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Xianjin Chen Postdoctoral Associate Institute
for Mathematics and Its Applications Office:
358
Lind Hall |
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---Recent papers |
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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. |
Education
2008,
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
Numerical
methods for multiple (unstable) solution problems Nonlinear
Schrodinger systems Nonlinear
elliptic systems Scientific
computing and computer simulation
"Computational
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
"A
numerical method for finding multiple co-existing solutions to
nonlinear cooperative
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
"A
Min-Max-Orthogonal method for multiple solutions of noncooperative
semilinear
elliptic systems" (with
J. Zhou), to appear on Math. Comp.
"A
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
Invited talks
”A numerical method and its demo on finding multiple unstable
solutions
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
”A
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
29th
Texas PDE conference, University of Texas at Arlington,
03/2006
27th
Texas PDE conference, TAMU, 04/2004
Texas
PDE conference, University of Texas at San Antonio, 02/2002
Operating
systems: Unix/Linux, Windows
Languages:
C/C++, Visual C++, MATLAB/FEMLAB, Latex, HTML
Packages
developed:
-- 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
"A
real-time demo on solving nonlinear PDEs for multiple
solutions",
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
(Co-author)
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
