to
noncooperative elliptic systems”,
Special Session on Nonlinear Differential Equations: Methods and Applications,
AMS Sectional Meeting, Salt Lake City, UT, October 7-8, 2006
”A stable method to solve nonlinear elliptic PDE systems for multiple vector solitons”,
AMS-SIAM Special Session on Nonlinear Dynamical Systems, Joint Mathematics Meetings,
San Antonio, TX, January 12-15, 2006
”Finding multiple co-existing solutions to semilinear elliptic systems via a local min-orthogonal method”,
Applied Mathematics Seminar, Department of Mathematics, Texas A&M University,
College Station, TX, November, 2005
Other conferences attended
Texas PDE conference, University of Texas at Arlington,
27th Texas PDE conference, TAMU, 04/2004
Texas PDE conference, University of Texas at San Antonio, 02/2002
systems: Unix/Linux, Windows
Languages: C/C++, Visual C++, MATLAB/FEMLAB, Latex, HTML
-- A nonlinear solver package for several classes of semilinear elliptic problems
including semilinear elliptic equations or systems, nonlinear biharmonic equations
-- A 2-D symmetric triangular mesh generator (written in Matlab) for symmetrical
domains such as rectangles, circles/ellipses, annuli, etc
real-time demo on solving nonlinear PDEs for multiple
Variational and Topological Methods: Theory, Applications, Numerical Simulations,
and Open Problems, Northern Arizona University, Flagstaff, AZ, May 2007
"A real-time demo on finding multiple solutions to the Henon equation" ,
Seminar in Applied Math, Texas A&M University, TX, March 2007
"A 3-D numerical simulation on oxygen leak and dispersion in a sealed chamber",
Wuhan Ship Design Institute, Wuhan, China, May 2001
Modeling and 3-D simulation of oxygen's leak and diffusion in a
sealed chamber, 2001
(Co-author) A ship scheduling optimization decision support system and computer simulation
on running of Three Gorges permanent ship lock, 2000
To visit my personal website: click here.
Last modified: 10-20-2008