Research interests
Analysis/modeling/computation (Applied/numerical analysis, multiscale modeling, parallel/adaptive algorithms) Applications in physical/biological/materials sciences (superfluids, complex fluids, biomembranes, phase transitions) Applications in information and data sciences (machine learning, model reduction, meshing, image analysis) 
List of publications from Google Scholar
List of Publications  Browse in Chronological Order or
publisher sites by clicking on journal names, you may email me for
reprints if you do not have access)
 Book

Nonlocal modeling, analysis and computation, CBMSNSF Regional Conference Series in Applied Mathematics, Vol.94, SIAM, 2019.
TOC/FrontMatter  Future Research  BackMatter/References  ICM 2018 Lecture (Youtube) 
BookReview (SIAM)  BookReview (MAA)  BookReview (IMA)  BookReview (zbMATH)
 Latest
(and to appear)

GinzburgLandau
functionals in the largegraph limit, with E. Zhang, J. Scott and M. Porter, submitted, 2024.

An optimal control model for synchronous influencer manipulation associated with network spreading dynamics, with M. Ihrig,
submitted, 2024.

Asymptotically compatible schemes for nonlinear variational models via Gammaconvergence and applications to nonlocal problems, with J. Scott and X. Tian,
submitted, 2024.

Convergence analysis for a nonlocal gradient descent method via directional Gaussian smoothing, with H. Tran and G. Zhang, submitted, 2023.

Nonlocal boundaryvalue problems with local boundary conditions II, Green's identities and regularity of solutions, with J. Scott, SIAM J. Math. Anal., to appear, 2024.

Discontinuous Galerkin methods for a firstorder semilinear hyperbolic continuum model of a topological resonator dimer array, with H. Li, M. Weinstein, L. Zhang, J. Scientific Computing, to appear, 2024.

Gammaconvergence of nonlocal Dirichlet energies with penalty formulations of Dirichlet boundary data, with W. Gan and Z. Shi, SIAM J. Math. Anal., to appear, 2024.

Numerical analysis of a class of penalty discontinuous Galerkin methods for nonlocal diffusion problems, with L. Ju, J. Lu, and X. Tian, ESIAM Mathematical Modelling and Numerical Analysis, to appear, 2024.
 2020present (please download directly from the publisher by clicking on journals, email me for reprints if you do not have access)

OhtaKawasaki energy for amphiphiles: asymptotics and phasefield simulations, with J. Scott and Z. Xu, Nonlinear Analysis TMA, 250, 113665,
2025.

Computational and analytical studies of a new nonlocal phasefield crystal models in two dimensions, with K. Wang and J. Yang, Mathematical Models and Methods in Applied Sciences, 34, 2099–2139, 2024.

Nonlocal boundaryvalue problems with local boundary conditions I, function spaces and variational principles, with J. Scott, SIAM J. Math. Anal., 56, 41854222, 2024.

Asymptotic compatibility of a class of numerical schemes for a nonlocal traffic flow model, with
K. Huang, SIAM J. Numer. Anal., 62, 10671097, 2024.

Stretched nonnegative matrix factorization, with R. Gu, Y. Rakita, L. Lan, Z. Thatcher, G. Kamm, D. O'Nolan, B. Mcbride, A. Wustrow, J. Neilson, K. Chapman, S. Billinge, npj Computational Materials, 10, 193,
2024.
 Revealing Excited States of Rotational BoseEinstein Condensates, with J Yin, Z Huang, Y Cai, and L Zhang, The Innovation, 5, 100546, 2024.
 Minimizing optimal transport for functions with fixedsize nodal sets, with A. Sagiv, J. Nonlinear Science, 33, 95, 2023.

L^{p} compactness criteria with an application to variational convergence of some nonlocal energy functionals,
with T. Mengsha and X. Tian, Mathematics in Engineering, 5, 1–31, 2023.

Nonlocal diffusion models with consistent local and fractional limits, with X. Tian and Z. Zhou, Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models (The 50th John H. Barrett Memorial Lectures), The IMA Volumes in Mathematics and its Applications, Springer, V165, 175213. 2023.

Bifurcation and fission in the liquid drop model: a phasefield approach, with Z. Xu, J. of Math Phys, 64, 071508, 2023.

A Spacetime Nonlocal Traffic Flow Model: Relaxation Representation and Local Limit, with K. Huang, J. Scott and W. Shen, Disc. Cont. Dyn. Sys. B., 43, 34563484, 2023.
 Nonlocalintime dynamics and crossover of diffusive regimes, with Z. Zhou, Intern. Numer. Anal. and Modeling, 20, 353370, 2023.
 A fast twostage algorithm for nonnegative matrix factorization in smoothly varying data, with R. Gu and S. Billinge, Acta Crystallographica Section A., 79, 203216,
2023.

On some nonlocal models with radially symmetric interaction domains and the effect of domain truncation, with H. Xie and X. Yin, SIAM J. Numer. Anal., 60, 2046–2068, 2022.

Second order accurate Dirichlet boundary conditions for linear nonlocal diffusion problems, with H. Lee, Comm. Math. Sci,,
20, 1815–1837, 2022.

The discovery of dynamics via linear multistep methods and deep learning: error estimation,
with Y. Gu, H. Yang and C. Zhou,
SIAM J. Numer. Anal.,
60, 20142045,
2022.

A nonlocal Stokes
system with volume constraints, with Z. Shi, Numer Math. Theo. Meth. Appl.,
15, 903937, 2022.

A physicsinformed deep learning paradigm for traffic state estimation and fundamental diagram estimation, with R. Shi, Z. Mo, K. Huang, and X. Di, IEEE Trans. Intelligent Transportation Systems, 23, 1168811698, 2022.

Automated discovery of fundamental variables hidden in experimental data, with B. Chen, K. Huang, S. Raghupathi, I. Chandratreya and H. Lipson, Nature Computational Sci, 2, 433442, 2022. (CoverArticle)

Numerical simulation of singularity propagation modeled by linear convection equations with spatially heterogeneous nonlocal interactions, with X. Yu and Y. Xu, J. Scientific Comp., 92:59, 2022.

On the ternary OhtaKawasaki free energy and its one dimensional global minimizers, with Z. Xu, J. Nonlinear Sci.,
32:61,
2022.

Nonlocal trace spaces and extension results for nonlocal calculus, with X. Tian, C. Wright and Y. Yu, J. Functional Analysis,
282, 109453, 2022.

Robustness test of the spacegroupmining space group determination model for atomic pair distribution functions, with L. Lan, C. Liu, and S. Billinge, Acta Crystallographica Sec. A., 55 (3), S5,
2022.

The average distance problem with an Euler elastica penalization, with X. Lu and C. Wang, Interfaces and Free Boundaries, 24, 137–162, 2022.

Fractional Hardytype and trace theorems for nonlocal function spaces with heterogeneous localization, with T. Mengesha and X. Tian,
Analysis and Applications, 20, 579614, 2022.

Stability of a nonlocal traffic flow model for connected vehicles, with K. Huang, SIAM J. Appl. Math., 82, 221243, 2022.

The average distance problem with perimetertoarea penalization, with X. Lu and C. Wang, SIAM J. Math. Anal., 54, 31223138, 2022.

Asymptotically compatible approximations of linear nonlocal conservation laws with variable horizon, with X. Yu and Y. Xu,
Numer. Meth. Partial Differential Equations, 38, 19481966, 2021.

Censored
stable subordinators and fractional derivative,
with L. Toniazzi and Z. Xu, Fract. Calc. Appl. Anal, 24, 10351068, 2021.

Positive semidefinite penalty method for quadratically constrained quadratic programming, with R. Gu and Y.X. Yuan, IMA J. Numer. Anal., 41, 2488–2515, 2021.

Deep ReLU networks overcome the curse of dimensionality for bandlimited functions, with H Montanell and H Yang, J. Computational Mathematics, 39, 799–813, 2021.

Efficient variational phase field method for phase transitions in ferroelectric thin films, with R. Li and L. Zhang, SIAM J. Appl. Math., 80, 1590–1606, 2021.

Maximum bound principles for a class of semilinear parabolic equations and exponential time differencing schemes, with L. Ju, X. Li, Z. Qiao, SIAM Review, (Research Spotlight),
63, 317359, 2021.

Discovery of dynamics using linear multistep methods, with R. Keller, SIAM J. Numer. Anal, 59, 429455, 2021.

Dynamic Driving and routing game for autonomous vehicles on a network: a mean field game approach, with K. Huang, X. Chen, X. Di, Transportation Research Part C: Emerging Technologies, 128, 103189,
2021.

The graph limit of the minimizer of the OnsagerMachlup functional and its computation, with X. Li, T. Li and W. Ren, Science China Mathematics, 64, 239–280, 2021.

A modified limited memory steepest descent method
motivated by an inexact superlinear convergence rate analysis, with R. Gu, IMA Numer. Anal., 41, 247270, 2021.

Numerical discretization of variational phase field model for phase transitions in ferroelectric thin films, with R. Li and L. Zhang, Comm. Comp. Phys.,
29, 729746, 2021.

A noncooperative metamodeling game for automated thirdparty calibrating, validating and falsifying constitutive laws with parallelized adversarial attacks, with K. Wang and W. Sun, Comp. Meth. Appl. Mech. Eng., 373, 113514, 2021.

An energystable scheme for a 2D simple fluidparticle interaction problem, with X. Li, L. Luo, and X. Wang, J. Comp. Phy.,
424, 109850, 2021.

Timefractional AllenCahn equations: analysis and numerical
methods, with J. Yang and Z. Zhou, J. Sci. Comp.,
85 (2), 130, 2020.

A gametheoretic framework for autonomous vehicles velocity
control: bridging microscopic differential games and macroscopic mean field
games, wih K. Huang, X. Di, X. Chen, Disc. Cont. Dyn. Sys. B, 25, 48694903, 2020.

Mathematics of Smoothed Particle Hydrodynamics: a study
via nonlocal Stokes equations,
with X. Tian, Foundation of Computational
Mathematics, 20, 801826, 2020.

Numerical methods for nonlocal and fractional models,
with M. DElia, C. Glusa, M. Gunzburger, X. Tian and Z. Zhou,
Acta Numerica, 29, 1124, 2020.

Stochastic training of residual networks: a differential equation viewpoint (the English arxiv version), with Q. Sun and Y. Tao, Mathematica Numerica Sinica (published Chinese version),
42, 349369, 2020.

Multiscale modeling,
homogenization and nonlocal effects: mathematical and computational
issues,
with B. Engquist and X. Tian, Contemporary Mathematics, 754, 115140, 75 Years of Mathematics of Computation, AMS, 2020.

Asymptotically compatible schemes
for robust discretization of parametrized problems
with applications to nonlocal models, with X. Tian,
SIAM Review, (SIAM Review SIGEST Award), 62, 199227, 2020.
The description by the editors can be found here. 
Stability and error analysis for a secondorder fast approximation of the local and nonlocal diffusion equations on the real line,
with C. Zheng, X. Ma and J. Zhang, SIAM J. Numer. Anal., 58, 1893–1917, 2020.

Analysis of coarsegrained lattice models and connections to nonlocal interactions,
with X. Li and L. Yuan,
CSIAM Transaction
on Applied Mathematics, 1, 155185, 2020.

Stochastic representation of solution to nonlocalintime diffusion, with L. Toniazzi and Z. Zhou,
Stochastic Processes and their Applications, 130, 20582085, 2020.

Energy decaying phasefield model for
fluidparticle interaction in twophase flow, with X. Li and X. Wang,
SIAM J. Appl. Math, 80, 572–598, 2020.

Nonlocal gradient operators with a nonspherical interaction neighborhood and their applications, with H. Lee,
ESAIM:
Mathematical Modelling and Numerical Analysis,
54, 105128, 2020

A distributed optimal control problem with averaged stochastic gradient descent, with Q. Sun, Comm. in Comp. Phys,
27, 753774, 2020.

The phase field method for geometric moving interfaces and their numerical approximations,
with X. Feng, in Geometric Partial Differential Equations,
Handbook of Numerical Analysis, 21, 425508, 2020.

Scalable traffic stability analysis in mixedautonomy using continuum models, with K. Huang, X. Di, X. Chen, Transportation Research Part C: Emerging Technologies, 111, 616630, 2020.

A discontinuous Galerkin
method with penalty for onedimensional nonlocal diffusion problems, with L. Ju, J. Lu and X. Tian, Comm. Appl. Math. Comput.,
2, 3155, 2020.
 20152019
(please download directly from the publisher
by clicking on journals,
email me for reprints if
you do not have access)

Nonlocal models with heterogeneous localization and their application to seamless localnonlocal coupling, with Y. Tao and X. Tian,
Multiscale Modeling and Simulations, 17(3), 1052–1075, 2019.

Recent progress in mathematical and
computational aspects of peridynamics,
with M. DElia and M, Gunzburger, in
Handbook of Nonlocal Continuum Mechanics for Materials and
Structures, Chapeter 15, Springer,
2019.

New error bounds for deep ReLU networks using sparse grids, with H Montanell,
SIAM Journal on Mathematics of Data Science, 1, 7892, 2019.

Stabilizing traffic via autonomous vehicles: a continuum mean
field game approach, with K. Huang, X. Di, X. Chen,
IEEE 22nd Intelligent Transportation Systems Conference (ITSC), 32693274, 2019.

On uniform second order nonlocal relaxations to linear twopoint boundary value problems, with J. Zhang and C. Zheng, Comm. Math. Sci., 17, 17371755, 2019.

Algorithm for distance list extraction from pair distribution functions, with
R. Gu, S. Banerjee and S. Billinge,
Acta Crystallographica Sec. A., A75, 658–668,
2019.

A conforming DG method for linear nonlocal models with integrable kernels, with X. Yin, J. Scientific Computing, 80, 19131935, 2019.

A cooperative game for automated learning of elastoplasticity
knowledge graphs and models with AIguided experimentation, with
K. Wang and W.C. Sun, Computational Mechanics,
64, 467–499, 2019.

Maximum principle preserving exponential time differencing schemes for the nonlocal AllenCahn equations, with L. Ju, X. Li, Z. Qiao, SIAM J. Numer. Anal., 57, 875898, 2019.

Using a machine learning approach to determine the space group of a structure from the
atomic pair distribution function, with
C.H. Liu, Y. Tao, D. Hsu and S. Billinge, Acta Crystallographica Section A., 75,
633643, 2019.

Asymptotically compatible SPHlike particle discretizations of one dimensional linear advection models, with H. Lee, SIAM J. Numer. Anal., 57, 127–147, 2019.

Analysis of fully discrete approximations for dissipative systems and application to timedependent nonlocal diffusion problems, with L. Ju and J. Lu, J. Scientific Computing,
78, 1438–1466, 2019.

Heterogeneously localized nonlocal operators, boundary traces
and variational problems, with X. Tian, Proceedings of the Seventh International Congress of Chinese Mathematicians, I (ICCM 2016), (Vol. 43 of the ALM series), 217236,
2019.

A discontinuous Galerkin method for onedimensional
timedependent nonlocal diffusion problems, with L. Ju and
J. Lu, Mathematics of Computation, 88, 123147, 2019.

Asymptotically compatible discretization of multidimensional nonlocal diffusion models and approximation of nonlocal Greens
functions, with Y. Tao, X. Tian and J. Yang, IMA J. Numer. Anal., 39, 607–625, 2019.

Nonlocalintime dynamics
and crossover of diffusive regimes, with Z. Zhou, arxiv2003.03618, 2019.

An invitation to nonlocal modeling, analysis and computation, Proceedings of the International Congress of Mathematicians (ICM 2018), 3, 3523–3552, 2018.

Nonlocal neural networks, nonlocal diffusion and nonlocal modeling,
with Y. Tao, Q. Sun and W. Liu, Advances in Neural Information Processing Systems 31 (NIPS 2018), 494504,
2018

A new phasefield approach to variational implicit solvation of charged molecules with the Coulombfield approximation, with
Y. Zhao, Y. Ma, H. Sun and B. Li,
Comm. Math. Sci.,
16, 12031223, 2018.

Hierarchical attentionbased recurrent highway networks for time series prediction,
with Y. Tao, L. Ma, W. Zhang, J. Liu and W. Liu,
arxiv preprint, 2018.

A reinforced topicaware convolutional sequencetosequence
model for abstractive text summarization, with
L. Wang, J. Yao, Y. Tao, L. Zhong,
and W. Liu,
Proceedings of the 27th International Joint Conference on Artificial Intelligence (IJCAI18), Stockholm, Sweden, 44534460, 2018.

Datadriven compressive sensing and applications in
uncertainty quantification, with
H. Liang and Q. Sun, J. Comp. Phys,
374, 787802, 2018

A peridynamic model of fracture mechanics with
bondbreaking, with
Y. Tao and X. Tian, Journal of Elasticity, 132, 197–218,
2018.

Stability of nonlocal Dirichlet integrals and implications
for peridynamic correspondence material modeling,
with X. Tian, SIAM J. Applied Mathematics, 78, 15361552,
2018.

Asymptotically compatible schemes for stochastic
homogenization, with
Q. Sun and J. Ming, SIAM J. Numer. Anal., 56, 19421960, 2018.

A quasinonlocal coupling method for nonlocal and local diffusion models, with X. Li, J. Lu and
X. Tian, SIAM J. Numer. Anal., 56 (3), 13861404, 2018.

Numerical solution of a twodimensional nonlocal wave equation
on unbounded domains, with H. Han, C. Zheng and J. Zhang,
SIAM
J. Sci. Computing, 40 (3), A1430–A1445,
2018.

Visualizing ion diffusion in battery systems by fluorescence microscopy: a case study on the dissolution of LiMn_{2}O_{4}, with
Y. Qiao, Z. Zhou, Z. Chem, S. Du, Q. Cheng, H. Zhai, N. Fritz and
Y. Yang,
Nano Energy,
45, 6874, 2018.

Stabilized linear semiimplicit schemes for the nonlocal CahnHilliard equation and their analysis, with X. Li, L. Ju, Z. Qiao, J. Computational Physics,
363, 3954, 2018.

A spectral method for nonlocal diffusion operators on the sphere, with R. Slevinsky and H. M.
J. Comp. Phys., 372, 893911, 2018.

Nonlocal Wave Propagation in Unbounded
MultiScale Media, with J. Zhang and C. Zheng,
Comm.
Comp. Phys., 24, 10491072, 2018.

Uniform L^{p}bound of the AllenCahn equation and its
numerical discretization, with
J. Yang and W. Zhang, International J. Numerical Anal.
Modeling, 18, 213–227,
2018.

Trace theorems for some nonlocal energy spaces
with heterogeneous localization,
with X. Tian,
SIAM J.
Math. Anal., 49, 1621–1644, 2017.

Nonlocal conservation laws. I.
A new class of monotonicitypreserving models,
with Z. Huang
and P. LeFloch,
SIAM
J. Numer. Analysis,
55, 24652489,
2017.

Numerical solution of nonlocal diffusion equations on
the real line, with C. Zheng, J. Hu and J. Zhang,
SIAM J. Sci. Comp.,
39, A19511968, 2017.

Nonlocal convectiondiffusion problems on bounded domains and finiterange jump processes,
with M DElia, M Gunzburger, R Lehoucq,
Compu. Meth. in Appl. Math.,
17, 707722, 2017.

Asymptotically compatible schemes for spacetime nonlocal
diffusion
equations, with A. Chen, C. Li and Z. Zhou, Chaos,
Solitons and Fractals, 102, 361371,
2017.

Calculating corner singularities by boundary integral
equations, with H. Shi and Y. Lu,
J. Optical Soc. of America A, 34, 961966, 2017.

General neck condition for the limit shape of budding
vesicles, with P. Yang and Z. Tu,
Physical Review E, 95, 042403, 2017.

A conservative nonlocal convectiondiffusion model and
asymptotically compatible finite difference discretization,
with L. Ju and H. Tian,
Comp. Meth.
Appl. Mech. Eng., 320,4667, 2017.

Nonlocal diffusion and peridynamic models with Neumann type constraints and their numerical approximations,
with Y. Tao and X. Tian, Appl. Math. Comp., 305, 282298, 2017.

Analysis of a nonlocalintime parabolic equation,
with J. Yang and Z. Zhou,
Disc Cont Dyn Sys B,
22, 339368,
2017.

Numerical solution of a scalar onedimensional monotonicitypreserving nonlocal nonlinear conservation law, with Z. Huang,
J. Math. Res. Appl., 37, 118,
2017.

Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications, with J. Yang,
J. Computational Phys., 332, 118–134,
2017.

Artificial boundary conditions for nonlocal heat equations on unbounded
domain,
with J. Yang, W. Zhang and J. Zhang,
Comm.
Comp. Phys., 21, 1639, 2017.

Extremescale phase field simulations of coarsening dynamics on the
Sunway Taihulight supercomputer,
with J. Zhang, C. Zhou, Y. Wang, L. Ju, X. Chi, D. Xu, D. Chen, Y. Liu, Z. Liu,
Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, Article No.4,
ACM Gordon Bell Finalist, SC2016, Salt Lake City, IEEE Press, 2016.

Asymptotically compatible schemes for the approximation of fractional Laplacian and related nonlocal diffusion problems on bounded domains, with X. Tian and M. Gunzburger,
Advances in Computational Mathematics, 42, 13631380, 2016.

Local limits of peridynamic models
and asymptotically compatible discretizations,
Handbook of Peridynamic Modeling,
Chap 3, 6385, Chapman and Hall/CRC Press, 2016.

Nonlocal calculus of variations and wellposedness of peridynamics,
in Handbook of Peridynamic Modeling, Chap 4, 87107, Chapman and Hall/CRC Press, 2016.

A class of high order nonlocal operators, with X. Tian, Arch Rat. Mech. Anal., 222, 15211553,
2016.

On the consistency between nearestneighbor peridynamic discretizations and discretized classical elasticity models,
with M. Parks and P. Seleson,
Comp. Meth. Applied Mech. and Eng.,
311, 698–722,
2016.

Multiscale analysis of an abstract evolution equation with applications to nonlocal models for heterogeneous media,
with R. Lipton and T. Mengesha. The original publication is available at
ESAIM: Math Mod Numer Ana, 50, 14251455, 2016.

Robust a posteriori stre
ss analysis for approximations
of nonlocal models via nonlocal gradients,
with Y. Tao, X. Tian and J. Yang,
Comp.
Meth. Applied Mech. and Eng., 310, 605627, 2016.

Recent
Developments in Computational Modeling of Nucleation
in Phase Transformations,
with L. Zhang, W.Q. Ren and A. Samanta,
npj
Computational Materials, 2, 16003, 2016 (open access).

Asymptotic compatible Fourier spectral approximations of nonlocal
AllenCahn equations, with J. Yang,
SIAM J. Numerical Analysis,
54, 1899–1919, 2016.

Efficient and stable exponential time differencing RungeKutta
methods for phase field elastic bending energy models,
with X. Wang and L. Ju, J. Computational Phys., 316, 2138, 2016.

Generalized local and nonlocal master equations for some stochastic processes,
with Y. Zhao, J.K. Wang, and Y. Ma,
Comp. Math. Appl., 71, 2497–2512, 2016.

Characterization of function spaces of vector fields and an
application in nonlinear peridynamics,
with T. Mengesha,
Nonlinear Analysis A:
Theory, Methods and Applications, 140, 82111, 2016.

Computational studies of coarsening rates of the
CahnHilliard equation with phasedependent diffusion
mobility, with S. Dai,
J.
Comput. Phys.,
310, 85–108, 2016.

A multiscale implementation for the nonlocal peridynamics model
in one dimension,
with F. Xu, M. Gunzburger and J. Burkardt,
Multi Modeling Simu.,
14, 398429, 2016.

Optimizationbased
shrinking dimer method for
finding transition states, with L. Zhang and Z. Zheng,
SIAM J. Sci. Compu.,
38, A528–A544,
2016.

Weak solutions for the CahnHilliard equation with phasedependent diffusion mobility, with S. Dai,
Arch Rat. Mech. Anal., 219, 11611184, 2016.

On the variational limit of some nonlocal convex functionals
of vector fields, with T. Mengesha,
Nonlinearity,
28, 39994035, 2015.

Fast and accurate algorithms for simulating coarsening dynamics of CahnHilliard equations,
with L. Ju and J. Zhang,
Computational Materials Science,
108, 272282, 2015.

Optimization of subdivision invariant tetrahedra,
with D.J.T. Liu, Inter. J. Comp. Geo. Appl., 25, 3756, 2015.

From peridynamics to stochastic jump process：illustrations of nonlocal balancee laws and nonlocal calculus framework,
Scientia Sinica Mathematica (in Chinese, special issue for Prof.Qun Lins 80th birthday),
45, 939–952, 2015. (Inaugural excellent paper prize for paper in Chinese, 2017).

Multiscale Analysis of Linearized Peridynamics,
T. Mengesha,
Comm. Math. Sci., 13, 1193 – 1218, 2015.

Nonconforming
discontinuous Galerkin methods for nonlocal variational
problems, with X. Tian,
SIAM J. Numer. Analysis,
53, 762–781,
2015.

Fractional diffusion in bounded domains,
with O. Defterli, and M. DElia, M. Gunzburger, R. Lehoucq, and
M. Meerschaert,
Fractional Calculus
and Applied Analysis,
18, 342–360, 2015.

Nonlocal convectiondiffusion problems and finite element
approximations with H. Tian and L. Ju,
Comp. Meth.
Appl. Mech. Eng., 289, 60–78, 2015.

Fast explicit
integration factor methods for semilinear parabolic equations, with L. Ju, J. Zhang, L. Zhu,
J. Scientific Comp., 62, 431455, 2015.

Integral approximations
to classical diffusion and smoothed particle hydrodynamics,
with R. Lehoucq and A Tartakovsky,
Comp. Meth. Appl. Mech. Eng., 286, 216–229,
2015.
 20102014
(please download directly from the publisher
by clicking on journals,
email me for reprints if
you do not have access)

Coarsening mechanism for systems governed by the
CahnHilliard equation with degenerate diffusion
mobility, with S. Dai,
Multiscale Modeling and Simulation,
12, 1870–1889, 2014.

Robust discretization of nonlocal
models related to peridynamics,
with X. Tian, in
Meshfree Methods for Partial Differential Equations VII,
Lecture Notes in Computational
Science and Engineering, 100, 97113, 2014.

Asymptotically compatible schemes and applications to robust discretization of nonlocal models, with X. Tian, SIAM J. Numer. Anal., 52, 16411665,
2014.

Finding critical nuclei in phase transformations
by shrinking dimer dynamics and its variants, with L. Zhang
and J.Y. Zhang,
Comm. in Comp.
Phys, 16, 781798, 2014.

Linear finite element superconvergence on
simplicial meshes, with J. Chen and D. Wang,
Mathematics of Computation, 83, 21612185, 2014.

Asymptotically compatible schemes for peridynamics based on numerical quadratures, X. Tian, ASME 2014 International Mechanical Engineering
Congress and Exposition, Volume 1, paper no. IMECE201439620, pp. V001T01A058,
2014.

Error estimates for approximations of a gradient
dynamics for phase field elastic bending energy of
vesicle membrane deformation, with L. Zhu,
Math Meth Appl
Sci, 37, 913930,
2014.

Nonlocal constrained value problems for
a linear peridynamic Navier equation,
with T. Mengesha,
J. of
Elasticity, 116, 2751,
2014.

The bondbased peridynamic system with
Dirichlettype volume constraint,
with T. Mengesha, Proc. of Royal Soc. Edinburgh A
144, 161186,
2014.

On balanced moving mesh methods, with J. Remski and
J.Y. Zhang, J. Comp. Appl. Math.,
265, 255263, 2014,

Constraintfree Adaptive FEMs on quadrilateral
nonconforming meshes, with X. Zhao and Z. Shi,
J.
Scientific Computing, 59, 5379,
2014.

Nonlocal convectiondiffusion volumeconstrained problems and jump processes,
with Z. Huang and R. Lehoucq,
Disc. Cont. Dyn. Sys. B,
19, 373389, 2014.

Mesh dependent stability and condition number estimates for
finite element approximations of parabolic problems, with L. Zhu,
Mathematics of Computation, 83, 3764, 2014

Analysis and comparison of different approximations to nonlocal diffusion and linear peridynamic equations, with X. Tian,
SIAM J. Numer. Anal.,
51, 34583482, 2013. (SIAM Outstanding Paper Prize, 2016)

Abstract Principal Component Analysis,
with T. Li,
Sci. China Math, 56, 27832798, 2013.

Analysis of a scalar peridynamic model with a sign changing
kernel, with T. Mengesha, Disc. Cont. Dyn. Sys. B, 18, 14151437,
2013

A posteriori error analysis of finite element method for linear nonlocal diffusion and peridynamic models, with
L. Ju. L. Tian and K. Zhou,
Mathematics of Computation, 82, 18891922,
2013.

Retrieving topological information of implicitly
represented diffuse interfaces with adaptive finite
element discretization, with J. Zhang,
Comm. Comp.
Phys, 13, 12091226, 2013.

Analysis
of the volumeconstrained peridynamic
Navier equation of linear elasticity,
with M. Gunzburger, R. Lehoucq and K. Zhou,
Journal of Elasticity, 113, 193217, 2013.

A convergent adaptive finite element algorithm for nonlocal diffusion and peridynamic
models, with L. Tian and X. Zhao,
SIAM J. Numer. Anal.,
51, 12111234, 2013

A nonlocal vector calculus, nonlocal volumeconstrained problems, and nonlocal balance laws,
with M. Gunzburger, R. Lehoucq and K. Zhou,
Math. Mod. Meth. Appl. Sci., 23, 493540, 2013.

A varianceestimationbased stopping rule
for symbolic dynamic filtering,
with Y. Wen and A. Ray,
Signal, Image and Video Processing, 7, 189195, 2013.

Shrinking dimer dynamics and its applications to
saddle point search, with
J.Y. Zhang,
SIAM J. Numer. Anal.
, 50, 18991921,
2012.

Constrained shrinking dimer dynamics
saddle point search with constraints, with
J.Y. Zhang,
J. Computational Phys.,
231, 47454758, 2012.

Degenerate ground state and quantum tunneling in rotating condensates, with M. LeBerre and Y. Pomeau, arxiv.org/abs/1209.1452, 2012.

Evaluating microstructural parameters of threedimensional
grains generated by phasefield simulation or other voxelbased
techniques, with K. Chung, C. Krill and L.Q. Chen,
Modelling Simul. Mater. Sci. Eng, 20, 075009, 2012.

Robust Modeling of Constant Mean Curvature Surfaces,
P. Hao, Y.K. Choi, Y. Liu,
W. Hu, K. Polthier, C. Zhang, W. Wang,
ACM Trans. on Graphics, 31, No.4,
Article number 85,
SIGGRAPH12,
2012

Analysis and approximation of nonlocal diffusion problems with volume constraints, with M. Gunzburger,
R. Lehoucq and K. Zhou,
SIAM Review, 54, 667696, 2012.

Motion of interfaces governed by the CahnHilliard equation
with highly disparate diffusion mobility, with S. Dai,
SIAM J. Appl. Math,
72, 18181841, 2012.

Periodic Centroidal voronoi tessellations,
with J.Y. Zhang and M. Emelianenko,
Intern. J. Num. Anal. Modeling, 9, 950969,
2012.

A new approach for a nonlocal, nonlinear conservation law, with
R. Lehoucq, J. Kamm and M. Parks,
SIAM J. Appl. Math.,
72, 467487, 2012.

A hybrid implicitexplicit adaptive multirate numerical scheme for timedependent equations, with B. Chabaud,
J. Scientific Computing, 51, 135157,
2012.

Multiscale Modeling
and Analysis for Materials Simulation,
a book coedited with W. Bao, Lecture Notes Series 22, IMS, NUS,
World Scientific, 2011.
Available at
Amazon.

A Diffuse Interface Model of Multicomponent Vesicle Adhesion and Fusion, with Y. Zhao,
Physical Rev E, 84, 011903, 2011.

Mathematical analysis for the peridynamic nonlocal
continuum theory, with K. Zhou,
ESAIM: Math. Mod. Numer. Anal., 45, 217234, 2011.

MeshDependent Stability for
Finite Element Approximations of Parabolic Problems
with Mass Lumping, with L. Zhu,
J.
Comp. Appl. Math., 236, 801811,
2011.

Finite element approximation of the CahnHilliard equation on surfaces, with
L. Tian and L. Ju,
Comp. Meth. Appl. Mech. Engr, 200, 24582470, 2011.

Analysis of a stochastic implicit interface model for
an immersed elastic surface in a fluctuating fluid, with M. Li,
Archive Rational Mech. Anal., 199, 329352, 2011.

Convergent adaptive finite element method based on centroidal
Voronoi tessellations and superconvergence, with
Y. Huang, H. Qin and D. Wang,
Comm. Comp. Phys.
,
10, 339370, 2011.

Adaptive Finite Element Methods for Elliptic Equations over Hierarchical Tmeshes, with L. Tian and F. Chen,
J. Comp. Appl. Math., 236, 878891, 2011.

Asymptotic analysis of
a diffuse interface relaxation to a nonlocal optimal partition
problem, with J.Y. Zhang,
Disc. Cont. Dyn. Sys. A, 29, 14431461, 2011.

Phase field calculus, curvaturedependent energies, and vesicle membranes,
Philosophical Magazine, 91, 165181, 2011

On the stochastic immersed boundary
method with an implicit interface formulation,
M. Li, Disc. Cont. Dyn. Sys. B, 15, 373389, 2011

Mathematical and Numerical Analysis of Linear
Peridynamic Models with Nonlocal Boundary Conditions, with
K. Zhou,
SIAM J. Numer. Anal., 48, 17591780, 2010.

DiffuseInterface Approach to Predict Morphologies of Critical
Nucleus and Equilibrium Structure for Cubic to Tetragonal
Transformations, with L. Zhang and L.Q. Chen,
J. Computational Phys., 229, 65746584, 2010

Vortex solutions of the highkappa highfield
GinzburgLandau model with an applied current,
with J. Wei and C. Zhao,
SIAM J. Math. Anal.,
42, 23682401, 2010

Adhesion of Multicomponent Vesicle Membranes, with
Y. Zhao and S. Das,
Phys. Rev. E, 81, 041919, 2010.
(Selected for the May 1, 2010 issue of Virtual Journal of Biological Physics Research).

Simultaneous
prediction of morphologies of a critical nucleus and an equilibrium precipitate in solids,
with L. Zhang and L.Q. Chen,
Comm. Comp. Phys., 7, 674682, 2010.

Advances in studies and applications of
centroidal Voronoi tessellations,
with M. Gunzburger and L. Ju,
Numer.
Math. Theo. Meth. Appl., 3, 119142, special issue
on CVTs, 2010.

Application of Population Dynamics to Study Heterotypic Cell Aggregations in the Nearwall Region of a Shear Flow, with
Y. Ma, J. Wang, S. Liang and C. Dong,
Cellular
and Molecular Bioengineering, 3, 319, 2010.

Incorporating Diffuse Interface
Nuclei in Phasefield Simulations
,
with T. Heo, L. Zhang and L.Q. Chen,
Scripta
Materialia, 63, 811, 2010

On some Probability Density
Function based moment closure approximations of
micromacro models for viscoelastic polymeric fluids,
with H. Hyon and C. Liu,
J. of Computational
and Theoretical Nanoscience, 7, 756765, 2010

An efficient explicit/implicit domain decomposition
method for convectiondiffusion equations, with L. Zhu and G. Yuan,
Numerical Methods
for Partial Differential Equations,26, 852873,
2010

Coarsening kinetics with large diffusional mobility disparity
of two phases, with G. Sheng, T. Wang,
K.G. Wang, Z.K. Liu and L.Q. Chen,
Comm.
Comp. Phys., 8, 249264, 2010.
 20052009
(please download directly from the publisher sites,
if you are unable to connect, please email me for a copy)

Numerical approximations of a norm preserving
gradient flow and applications to an optimal partition problem,
with F.H. Lin, Nonlinearity,
22, 6783, 2009.

A constrained string method and its
numerical analysis,
with L. Zhang,
Comm. Math. Sci.
, 7, 10391051, 2009.

On Mesh Geometry and Stiffness Matrix Conditioning
for General Finite Element Spaces, with D. Wang and L. Zhu,
SIAM J.
Numer. Analy., 47, 14211444,
2009.

A Generalization of the Threedimensional
MacPhersonSrolovitz Formula, with T. Le,
Comm. Math. Sci.,
7, 511520, 2009.

A phase field model for vesiclesubstrate adhesion,
with J. Zhang and S. Das,
J. Computational Phys.
, 228, 78377849, 2009

An explicitimplicit predictorcorrector
domain decomposition method for time dependent
multidimensional convection diffusion equations,
with L. Zhu and G. Yuan,
Numerical
Mathematics: Theory, Methods and Applications, 2, 301325, 2009

Adaptive CVTbased reducedorder modeling of Burgers
equation, with G. Piao and H.C. Lee,
J. Korean SIAM, 13, 141159, 2009

Numerical studies of discrete approximations to the AllenCahn equation
in the sharp interface limit, with J. Zhang,
SIAM J. Sci. Comp.
,31, 30423063
2009

Energetic Variatioal Approaches to
Modeling Vesicle and Fluid Interactions, with C. Liu,
R. Ryham, X. Wang,
Physica
D, 238, 923930, 2009

Analysis of a mixed
finite volume discretization of
fourthorder equations on general surfaces,
with L. Ju and L. Tian,
IMA Numerical Analysis, 29, 376403,
2009.

A Fourier Spectral Moving
Mesh Method for the CahnHilliard Equation
with Elasticity,
with W. Feng, P. Yu, S. Hu, Z. Liu and L. Chen,
Comm.
in Computational Phys., 5, 582599, 2009

Analysis of
finite volume methods for elliptic
equations on general surfaces,
with L. Ju, J. Math. Anal. Appl., 352, no2, 645668, 2009

Modelling and Simulations of Multicomponent Lipid
Membranes and Open Membranes via Diffuse Interface Approaches,
with X. Wang,
J.
Mathematical Biology, 56, no3, 347371, 2008

Mathematical and numerical aspects of phasefield
approach to critical nuclei morphology in solids,
with L.Q. Chen and L. Zhang,
J. Scientific
Computing, 37, 89102, 2008
(special volume to
the 2007 John Barrett Memorial Lectures).

Applications of Moving Mesh Methods to
the Fourier Spectral Approximations of PhaseField Equations,
with P. Yu and L. Chen,
Recent Advances in Computational Sciences: Selected Papers from
the International Workshop on Computational Sciences and Its Education,
8099,
edited by Jorgensen et. al., World Scientific, 2008
(ISBN: 981270700X, the book cover features a
picture in our paper).

Adhesion of vesicles to curved substrates, with
S. Das, Phys.
Rev. E, 77, 011907(17), 2008

An enhanced macroscopic closure approximation to the micromacro
FENE models for polymeric materials,
with Y. Hyon and C. Liu,
SIAM
Multiscale Modelling and Simulation, 7, 9781002, 2008

DiffuseInterface Description of StrainDominated Morphology of Critical
Nuclei in Phase Transformations,
with L. Zhang and L.Q. Chen,
Acta
Materialia, 56, 35683576, 2008.

Cascadic multigrid algorithms for parabolic equations,
with P. Ming,
Science in China A, 51, 14151439, 2008

Adaptive Finite Element Method for a Phase Field Bending Elasticity Model
of Vesicle Membrane Deformations, with J. Zhang,
SIAM J. Sci. Comp.,
30, no3, 16341657, 2008

A Maximum Entropy Principle Based Closure Method for
MacroMicro Models of Polymeric Materials,
with Y. Hyon, C. Liu and J. Carrillo,
Kinetic and Related Models,
1, no2, 171184, 2008

Intelligent and Informative Scientific Computation,
Trends and Examples,
in Third International Congress of Chinese Mathematicians,
(2004 : Chinese University of Hong Kong),
KS Lau, ZP Xin and ST Yau editors,
Studies in
Advanced Mathematics, ISBN100821844164,
AMS/IP, Vol 42, 731748, 2008

Uniform Convergence of A Nonlinear Energybased Multilevel
Quantization Scheme, with M. Emelianenko, SIAM J. Numer. Anal., 46, no3, 14831502,
2008

Morphology of critical nuclei in solid state phase
transformations, with L. Zhang and L.Q. Chen,
Physical
Review Letters, 98, 265703, 2007

The dynamics and interaction of quantized vortices in GinzburgLandauSchroedinger equations,
with Y. Zhang and W. Bao,
SIAM J. Appl Math,
67, 17401775, 2007

Numerical simulation of vortex dynamics in
GinzburgLandauSchrodinger equation,
with W. Bao and Y. Zhang,
Euro. J. Appl. Math., 18, 607630, 2007

Analysis of a Phase Field NavierStokes
VesicleFluid Interaction Model, with M. Li and C. Liu,
Disc. Cont. Dyn. Sys. B, 8, No3,
539556,
2007

A Multilevel Energybased Quantization Scheme,
with M. Emelianenko,
Domain Decomposition Methods in Science and Engineering XVI,
Lecture Notes in Computational Science and Engineering, 55,
533541, SpringerVerlag, New York, 2007.

Diffuse Interface Energies Capturing the
Euler Number: Relaxation and Renomalization, with C. Liu,
R. Ryham, X. Wang,
Comm. Math. Sci,
5, 233242,
2007

Convergence
of numerical approximations to a phase field
bending elasticity model of membrane deformations, with X. Wang,
Inter. J. Numer. Anal and Modeling, 4, 441459, 2007

Quantized vortices in superfluids,
an mathematical and computational study,
a book chapter in
Dynamics in Models of Coarsening, Coagulation, Condensation and
Quantization,
Lecture Notes Series,
Institute for Mathematical Sciences of NUS,
Vol 9, ISBN 9789812708502,
World Scientific Press, Singapore 2007.

Dynamics of Rotating BoseEinstein Condensates and its Efficient and Accurate Numerical Computation,
with W. Bao and Y. Zhang,
SIAM J. Appl. Math., 66, 758786, 2006

Centroidal Voronoi Tessellation Algorithms for Image Compression, Segmentation, and Multichannel Restoration,
with M. Gunzburger, L. Ju and X. Wang,
J. of Mathematical Imaging and Vision, 24, 177194, 2006

Acceleration schemes for computing centroidal Voronoi tessellations,
with M. Emelianenko,
Numer Linear Algebra and Appl,
13, 173  192, 2006

A Variational Construction of
Anisotropic Mobility in PhaseField Simulation, with P. Yu,
Discrete and Continous Dynamic Systems B,
6, no2, 391406, 2006
 On GinzburgLandau Vortices of
Superconducting Thin Films,
with S. Ding,
Acta Mathematica Sinica, 22, 469476,
2006,

A new
algorithm for the automation of phase diagram calculation,
with M. Emelianenko and Z. Liu,
Computational
Materials Sciences, 35, 6174, 2006.
(ScienceDirect Top 25 hottest articles)

Simulating
the deformation of vesicle
membranes under elastic bending energy in three dimensions,
with C. Liu and X. Wang,
J.
Computational Phys., 212, no2, 757777, 2006.

Convergence of the Lloyd Algorithm
for Computing Centroidal Voronoi Tessellations, with M. Emeliaenko
and L. Ju,
SIAM J.
Numer. Anal., 44, 102119, 2006

Analysis of a Mixed
Finite Element Method for a Phase Field Bending Elasticity Model
of Vesicle Membrane Deformation,
with L. Zhu,
J. Computational Math., 24 (3), 265280, 2006.

Monte Carlo
simulation of heterotypic cell aggregation in nonlinear shear flow,
with J. Wang, M. Slattery, M. Hoskins, S. Liang and C. Dong,
Mathematical Biosciences and Engineering,
3, 683696, 2006

Spectral
Implementation of An Adaptive Moving Mesh
Method for Phasefield Equations,
with W. Feng, P. Yu, S. Hu, Z. Liu and L. Chen,
J. Computational Phys., 220, 498510, 2006.

Recent progress in robust and
quality Delaunay mesh generation,
with D. Wang,
J. Computational Applied Mathematics, 195, 823, 2006.
(was a top download after publication)

Mesh and Solver
Coadaptation in Finite Element Methods
for Anisotropic Problems, with Z. Huang and D. Wang,
Numerical Methods
for Partial Differential Equations,
21, 859874, 2005

Mesh Optimization Based on the Centroidal Voronoi
Tessellation, with D. Wang,
International Journal of Numerical Analysis and Modeling, 2, Supp,
100113, 2005

Finite Volume Methods on Spheres
and Spherical Centroidal Voronoi Meshes,
with L. Ju,
SIAM
J. Numer. Anal., 43, 16731692, 2005

An iterativeperturbation scheme
for treating inhomogeneous elasticity in phasefield models,
with Longqing Chen, S. Hu and P. Yu,
J. Computational Phys., 208, 3450, 2005

Modeling the spontaneous curvature effect
in static cell membrane deformations by a phase field formulation,
with C. Liu, R. Ryham and X. Wang,
Comm Pure Appl Anal, 4, 537548, 2005

A phase field formulation of the Willmore
problem,
with C. Liu, R. Ryham and X. Wang,
Nonlinearity, 18, 12491267, 2005.
 The optimal centroidal Voronoi tessellations and the Gersho conjecture in the threedimensional space,
with D. Wang,
Computers and Mathematics with
Applications, 49, 13551373, 2005.
(ScienceDirect Top 25 hottest articles)

Retrieving Topological Information
for Phase Field Models, with C. Liu and X. Wang,
SIAM
J. Appl. Math,
65, 19131932, 2005

FENE Dumbbell Model
and Its Several Linear and Nonlinear Closure Approximations, with
P. Yu and C. Liu,
SIAM
Multiscale Modelling and Simulations, 4, 709731, 2005

From Micro to Macro Dynamics Via
a New Closure Approximation to the FENE Model of Polymeric Fluids,
with C. Liu and P. Yu,
SIAM Multiscale Modeling
and Simulations, 3, 895917, 2005

A preliminary
investigation of the pseudospectral method numerical solution of the
Perkins instability equations in the homogeneous TEC case,
with Q. Zhou, J. Mathews and C. Miller,
Journal of Atmospheric and Terrestrial Physics,
67, 325335, 2005

Anisotropic Centroidal Voronoi
Tessellations and Their Applications, with D. Wang,
SIAM
J. Sci Comp., 26, 737761, 2005

Analysis and Applications of the
Exponential Time Differencing Schemes and Their Contour Integration Modifications, with W. Zhu,
BIT,
Numerical Mathematics, 45, no2, pp307328, 2005

Ideal Point
Distributions, Best Mode Selections and Optimal
Spatial Partitions via Centroidal Voronoi Tessellations,
with M. Emelianenko, Hyungchun Lee and Xiaoqiang Wang,
Proceeding of 2nd Inter Symposium on Voronoi Diagrams in
Sciences and Engineering, 325333,
Seoul, Korea, Oct, 2005

Optimizationbased methods for multidisciplinary simulation and optimization, with J. Lee and M. Gunzburger,
Journal of
Proceedings of the Korean SIAM,
177182, 2005

Numerical approximations of
the GinzburgLandau Models for Superconductivity,
Journal of
Mathematical Physics,
46, 095109(122), 2005
(an invited survey article)


20002004
(please download directly from the publisher sites,
if you are unable to connect, please email me to request a copy)

Tessellation and Clustering
by Mixture Models and Their Parallel Implementations,
with X. Wang,
Proceeding of the fourth SIAM international
conference on Data Mining, Lake Buena Vista, FL, 2004, SIAM, pp257268.

Boundary recovery
for three dimensional conforming Delaunay triangulation, with
D. Wang,
Comp. Meth.
Appl. Mech. Engr, 193, no2326, 25472563, 2004

Constrained boundary
recovery for three dimensional Delaunay triangulations,
with D. Wang, Int.
J.
Numer. Meth. Eng., 61, pp14711500,
2004
 A phase field approach in the numerical study of the elastic bending energy for vesicle membranes, with C. Liu and X. Wang,
J. Computational
Physics, 198, pp450468, 2004

Centroidal Voronoi tessellation based algorithms for vector fields visualization and segmentation, with X. Wang,
IEEE Proceedings of Visualization 2004 (VIS2004), IEEE,
pp4350, Austin, TX, 2004.

Semidiscrete Finite Element
Approximations of a Linear FluidStructure Interaction Problem,
with M. Gunzburger, L. Hou, and J. Lee,
SIAM J. Numer. Anal., 42, 129, 2004.
 Stability analysis
and applications of the exponential time differencing schemes, with
W. Zhu,
J. Computational Math., 22, pp200209, 2004.
 Computing
the Ground State Solution of BoseEinstein Condensates by a Normalized
Gradient Flow, with W. Bao,
SIAM J. Scientific Comp., 25,
16741697, 2004

Numerical
simulations of the quantized vortices on a thin superconducting hollow
sphere, with L. Ju,
J. Computational Phys., 201, 511530, 2004

Approximations of a GinzburgLandau model for superconducting hollow spheres based on spherical centroidal Voronoi tessellations, with L. Ju,
Mathematics of
Computation,
74, 12571280, 2004.

An integrated framework for
multiscale materials simulation and design, with
Z. Liu, L. Chen, P. Raghavan, J. Sofo,
S. Langer and C. Wolverton,
J. Computer Aided
Materials Design, 11, 183199, 2004
 Existence
of Weak Solutions to Some Vortex Density Models, with P. Zhang,
SIAM J. Math. Anal., 34, 12781298, 2003
 Voronoibased
finite volume methods, optimal Voronoi meshes, and PDEs on the
sphere,
with M. Gunzburger and L. Ju,
Comput. Meth. Appl. Mech. Engrg.
, 192, 39333957, 2003
 Reduced Order
Modeling of Complex Systems,
with J. Burkardt, M. Gunzburger & H.C. Lee,
in Proceeding
of the 20th Biennial Conference on Numerical Analysis,
Ed. by D F Griffiths & G A Watson, University of Dundee, June, 2003,
2938.

Diverse vortex dynamics in superfluids,
Current trends in scientific computing,
Contemporary Mathematics, 329, pp105117, AMS, 2003.
 Dissipative
flow and vortex shedding in the Painleve boundary layer of a Bose Einstein
condensate,
with A. Aftalion and Y.Pomeau,
Physical Review
Letters,91 (2003), 090407
 Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations, with D. Wang,
Int.
J. Numer. Meth. Eng., 56, No.9, 13551373,
2003
 Constrained
Centroidal Voronoi Tessellations for Surfaces,
with M. Gunzburger and L. Ju,
SIAM Journal on Scientific Computing,
24, No.5, pp14881506, 2003.
 Analysis of a fluid elastic structure interaction model
, with M. Gunzburger, S.Hou and J. Lee,
Dis. Cont. Dyn. Systems A., 9, 633650, 2003
 Convergence
Analysis of a Finite Volume Method for Maxwell's Equations in Nonhomogeneous Media,
with E. Chung and J. Zou,
SIAM J. Numer. Anal.,
41, 3763, 2003
 Grid generation and optimization based on centroidal Voronoi tessellations, with M. Gunzburger,
Appl. Math. Comp.,
133, No. 23, 591607, 2002
 Numerical
studies of MacQueen's kmeans algorithm for computing the centroidal voronoi tessellations, with T. Wong,
Comp. Math. Appl., 44, 511523, 2002.
 Limiting
Models for Josephson Junctions and Superconducting Weak Links,
with J.
Remski, J. Math Anal Appl, 266, pp357382, 2002
 Meshfree,
probabilistic determination of point sets and support regions for
meshless computing,
with M. Gunzburger and L., Ju, Computer
Methods in Applied Mechanics and Engineering, 191, 13491366, 2002
 Centroidal
Voronoi Tessellation Based Proper Orthogonal Decomposition Analysis,
with M. Gunzburger,
International series of Numerical Mathematics,
143, 137150,
Birkhauser, 2002

Probabilistic
methods for centroidal Voronoi tessellations and their parallel
implementations, with
M. Gunzburger, L. Ju, Parallel
Computing, 28, 14771500, 2002 (was a top download after publication)
 Numerical
Approximation of Some Linear Stochastic Partial Differential Equations
Driven by Special Additive Noises, with T. Zhang,
SIAM J.
Numer. Anal., 40, 14211445, 2002
 Model reduction by proper orthogonal decomposition coupled with centroidal Voronoi tessellation, with M. Gunzburger,
Proc. Fluids Engineering Division
Summer Meeting, FEDSM200231051, ASME, 2002
 Numerical computations of
quantized vortices in BoseEinstein condensate,
in Recent Progress in computational and applied PDEs,
Proceedings for the
international conference held in ZhangJiaJie, 2001, edited by T.Chan,
et. al., Kluwer Academic Publisher, 155168, 2002.
 The Global Minimizers and
vortex solutions to a GinzburgLandau model of superconducting films,
with S. Ding,
Comm on Pure and Applied Analysis, 1, No.3,
pp327340, 2002.
 Modeling
and Computation of Random Thermal Fluctuations and Material Defects in the GinzburgLandau Model for Superconductivity,
with J. Deang, M.Gunzburger,
J. Computational
Physics,
181, no.1, p.4567, 2002
 Critical
Magnetic Field and Asymptotic Behavior of Superconducting Thin Films,
with S. Ding,
SIAM Math.
Anal., 34, 239256, 2002
 Fourier
Spectral Approximation to a Dissipative System Modeling the Flow of Liquid Crystals, with B. Guo and J. Shen,
SIAM J. Num. Anal, 39, 735762, 2001
 Stochastic
dynamics of GinzburgLandau vortices in superconductors, with
J. Deang, M.Gunzburger,
Physical
Review B, 64, 5250652510, 2001
 Optimization
Based Nonoverlapping Domain Decomposition Algorithms and Their
Convergence,
SIAM J. Numer. Analysis,
39, pp10561077, 2001
 Vortices
in a rotating BoseEinstein condensate: Critical angular velocities and energy diagrams in the ThomasFermi regime,
with A. Aftalion,
Physical
Review A, 64, 063603(111), 2001
 Efficient
Parallel Algorithms for Parabolic Problems,
with M. Mu and Z. Wu,
SIAM J. Numer. Anal., 39,
14691487, 2001
 The bifurcation diagrams for the GinzburgLandau system of superconductivity,
with A. Aftalion, Physica D, 163, 94105, 2001
 An upwinding mixed finite element method for a mean field model of superconducting vortices,with Z. Chen, ESAIM: Mathematical Modelling and Numerical Analysis, 34, 687706, 2000.
 Optimizationbased methods for multidisciplinary simulation and
optimization, with M. Gunzburger and J. Lee, in
Proc. 8th Annual Conference of the CFD Society of Canada,
CERCA, Montreal, 689694, 2000.
 Convergence Analysis of a Numerical Method for a Mean Field Model of Superconducting Vortices,
SIAM J. Numer. Anal,
37, 911926,
2000;
 A Gradient Method Approach to OptimizationBased Multidisciplinary Simulations and Nonoverlapping Domain Decomposition Algorithms, with M. Gunzburger,
SIAM J. Numer. Anal , 37, 15131541, 2000.

Finite Element Methods with Matching and Nonmatching Meshes for Maxwell Equations with Discontinuous Coefficients,
with Z. Chen and J. Zou,
SIAM J. Numer. Anal, 37, 15421570, 2000.
 19951999

 Simplified models of the JosephsonJunctions and
its finite element approximations, with J. Remski,
E.
J. Applied. Math., 10, 125, 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, 6172,
1999;

Analysis and computation of a mean field model for superconductivity, with M. Gunzburger and H. Lee,
Numerische Mathematik, Vol 81, No.4, pp539560, 1999;
 Numerical
Algorithms of the LawrenceDoniach Model for Layered Superconductors and their Parallel Implementation,
with P. Gray,
SIAM J. Sci. Comp.,Vol 20, No4, p21222139, 1999;

Numerical Solution of the ThreeDimensional GinzburgLandau Models Using Artificial Boundary, with X. Wu,
SIAM J. Numer. Anal., 36, 14821506,
1999;
 Centroidal
Voronoi Tessellations: Applications and Algorithms,
with V. Faber and M. Gunzburger,
SIAM
Review, 41, p637676, 1999;
 Studies of a GinzburgLandau Model for dWave Superconductors,
SIAM J. Applied Math., 59, no.4,
p12251250,
1999;
 Discrete gauge invariant approximations of a time dependent GinzburgLandau model of superconductivity,
Math. Comp., 67, 965986, 1998;
 Analysis and Convergence of a Covolume Approximation of the GinzburgLandau Model of Superconductivity, with R. Nicolaides and
X. Wu,
SIAM J. Numer. Anal., 35, pp10491072, 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, pp153155, edited by CAST, Beijing, China Science and
Technology Press, 1998 (ISBN 7504625191).
 The QuasiLaguerre iteration, with M. Jin, TY Li and
Z. Zeng; Math. Comp., 66, pp345361, 1997;
 GinzburgLandau Vortices: Dynamics, Pinning, and Hysteresis,
with F.H. Lin,
SIAM J. Math. Anal., 28, pp12651293, 1997;
 Impulsive Stretching of a Surface in a Viscous Fluid,
with C. Y. Wang, M. Miklavcic & C. Chang,
SIAM J. Appl. Math., 57, 114, 1997;

Vortices in superconductors: modelling and computer simulations
,
with J. Deang, M. Gunzburger and J. Peterson,
Philos. Trans. Roy. Soc. London Ser. A, 355, 19571968, 1997;
 GinzburgLandau 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 GinzburgLandau models for
superconductivity, in World congress of nonlinear analysts 92,
(refereed), de Gruyter, Berlin, 37893801, 1996;

QuasiLaguerre Iteration in Solving Symmetric Tridiagonal Eigenvalue Problems
, with M. Jin, TY Li and Z. Zeng,
SIAM J. Sci. Comp., 17, pp13471368, 1996;

A
variable thickness thin film model for superconductivity,
with J. Chapman and M. Gunzburger,
Z. Angew Math Phys,
47, pp410431, 1996;

HighKappa Limits of the TimeDependent GinzburgLandau Model
, with P. Gray,
SIAM J. Appl. Math., 56, pp10601093, 1996;

Computational methods for the time dependent GinzburgLandau model for superconductivity
, in
Numerical
methods in applied sciences,
edited by W. Cai, et. al., Science Press, New York, 5165, 1996;
 Study of an inclined, segmented cantilever with tip
load, with C. Wang,
Quart. Applied Math.,
53, pp8193, 1995;
 Simplified
GinzburgLandau 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
193218, 1995;
 A
GinzburgLandau type model of superconducting/normal
junctions including Josephson Junctions, with J. Chapman & M. Gunzburger, Euro. J. Appl. Math., Vol.6, no. 2, pp97114,1995;

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 323343, 1995;

Computational simulation of typeII superconductivity including pinning phenomena
, with M. Gunzburger and J. Peterson,
Phy. Rev. B, 51, pp1619416203, 1995;

On the LawrenceDoniach and Anisotropic GinzburgLandau Models for Layered Superconductors
,with J. Chapman &
M. Gunzburger,
SIAM J. Applied Math., 55, 156174, 1995;
 19901994

The Spectral Analysis of FrobeniusPerron Operators
, with J. Ding and T. Y. Li, J. Math.
Anal. Appl., V.184, pp285301,1994;

Finite element methods for the timedependent GinzburgLandau model of superconductivity
, Comp. Math. Appl.,
Vol.27, No 12, pp119133, 1994;

Global
existence and uniqueness of solutions of the
timedependent GinzburgLandau equations in superconductivity,
Applicable Anal., Vol 53, 12, pp117, 1994;
 Spectral
Viscosity Approximations to Multidimensional Scalar Conservation Laws
, with G. Chen and E. Tadmor,
Mathematics
of Computation, Vol. 61, No. 204, pp 629643, 1993;

Modeling and Analysis of a Periodic GinzburgLandau Model for TypeII Superconductors
, with M. Gunzburger and J. Peterson,
SIAM J. Applied Math., Vol.53, No.3, pp689717, 1993;

Finite element approximation of a periodic GinzburgLandau model for typeII superconductors
, with
M. Gunzburger and J. Peterson,
Numer. Math., 64, No.1, pp85114, 1993;

High order approximation of the FrobeniusPerron operator
, with J. Ding and T. Y. Li, Appl. Math.
Comp., Vol 53, pp151171, 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, pp269273, 1993;

A model for superconducting thin films having variable thickness
, with M. Gunzburger,
Physica. D,
Nonlinear phenomena, Vol. 69, pp215231, 1993;

The
critical temperature and gap solution in the BardeenCooperSchrieffer theory of superconductivity
, with Y. Yang,
Lett. Math. Phys.,
29, pp133150, 1993;
 An Empirical Study of Scalable Domain Decomposition Methods for a 2D 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, 687690,
1993;
 Analysis and Approximation of the GinzburgLandau Model of
Superconductivity, with M. Gunzburger and J. Peterson,
SIAM Review, Vol.34, No.1, pp 5481, 1992;

Error estimates of the Markov finite approximation of the FrobeniusPerron operator
, with C. Chiu and T.Y. Li,
Nonlinear
Analysis, theory, methods & applications,
19, pp291308, 1992;

Solving the GinzburgLandau equations by finite element methods
, with M. Gunzburger and J. Peterson,
Physical
Rev. B., 46, pp90279034, 1992;

On the GinzburgLandau 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 5862, 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, pp284293, Beijing, China, 1992;
 Analysis of a Ladyzhenskaya model of incompressible viscous
flow, with M. D. Gunzburger,
J. Math. Anal. & Appl.; 155,pp2145, 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,
pp6371, 1991;
 Numerical Analysis of a Continuum Model of Phase Transition
,
with R. A. Nicolaides,
SIAM J. Numer. Anal.,
V.28, No.5, pp13101322, 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,
pp255263, SIAM,
Philadelphia, 1991;

Vorticity constraints in velocityvorticity formulations of steady, viscous, incompressible flow, with M. Gunzburger and A.
Meir., in Numerical Methods in Laminar and Turbulent Flow, VII, Pineridge
Press, 774781, Stanford, CA, 1991;

FiniteElement Approximations of a Ladyzhenskaya Model for Stationary Incompressible Viscous Flow, with M. D. Gunzburger,
SIAM J. Numer. Analysis, V.27, No.1, pp119, 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.68, pp447457, 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, 161169, 1987;
 A nonstandard 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, 9297, 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 GinzburgLandau Model of Superconductivity,
SIAM Review, 34, 5481, 1992 (citation in google scholars)

Computational simulation of typeII superconductivity including pinning phenomena,
Phy. Rev. B, 51, 1619416203, 1995
 Discrete gauge
invariant approximations of the GinzburgLandau models,
Mathematics of Computation, 67, 965986, 1998

Vortices
in a rotating BoseEinstein condensate: Critical angular velocities and energy diagrams in the ThomasFermi regime,
Physical Review A, 64, 063603(111), 2001
 Dissipative
Flow and Vortex Shedding in the Painleve Boundary Layer of a BoseEinstein Condensate,
Phys. Rev. Lett., 91, 090407, 2003

Computing the ground state of the BoseEinstein condensate
via normalized gradient flow,
SIAM J. Scientific Comp., 25, 16741697, 2004
 Numerical
approximations of the
GinzburgLandau Models for Superconductivity,
J. Mathematical Physics, 46, 095109(122), 2005
CVTs, Meshes and Geometry

Centroidal Voronoi
Tessellations: Applications and Algorithms,
SIAM Review, 41, 637676, 1999 (citation in google scholars)  Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations,
Int. J. Numer. Meth. in Eng., 56, 13551373, 2002
 Probabilistic
methods for centroidal Voronoi tessellations and their parallel implementations,
Parallel Computing, 28, 14771500, 2002
Numerical PDE

A Finite Difference Domain Decomposition Algorithm for Numerical Solution of the Heat Equation,
Mathematics of Computation, 57, 6371, 1991
 Optimization based
nonoverlapping domain decomposition algorithms and their convergence,
SIAM J Numer. Anal., 39, 10561077, 2001

Spectral
Implementation of An Adaptive Moving Mesh
Method for Phasefield Equations,
J. Computational Phys., 220, 498510, 2006

Finite Volume
Methods on Spheres
and Spherical Centroidal Voronoi Meshes,
SIAM J. Numer. Anal., 43, 16731692, 2005

On Mesh Geometry and Stiffness Matrix Conditioning
for General Finite Element Spaces,
SIAM J. Numer. Analy., 47, 14211444, 2009  Linear finite element superconvergence on
simplicial meshes,
Mathematics of Computation, 83, 21612185, 2014  Maximum bound principles for a class of semilinear parabolic equations and exponential time differencing schemes,
SIAM Review, (Research Spotlight), 63, 317359, 2021.
Rare events and transition states

Shrinking dimer dynamics and its applications to
saddle point search,
SIAM J. Numer. Anal. , 50, 18991921, 2012 
Morphology of
critical nuclei in solid state phase transformations,
Physical Review Letters, 98, 265703, 2007
 Recent
Developments in Computational Modeling of Nucleation
in Phase Transformations,
npj Computational Materials, 2, 16003, 2016
Diffuseinterface/Phasefield
 The phase field method for geometric moving interfaces and their numerical approximations,
Geometric Partial Differential Equations, Handbook of Numerical Analysis, 21, 425508, 2020.  Phase field calculus, curvaturedependent energies, and vesicle membranes,
Philosophical Magazine, 91, 165181, 2011. 1  DiffuseInterface Description of StrainDominated Morphology of Critical
Nuclei in Phase Transformations,
Acta Materialia, 56, 35683576, 2008. 
Numerical Analysis of a Continuum Model of Phase Transition
SIAM J. Numer. Anal., 28, 5, 13101322, 1991.
Nonlocal models
 Analysis and approximation of nonlocal
diffusion problems with volume constraints,
SIAM Review, 54, 667696, 2012. 
A nonlocal vector calculus, nonlocal volumeconstrained problems, and nonlocal balance laws,
Math. Mod. Meth. Appl. Sci., 23, 493540, 2013. 
Analysis and comparison of different approximations to nonlocal diffusion and linear peridynamic equations,
SIAM J. Numer. Anal., 51, 34583482, 2013. 
Asymptotically compatible schemes and applications to robust discretization of nonlocal models,
SIAM J. Numer. Anal., 52, 16411665, 2014.  An invitation to nonlocal modeling, analysis and computation,
Proceedings of the International Congress of Mathematicians (ICM 2018), 3, 3523–3552, 2018. 
Asymptotically compatible schemes for Robust Discretization of Parametrized Problems
with Applications to Nonlocal Models
SIAM Review, (SIAM Review SIGEST Award), 62, 199227, 2020.
The description by the editors can be found here

Nonlocal trace spaces and extension results for nonlocal calculus,
J. Functional Analysis, 282, 109453, 2022.

The
QuasiLaguerre iteration,
Mathematics of Computation, 66, 345361, 1997
 A phase field approach in the numerical study of the elastic bending energy for vesicle membranes,
J. Comp. Phy., 198, 450468, 2004
 Adhesion of Multicomponent Vesicle Membranes,
Phys. Rev. E, 81, 041919, 2010 (selected for Virtual Journal of Biological Physics Research)

From micro to macro dynamics via a new closure approximation to the FENE model of polymeric fluids,
SIAM MMS, 3, 895917, 2005
 Incorporating Diffuse Interface
Nuclei in Phasefield Simulations
,
Scripta Materialia, 63, 811, 2010
 Coarsening mechanism for systems governed by the
CahnHilliard equation with degenerate diffusion
mobility,
Multiscale Modeling and Simulation, 12, 1870–1889, 2014. 
Extremescale phase field simulations of coarsening dynamics on the Sunway Taihulight supercomputer,
Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis (SC2016), Article No.4, IEEE Press, 2016.

New error bounds for deep ReLU networks using sparse grids,
SIAM Journal on Mathematics of Data Science, 1, 7892, 2019. 
A physicsinformed deep learning paradigm for traffic state estimation and fundamental diagram estimation,
IEEE Trans. Intelligent Transportation Systems, 23, 1168811698, 2022. 
Automated discovery of fundamental variables hidden in experimental data,
Nature Computational Sci, 2, 433442, 2022. (CoverArticle)
 A new AMS journal launching in 2021, with R. Cohen, AMS News, 10/14/2021, Notices of the AMS, 68 (20), 18121813, 2021.
 Peridynamics, Fracture, and Nonlocal Continuum Models, with R. Lipton, SIAM News, 47, no.3, April 2014

Some perspective on the large scale scientific computation research,
Science in China A: Mathematics, 47, 13, 2004

Analysis and Approximation of the GinzburgLandau Model of Superconductivity,