1995-1999
Simplified models of the Josephson-Junctions and
its finite element approximations, with J. Remski,
E.
J. Applied. Math., 10, 1-25, 1999;
Approximation of a mean field model for superconductivity;
with H. Lee and M. Gunzburger, in Proc. Korean Advanced Institute for
Science and Mathematics Technology Workshop on Finite Elements, 61-72,
1999;
Analysis and computation of a mean field model for superconductivity, with M. Gunzburger and H. Lee,
Numerische Mathematik, Vol 81, No.4, pp539-560, 1999;
Numerical
Algorithms of the Lawrence--Doniach Model for Layered Superconductors and their Parallel Implementation,
with P. Gray,
SIAM J. Sci. Comp.,Vol 20, No4, p2122-2139, 1999;
Numerical Solution of the Three-Dimensional Ginzburg-Landau Models Using Artificial Boundary, with X. Wu,
SIAM J. Numer. Anal., 36, 1482-1506,
1999;
Centroidal
Voronoi Tessellations: Applications and Algorithms,
with V. Faber and M. Gunzburger,
SIAM
Review, 41, p637-676, 1999;
Studies of a Ginzburg-Landau Model for d-Wave Superconductors,
SIAM J. Applied Math., 59, no.4,
p1225-1250,
1999;
Discrete gauge invariant approximations of a time dependent Ginzburg-Landau model of superconductivity,
Math. Comp., 67, 965-986, 1998;
Analysis and Convergence of a Covolume Approximation of the Ginzburg-Landau Model of Superconductivity, with R. Nicolaides and
X. Wu,
SIAM J. Numer. Anal., 35, pp1049-1072, 1998;
Large scale scientific computation and its application
in material sciences, Proceedings of the CAST 3rd Academic Conference
held in Beijing 1998 (in Chinese, refereed), V4,
Information Science and Microelectronic
Technology, pp153-155, edited by CAST, Beijing, China Science and
Technology Press, 1998 (ISBN 7-5046-2519-1).
The Quasi-Laguerre iteration, with M. Jin, T-Y Li and
Z. Zeng; Math. Comp., 66, pp345-361, 1997;
Ginzburg-Landau Vortices: Dynamics, Pinning, and Hysteresis,
with F.H. Lin,
SIAM J. Math. Anal., 28, pp1265-1293, 1997;
Impulsive Stretching of a Surface in a Viscous Fluid,
with C. Y. Wang, M. Miklavcic & C. Chang,
SIAM J. Appl. Math., 57, pp1-14, 1997;
Vortices in superconductors: modelling and computer simulations
,
with J. Deang, M. Gunzburger and J. Peterson,
Philos. Trans. Roy. Soc. London Ser. A, 355, pp1957-1968, 1997;
Ginzburg-Landau type models for superconductivity,
with M. Gunzburger, and J. Peterson,
in World congress of nonlinear analysts 92,
(refereed), de Gruyter, Berlin, 3779 - 3788, 1996;
Time dependent Ginzburg-Landau models for
superconductivity, in World congress of nonlinear analysts 92,
(refereed), de Gruyter, Berlin, 3789-3801, 1996;
Quasi-Laguerre Iteration in Solving Symmetric Tridiagonal Eigenvalue Problems
, with M. Jin, T-Y Li and Z. Zeng,
SIAM J. Sci. Comp., 17, pp1347-1368, 1996;
A
variable thickness thin film model for superconductivity,
with J. Chapman and M. Gunzburger,
Z. Angew Math Phys,
47, pp410-431, 1996;
High-Kappa Limits of the Time-Dependent Ginzburg-Landau Model
, with P. Gray,
SIAM J. Appl. Math., 56, pp1060-1093, 1996;
Computational methods for the time dependent Ginzburg-Landau model for superconductivity
, in
Numerical
methods in applied sciences,
edited by W. Cai, et. al., Science Press, New York, 51-65, 1996;
Study of an inclined, segmented cantilever with tip
load, with C. Wang,
Quart. Applied Math.,
53, pp81-93, 1995;
Simplified
Ginzburg-Landau models for superconductivity
valid for high Kappa and high fields
, with J. Chapman & M. Gunzburger,
and J. Peterson, Advances in Math. Sci. Appl., 5, no.1, pp
193-218, 1995;
A
Ginzburg-Landau type model of superconducting/normal
junctions including Josephson Junctions, with J. Chapman & M. Gunzburger, Euro. J. Appl. Math., Vol.6, no. 2, pp97-114,1995;
Analysis and finite element approximation of optimal control problems for a Ladyzhenskaya model for stationary, incompressible, viscous flows
, with M. Gunzburger
and S. Hou, Comp. &
Applied Math., 61, pp 323-343, 1995;
Computational simulation of type-II superconductivity including pinning phenomena
, with M. Gunzburger and J. Peterson,
Phy. Rev. B, 51, pp16194-16203, 1995;
On the Lawrence-Doniach and Anisotropic Ginzburg-Landau Models for Layered Superconductors
,with J. Chapman &
M. Gunzburger,
SIAM J. Applied Math., 55, 156-174, 1995;
1990-1994
The Spectral Analysis of Frobenius-Perron Operators
, with J. Ding and T. Y. Li, J. Math.
Anal. Appl., V.184, pp285-301,1994;
Finite element methods for the time-dependent Ginzburg-Landau model of superconductivity
, Comp. Math. Appl.,
Vol.27, No 12, pp119-133, 1994;
Global
existence and uniqueness of solutions of the
time-dependent Ginzburg-Landau equations in superconductivity,
Applicable Anal., Vol 53, 1-2, pp1-17, 1994;
Spectral
Viscosity Approximations to Multidimensional Scalar Conservation Laws
, with G. Chen and E. Tadmor,
Mathematics
of Computation, Vol. 61, No. 204, pp 629-643, 1993;
Modeling and Analysis of a Periodic Ginzburg-Landau Model for Type-II Superconductors
, with M. Gunzburger and J. Peterson,
SIAM J. Applied Math., Vol.53, No.3, pp689-717, 1993;
Finite element approximation of a periodic Ginzburg-Landau model for type-II superconductors
, with
M. Gunzburger and J. Peterson,
Numer. Math., 64, No.1, pp85-114, 1993;
High order approximation of the Frobenius-Perron operator
, with J. Ding and T. Y. Li, Appl. Math.
Comp., Vol 53, pp151-171, 1993;
The inclined segmented cantilever with tip
load, with C. Wang, in Proceedings of the 2nd international conf. on
nonlinear mechanics, Beijing, Peking University Press, pp269-273, 1993;
A model for superconducting thin films having variable thickness
, with M. Gunzburger,
Physica. D,
Nonlinear phenomena, Vol. 69, pp215-231, 1993;
The
critical temperature and gap solution in the Bardeen-Cooper-Schrieffer theory of superconductivity
, with Y. Yang,
Lett. Math. Phys.,
29, pp133-150, 1993;
An Empirical Study of Scalable Domain Decomposition Methods for a 2-D Parabolic Equation Solver,
with C. Chiang, M. Mutka and R. Sass,
Proceedings of the Sixth SIAM Conference on Parallel Processing for
Scientific Computing (PPSC93), Norfolk, Virginia, USA, published by
SIAM, 687-690,
1993;
Analysis and Approximation of the Ginzburg-Landau Model of
Superconductivity, with M. Gunzburger and J. Peterson,
SIAM Review, Vol.34, No.1, pp 54-81, 1992;
Error estimates of the Markov finite approximation of the Frobenius-Perron operator
, with C. Chiu and T.Y. Li,
Nonlinear
Analysis, theory, methods & applications,
19, pp291-308, 1992;
Solving the Ginzburg-Landau equations by finite element methods
, with M. Gunzburger and J. Peterson,
Physical
Rev. B., 46, pp9027-9034, 1992;
On the Ginzburg-Landau equations for superconductivity,
with M. Gunzburger and J. Peterson, in
Partial Differential Equations,
(J. Wiener & J. Hale, ed.), Pitman Res. Notes in Math.,
273, pp 58-62, 1992;
Mathematical and computational studies of macroscopic
models of superconductivity, with M. Gunzburger and J. Peterson,
in Proceedings of the symposium on applied mathematics at the
Chinese Academy of Sciences, pp284-293, Beijing, China, 1992;
Analysis of a Ladyzhenskaya model of incompressible viscous
flow, with M. D. Gunzburger,
J. Math. Anal. & Appl.; 155,pp21-45, 1991;
A Finite Difference Domain Decomposition Algorithm for Numerical Solution of the Heat Equation
, with C. Dawson, & T. Dupont,
Mathematics of
Computation, V.57, No.195,
pp63-71, 1991;
Numerical Analysis of a Continuum Model of Phase Transition
,
with R. A. Nicolaides,
SIAM J. Numer. Anal.,
V.28, No.5, pp1310-1322, 1991;
A domain decomposition method for parabolic equations based on
finite elements, with C. Dawson, in
Fourth International
Symposium on Domain Decomposition
Methods for PDEs, edited by R. Glowinski et al,
pp255-263, SIAM,
Philadelphia, 1991;
Vorticity constraints in velocity-vorticity formulations of steady, viscous, incompressible flow, with M. Gunzburger and A.
Meir., in Numerical Methods in Laminar and Turbulent Flow, VII, Pineridge
Press, 774-781, Stanford, CA, 1991;
Finite-Element Approximations of a Ladyzhenskaya Model for Stationary Incompressible Viscous Flow, with M. D. Gunzburger,
SIAM J. Numer. Analysis, V.27, No.1, pp1-19, 1990;
1980s
A low dispersion, high accuracy finite element method for first order hyperbolic systems in several space variables, with M. Gunzburger
and W. Layton, Comp. & Math. Appl., V.15, No.6-8, pp447-457, 1988;
Finite element methods for a Ladyzhenskaya model of
incompressible viscous flow, with M. D. Gunzburger, in
Numerical Methods
in Laminar and Turbulent Flow,Vol 5, Pineridge Press, 161-169, 1987;
A non-standard finite element method of
higher accuracy for hyperbolic systems in several space variables, with M. Gunzburer and
W. Layton, in Advances
in Computer Methods for Partial Differential Equations VI IMACS, 92-97, 1987;
Calculation of a class of determinants, J.
of the Univ. of Sci. and Tech. of China, (in Chinese),
Vol.12, No.4, 1982;
Representative papers
Quantized vortices
Analysis and Approximation of the Ginzburg-Landau Model of Superconductivity,
SIAM Review,
34, 54-81, 1992 (citation in google scholars)
-
Computational simulation of type-II superconductivity including pinning phenomena,
Phy. Rev. B, 51, 16194-16203, 1995
- Discrete gauge
invariant approximations of the Ginzburg-Landau models,
Mathematics of Computation, 67, 965-986, 1998
- Dissipative
Flow and Vortex Shedding in the Painleve Boundary Layer of a Bose-Einstein Condensate,
Phys. Rev. Lett., 91, 090407, (2003)
-
Numerical approximations of the
Ginzburg-Landau Models for Superconductivity,
J. Mathematical Physics,
46, 095109(1-22), 2005
CVTs, Meshes and Geometry
-
Centroidal Voronoi
Tessellations: Applications and Algorithms,
SIAM Review, 41, 637-676, 1999
(citation in google scholars)
- Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations,
Int. J. Numer. Meth. in Eng., 56, 1355-1373, 2002
-
Probabilistic
methods for centroidal Voronoi tessellations and their parallel implementations,
Parallel Computing, 28, 1477-1500, 2002
Numerical PDE
-
A Finite Difference Domain Decomposition Algorithm for Numerical Solution of the Heat Equation,
Mathematics of Computation, 57, 63-71, 1991
- Optimization based
nonoverlapping domain decomposition algorithms and their convergence,
SIAM J Numer. Anal., 39, 1056-1077, 2001
-
Spectral
Implementation of An Adaptive Moving Mesh
Method for Phase-field Equations,
J. Computational Phys., 220, 498-510, 2006.
-
Finite Volume
Methods on Spheres
and Spherical Centroidal Voronoi Meshes,
SIAM
J. Numer. Anal., 43, 1673-1692, 2005.
-
On Mesh Geometry and Stiffness Matrix Conditioning
for General Finite Element Spaces,
SIAM J.
Numer. Analy., 47, 1421-1444, 2009
-
Shrinking dimer dynamics and its applications to
saddle point search,
SIAM J. Numer. Anal.
, 50, 1899-1921, 2012.
Nonlocal models
Numerical algebra
Complex fluids and materials
-
From micro to macro dynamics via a new closure approximation to the FENE model of polymeric fluids,
SIAM MMS,
3, 895-917, 2005
- A phase field approach in the numerical study of the elastic bending energy for vesicle membranes,
J. Comp. Phy.,
198, 450-468, 2004
-
Morphology of
critical nuclei in solid state phase transformations,
Physical Review Letters, 98, 265703, (2007)
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