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Qiang Du's Publications

Research interests
-Analysis/umerical methods/modeling/computation
 (numerical/applied analysis, 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
   (you are strongly encouraged to download papers directly from the
   publisher sites by clicking on journal names, you may email me for
   reprints if you do not have access)


Nonlocal modeling, analysis and computation,

CBMS-NSF Regional Conference Series in Applied Mathematics, Vol.94, SIAM, 2019.

TOC/Front-Matter | Future Research | Back-Matter/References | ICM 2018 Lecture (Youtube) |

Book-Review (SIAM) | Book-Review (MAA) | Book-Review (zbMATH)

Latest (and to appear)

On the ternary Ohta-Kawasaki free energy and its one dimensional global minimizers, with Z. Xu, 2021.

Minimizing optimal transport for functions with fixed-size nodal sets, with A. Sagiv, arxiv:2110.14837, 2021.

On some nonlocal models with radially symmetric interaction domains and the effect of domain truncation, with H. Xie and X. Yin, arxiv:2109.1248, 2021.

Second order accurate Dirichlet boundary conditions for linear nonlocal diffusion problems, with H. Lee, arxiv:2108.11817, submitted, 2021.

Nonlocal trace spaces and extension results for nonlocal calculus, with X. Tian, C. Wright and Y. Yu, arxiv:2107.00177, submitted, 2021.

The average distance problem with perimeter-to-area penalization, with X. Lu and C. Wang, submitted, 2021.

The discovery of dynamics via linear multistep methods and deep learning: error estimation, with Y. Gu, H. Yang and C. Zhou, arxiv:2103.11488, submitted, 2021.

Fractional Hardy-type and trace theorems for nonlocal function spaces with heterogeneous localization, with T. Mengesha and X. Tian, arxiv:2103.0938, submitted, 2021.

A fast two-stage algorithm for non-negative matrix factorization in streaming data, with R. Gu and S. Billinge, submitted, 2021.

Nonlocal Stokes equation with relaxation on the divergence free equation, with Z. Shi and Y. Zhang, submitted, 2020.

Nonlocal criteria for compactness in the space of Lp vector fields, with T. Mengsha and X. Tian, arxiv:1801.08000, submitted, 2018.

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

Stability of a nonlocal traffic flow model for connected vehicles, with K. Huang, SIAM J. Appl. Math., to appear, 2021.

The average distance problem with an Euler elastica penalization, with X. Lu and C. Wang, Interfaces and Free Boundaries, to appear, 2021.

A physics-informed 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, online, 2021.

2020-present (please download directly from the publisher by clicking on journals, email me for reprints if you do not have access)

Censored stable subordinators and fractional derivative, with L. Toniazzi and Z. Xu, Fract. Calc. Appl. Anal, 24, 1035-1068, 2021.

Positive semi-definite 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, 317-359, 2021.

Discovery of dynamics using linear multistep methods, with R. Keller, SIAM J. Numer. Anal, 59, 429-455, 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 Onsager-Machlup 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, 247-270, 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, 729-746, 2021.

A non-cooperative meta-modeling game for automated third-party 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 energy-stable scheme for a 2D simple fluid-particle interaction problem, with X. Li, L. Luo, and X. Wang, J. Comp. Phy., 424, 109850, 2021.

Time-fractional Allen-Cahn equations: analysis and numerical methods, with J. Yang and Z. Zhou, J. Sci. Comp., 85 (2), 1-30, 2020.

A game-theoretic 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, 4869-4903, 2020.

Mathematics of Smoothed Particle Hydrodynamics: a study via nonlocal Stokes equations, with X. Tian, Foundation of Computational Mathematics, 20, 801-826, 2020.

Numerical methods for nonlocal and fractional models, with M. DElia, C. Glusa, M. Gunzburger, X. Tian and Z. Zhou, Acta Numerica, 29, 1-124, 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, 349-369, 2020.

Multiscale modeling, homogenization and nonlocal effects: mathematical and computational issues, with B. Engquist and X. Tian, Contemporary Mathematics, 754, 115-140, 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, 199-227, 2020.
The description by the editors can be found here.

Stability and error analysis for a second-order 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 coarse-grained lattice models and connections to nonlocal interactions, with X. Li and L. Yuan, CSIAM Transaction on Applied Mathematics, 1, 155-185, 2020.

Stochastic representation of solution to nonlocal-in-time diffusion, with L. Toniazzi and Z. Zhou, Stochastic Processes and their Applications, 130, 2058-2085, 2020.

Energy decaying phase-field model for fluid-particle interaction in two-phase 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, 105-128, 2020

A distributed optimal control problem with averaged stochastic gradient descent, with Q. Sun, Comm. in Comp. Phys, 27, 753-774, 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, 425-508, 2020.

Scalable traffic stability analysis in mixed-autonomy using continuum models, with K. Huang, X. Di, X. Chen, Transportation Research Part C: Emerging Technologies, 111, 616-630, 2020.

A discontinuous Galerkin method with penalty for one-dimensional nonlocal diffusion problems, with L. Ju, J. Lu and X. Tian, Comm. Appl. Math. Comput., 2, 31-55, 2020.

2015-2019 (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 local-nonlocal coupling, with R. 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, 78-92, 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), 3269-3274, 2019.

On uniform second order nonlocal relaxations to linear two-point boundary value problems, with J. Zhang and C. Zheng, Comm. Math. Sci., 17, 1737-1755, 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, 1913-1935, 2019.

A cooperative game for automated learning of elasto-plasticity knowledge graphs and models with AI-guided experimentation, with K. Wang and W.C. Sun, Computational Mechanics, 64, 467–499, 2019.

Maximum principle preserving exponential time differencing schemes for the nonlocal Allen-Cahn equations, with L. Ju, X. Li, Z. Qiao, SIAM J. Numer. Anal., 57, 875-898, 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, 633-643, 2019.

Asymptotically compatible SPH-like 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 time-dependent 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), 217-236, 2019.

A discontinuous Galerkin method for one-dimensional time-dependent nonlocal diffusion problems, with L. Ju and J. Lu, Mathematics of Computation, 88, 123-147, 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.

Nonlocal-in-time 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), 494-504, 2018

A new phase-field approach to variational implicit solvation of charged molecules with the Coulomb-field approximation, with Y. Zhao, Y. Ma, H. Sun and B. Li, Comm. Math. Sci., 16, 1203-1223, 2018.

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

A reinforced topic-aware convolutional sequence-to-sequence 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 (IJCAI-18), Stockholm, Sweden, 4453-4460, 2018.

Data-driven compressive sensing and applications in uncertainty quantification, with H. Liang and Q. Sun, J. Comp. Phys, 374, 787-802, 2018

A peridynamic model of fracture mechanics with bond-breaking, 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, 1536-1552, 2018.

A spectral method for nonlocal diffusion operators on the sphere, with H Montanell, Journal of Computational Phys , 372, 893-911, 2018.

Asymptotically compatible schemes for stochastic homogenization, with Q. Sun and J. Ming, SIAM J. Numer. Anal., 56, 1942-1960, 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), 1386-1404, 2018.

Numerical solution of a two-dimensional 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 LiMn2O4, with Y. Qiao, Z. Zhou, Z. Chem, S. Du, Q. Cheng, H. Zhai, N. Fritz and Y. Yang, Nano Energy, 45, 68-74, 2018.

Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation and their analysis, with X. Li, L. Ju, Z. Qiao, J. Computational Physics, 363, 39-54, 2018.

A spectral method for nonlocal diffusion operators on the sphere, with R. Slevinsky and H. M. J. Comp. Phys., 372, 893-911, 2018.

Nonlocal Wave Propagation in Unbounded Multi-Scale Media, with J. Zhang and C. Zheng, Comm. Comp. Phys., 24, 1049-1072, 2018.

Uniform Lp-bound of the Allen--Cahn 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 monotonicity-preserving models, with Z. Huang and P. LeFloch, SIAM J. Numer. Analysis, 55, 2465-2489, 2017.

Numerical solution of nonlocal diffusion equations on the real line, with C. Zheng, J. Hu and J. Zhang, SIAM J. Sci. Comp., 39, A1951-1968, 2017.

Nonlocal convection-diffusion problems on bounded domains and finite-range jump processes, with M DElia, M Gunzburger, R Lehoucq, Compu. Meth. in Appl. Math., 17, 707-722, 2017.

Asymptotically compatible schemes for space-time nonlocal diffusion equations, with A. Chen, C. Li and Z. Zhou, Chaos, Solitons and Fractals, 102, 361-371, 2017.

Calculating corner singularities by boundary integral equations, with H. Shi and Y. Lu, J. Optical Soc. of America A, 34, 961-966, 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 convection-diffusion model and asymptotically compatible finite difference discretization, with L. Ju and H. Tian, Comp. Meth. Appl. Mech. Eng., 320,46-67, 2017.

Nonlocal diffusion and peridynamic models with Neumann type constraints and their numerical approximations, with Y. Tao and X. Tian, Appl. Math. Comp., 305, 282-298, 2017.

Analysis of a nonlocal-in-time parabolic equation, with J. Yang and Z. Zhou, Disc Cont Dyn Sys B, 22, 339-368, 2017.

Numerical solution of a scalar one-dimensional monotonicity-preserving nonlocal nonlinear conservation law, with Z. Huang, J. Math. Res. Appl., 37, 1-18, 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, 16-39, 2017.

Extreme-scale 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, 1363-1380, 2016.

Local limits of peridynamic models and asymptotically compatible discretizations, Handbook of Peridynamic Modeling, Chap 3, 63-85, Chapman and Hall/CRC Press, 2016.

Nonlocal calculus of variations and well-posedness of peridynamics, in Handbook of Peridynamic Modeling, Chap 4, 87-107, Chapman and Hall/CRC Press, 2016.

A class of high order nonlocal operators, with X. Tian, Arch Rat. Mech. Anal., 222, 1521-1553, 2016.

On the consistency between nearest-neighbor 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, 1425-1455, 2016.

Robust a posteriori stress analysis for approximations of nonlocal models via nonlocal gradients, with Y. Tao, X. Tian and J. Yang, Comp. Meth. Applied Mech. and Eng., 310, 605-627, 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 Allen-Cahn equations, with J. Yang, SIAM J. Numerical Analysis, 54, 1899–1919, 2016.

Efficient and stable exponential time differencing Runge-Kutta methods for phase field elastic bending energy models, with X. Wang and L. Ju, J. Computational Phys., 316, 21-38, 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, 82-111, 2016.

Computational studies of coarsening rates of the Cahn-Hilliard equation with phase-dependent 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, 398-429, 2016.

Optimization-based 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 Cahn-Hilliard equation with phase-dependent diffusion mobility, with S. Dai, Arch Rat. Mech. Anal., 219, 1161-1184, 2016.

On the variational limit of some nonlocal convex functionals of vector fields, with T. Mengesha, Nonlinearity, 28, 3999-4035, 2015.

Fast and accurate algorithms for simulating coarsening dynamics of Cahn-Hilliard equations, with L. Ju and J. Zhang, Computational Materials Science, 108, 272-282, 2015.

Optimization of subdivision invariant tetrahedra, with D.J.T. Liu, Inter. J. Comp. Geo. Appl., 25, 37-56, 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 convection-diffusion problems and finite element approximations with H. Tian and L. Ju, Comp. Meth. Appl. Mech. Eng., 289, 60–78, 2015.

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, 97-113, 2015.

Fast explicit integration factor methods for semilinear parabolic equations, with L. Ju, J. Zhang, L. Zhu, J. Scientific Comp., 62, 431-455, 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.

2010-2014 (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 Cahn-Hilliard equation with degenerate diffusion mobility, with S. Dai, Multiscale Modeling and Simulation, 12, 1870–1889, 2014.

Asymptotically compatible schemes and applications to robust discretization of nonlocal models, with X. Tian, SIAM J. Numer. Anal., 52, 1641-1665, 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, 781-798, 2014.

Linear finite element superconvergence on simplicial meshes, with J. Chen and D. Wang, Mathematics of Computation, 83, 2161-2185, 2014.

Asymptotically compatible schemes for peridynamics based on numerical quadratures, X. Tian, ASME 2014 International Mechanical Engineering Congress and Exposition, Volume 1, paper no. IMECE2014-39620, 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, 913-930, 2014.

Nonlocal constrained value problems for a linear peridynamic Navier equation, with T. Mengesha, J. of Elasticity, 116, 27-51, 2014.

The bond-based peridynamic system with Dirichlet-type volume constraint, with T. Mengesha, Proc. of Royal Soc. Edinburgh A 144, 161-186, 2014.

On balanced moving mesh methods, with J. Remski and J.Y. Zhang, J. Comp. Appl. Math., 265, 255-263, 2014,

Constraint-free Adaptive FEMs on quadrilateral nonconforming meshes, with X. Zhao and Z. Shi, J. Scientific Computing, 59, 53-79, 2014.

Nonlocal convection-diffusion volume-constrained problems and jump processes, with Z. Huang and R. Lehoucq, Disc. Cont. Dyn. Sys. B, 19, 373-389, 2014.

Mesh dependent stability and condition number estimates for finite element approximations of parabolic problems, with L. Zhu, Mathematics of Computation, 83, 37-64, 2014

Analysis and comparison of different approximations to nonlocal diffusion and linear peridynamic equations, with X. Tian, SIAM J. Numer. Anal., 51, 3458-3482, 2013. (SIAM Outstanding Paper Prize, 2016)

Abstract Principal Component Analysis, with T. Li, Sci. China Math, 56, 2783-2798, 2013.

Analysis of a scalar peridynamic model with a sign changing kernel, with T. Mengesha, Disc. Cont. Dyn. Sys. B, 18, 1415-1437, 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, 1889-1922, 2013.

Retrieving topological information of implicitly represented diffuse interfaces with adaptive finite element discretization, with J. Zhang, Comm. Comp. Phys, 13, 1209-1226, 2013.

Analysis of the volume-constrained peridynamic Navier equation of linear elasticity, with M. Gunzburger, R. Lehoucq and K. Zhou, Journal of Elasticity, 113, 193-217, 2013.

A convergent adaptive finite element algorithm for nonlocal diffusion and peridynamic models, with L. Tian and X. Zhao, SIAM J. Numer. Anal., 51, 1211-1234, 2013

A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws, with M. Gunzburger, R. Lehoucq and K. Zhou, Math. Mod. Meth. Appl. Sci., 23, 493-540, 2013.

A variance-estimation-based stopping rule for symbolic dynamic filtering, with Y. Wen and A. Ray, Signal, Image and Video Processing, 7, 189-195, 2013.

Shrinking dimer dynamics and its applications to saddle point search, with J.Y. Zhang, SIAM J. Numer. Anal. , 50, 1899-1921, 2012.

Constrained shrinking dimer dynamics saddle point search with constraints, with J.Y. Zhang, J. Computational Phys., 231, 4745-4758, 2012.

Degenerate ground state and quantum tunneling in rotating condensates, with M. LeBerre and Y. Pomeau,, 2012.

Evaluating microstructural parameters of three-dimensional grains generated by phase-field simulation or other voxel-based 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, 667-696, 2012.

Motion of interfaces governed by the Cahn-Hilliard equation with highly disparate diffusion mobility, with S. Dai, SIAM J. Appl. Math, 72, 1818-1841, 2012.

Periodic Centroidal voronoi tessellations, with J.Y. Zhang and M. Emelianenko, Intern. J. Num. Anal. Modeling, 9, 950-969, 2012.

A new approach for a nonlocal, nonlinear conservation law, with R. Lehoucq, J. Kamm and M. Parks, SIAM J. Appl. Math., 72, 467-487, 2012.

A hybrid implicit-explicit adaptive multirate numerical scheme for time-dependent equations, with B. Chabaud, J. Scientific Computing, 51, 135-157, 2012.

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

A Diffuse Interface Model of Multi-component 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, 217-234, 2011.

Mesh-Dependent Stability for Finite Element Approximations of Parabolic Problems with Mass Lumping, with L. Zhu, J. Comp. Appl. Math., 236, 801-811, 2011.

Finite element approximation of the Cahn-Hilliard equation on surfaces, with L. Tian and L. Ju, Comp. Meth. Appl. Mech. Engr, 200, 2458-2470, 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, 329-352, 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, 339-370, 2011.

Adaptive Finite Element Methods for Elliptic Equations over Hierarchical T-meshes, with L. Tian and F. Chen, J. Comp. Appl. Math., 236, 878-891, 2011.

Asymptotic analysis of a diffuse interface relaxation to a nonlocal optimal partition problem, with J.Y. Zhang, Disc. Cont. Dyn. Sys. A, 29, 1443-1461, 2011.

Phase field calculus, curvature-dependent energies, and vesicle membranes, Philosophical Magazine, 91, 165-181, 2011

On the stochastic immersed boundary method with an implicit interface formulation, M. Li, Disc. Cont. Dyn. Sys. B, 15, 373-389, 2011

Mathematical and Numerical Analysis of Linear Peridynamic Models with Nonlocal Boundary Conditions, with K. Zhou, SIAM J. Numer. Anal., 48, 1759-1780, 2010.

Diffuse-Interface 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, 6574-6584, 2010

Vortex solutions of the high-kappa high-field Ginzburg-Landau model with an applied current, with J. Wei and C. Zhao, SIAM J. Math. Anal., 42, 2368-2401, 2010

Adhesion of Multi-component 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, 674-682, 2010.

Advances in studies and applications of centroidal Voronoi tessellations, with M. Gunzburger and L. Ju, Numer. Math. Theo. Meth. Appl., 3, 119-142, special issue on CVTs, 2010.

Application of Population Dynamics to Study Heterotypic Cell Aggregations in the Near-wall Region of a Shear Flow, with Y. Ma, J. Wang, S. Liang and C. Dong, Cellular and Molecular Bioengineering, 3, 3-19, 2010.

Incorporating Diffuse Interface Nuclei in Phase-field Simulations , with T. Heo, L. Zhang and L.-Q. Chen, Scripta Materialia, 63, 8-11, 2010

On some Probability Density Function based moment closure approximations of micro-macro models for viscoelastic polymeric fluids, with H. Hyon and C. Liu, J. of Computational and Theoretical Nanoscience, 7, 756-765, 2010

An efficient explicit/implicit domain decomposition method for convection-diffusion equations, with L. Zhu and G. Yuan, Numerical Methods for Partial Differential Equations,26, 852-873, 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, 249-264, 2010

2005-2009 (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, 67-83, 2009.

A constrained string method and its numerical analysis, with L. Zhang, Comm. Math. Sci., 7, 1039-1051, 2009.

On Mesh Geometry and Stiffness Matrix Conditioning for General Finite Element Spaces, with D. Wang and L. Zhu, SIAM J. Numer. Analy., 47, 1421-1444, 2009

A Generalization of the Three-dimensional MacPherson-Srolovitz Formula, with T. Le, Comm. Math. Sci., 7, 511-520, 2009.

A phase field model for vesicle-substrate adhesion, with J. Zhang and S. Das, J. Computational Phys. , 228, 7837-7849, 2009

An explicit-implicit predictor-corrector domain decomposition method for time dependent multi-dimensional convection diffusion equations, with L. Zhu and G. Yuan, Numerical Mathematics: Theory, Methods and Applications, 2, 301-325, 2009

Adaptive CVT-based reduced-order modeling of Burgers equation, with G. Piao and H.-C. Lee, J. Korean SIAM, 13, 141-159, 2009

Numerical studies of discrete approximations to the Allen-Cahn equation in the sharp interface limit, with J. Zhang, SIAM J. Sci. Comp. ,31, 3042-3063 2009

Energetic Variatioal Approaches to Modeling Vesicle and Fluid Interactions, with C. Liu, R. Ryham, X. Wang, Physica D, 238, 923-930, 2009

Analysis of a mixed finite volume discretization of fourth-order equations on general surfaces, with L. Ju and L. Tian, IMA Numerical Analysis, 29, 376-403, 2009.

A Fourier Spectral Moving Mesh Method for the Cahn-Hilliard Equation with Elasticity, with W. Feng, P. Yu, S. Hu, Z. Liu and L. Chen, Comm. in Computational Phys., 5, 582-599, 2009

Analysis of finite volume methods for elliptic equations on general surfaces, with L. Ju, J. Math. Anal. Appl., 352, no2, 645-668, 2009

Modelling and Simulations of Multi-component Lipid Membranes and Open Membranes via Diffuse Interface Approaches, with X. Wang, J. Mathematical Biology, 56, no3, 347-371, 2008

Mathematical and numerical aspects of phase-field approach to critical nuclei morphology in solids, with L.Q. Chen and L. Zhang, J. Scientific Computing, 37, 89-102, 2008 (special volume to the 2007 John Barrett Memorial Lectures).

Applications of Moving Mesh Methods to the Fourier Spectral Approximations of Phase-Field Equations, with P. Yu and L. Chen, Recent Advances in Computational Sciences: Selected Papers from the International Workshop on Computational Sciences and Its Education, 80-99, 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(1-7), 2008

An enhanced macroscopic closure approximation to the micro-macro FENE models for polymeric materials, with Y. Hyon and C. Liu, SIAM Multiscale Modelling and Simulation, 7, 978-1002, 2008

Diffuse-Interface Description of Strain-Dominated Morphology of Critical Nuclei in Phase Transformations, with L. Zhang and L.Q. Chen, Acta Materialia, 56, 3568-3576, 2008.

Cascadic multigrid algorithms for parabolic equations, with P. Ming, Science in China A, 51, 1415-1439, 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, 1634-1657, 2008

A Maximum Entropy Principle Based Closure Method for Macro-Micro Models of Polymeric Materials, with Y. Hyon, C. Liu and J. Carrillo, Kinetic and Related Models, 1, no2, 171-184, 2008

Intelligent and Informative Scientific Computation, Trends and Examples, in Third International Congress of Chinese Mathematicians, (2004 : Chinese University of Hong Kong), K-S Lau, Z-P Xin and S-T Yau editors, Studies in Advanced Mathematics, ISBN-10-0-8218-4416-4, AMS/IP, Vol 42, 731-748, 2008

Uniform Convergence of A Nonlinear Energy-based Multilevel Quantization Scheme, with M. Emelianenko, SIAM J. Numer. Anal., 46, no3, 1483-1502, 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 Ginzburg-Landau-Schroedinger equations, with Y. Zhang and W. Bao, SIAM J. Appl Math, 67, 1740-1775, 2007

Numerical simulation of vortex dynamics in Ginzburg-Landau-Schrodinger equation, with W. Bao and Y. Zhang, Euro. J. Appl. Math., 18, 607-630, 2007

Analysis of a Phase Field Navier-Stokes Vesicle-Fluid Interaction Model, with M. Li and C. Liu, Disc. Cont. Dyn. Sys. B, 8, No3, 539-556, 2007

A Multilevel Energy-based Quantization Scheme, with M. Emelianenko, Domain Decomposition Methods in Science and Engineering XVI, Lecture Notes in Computational Science and Engineering, 55, 533-541, Springer-Verlag, New York, 2007.

Diffuse Interface Energies Capturing the Euler Number: Relaxation and Renomalization, with C. Liu, R. Ryham, X. Wang, Comm. Math. Sci, 5, 233-242, 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, 441-459, 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 978-981-270-850-2, World Scientific Press, Singapore 2007.

Dynamics of Rotating Bose--Einstein Condensates and its Efficient and Accurate Numerical Computation, with W. Bao and Y. Zhang, SIAM J. Appl. Math., 66, 758-786, 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, 177-194, 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 Phase-Field Simulation, with P. Yu, Discrete and Continous Dynamic Systems B, 6, no2, 391-406, 2006

On Ginzburg-Landau Vortices of Superconducting Thin Films, with S. Ding, Acta Mathematica Sinica, 22, 469-476, 2006,

A new algorithm for the automation of phase diagram calculation, with M. Emelianenko and Z. Liu, Computational Materials Sciences, 35, 61-74, 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, 757-777, 2006.

Convergence of the Lloyd Algorithm for Computing Centroidal Voronoi Tessellations, with M. Emeliaenko and L. Ju, SIAM J. Numer. Anal., 44, 102-119, 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), 265-280, 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, 683-696, 2006

Spectral Implementation of An Adaptive Moving Mesh Method for Phase-field Equations, with W. Feng, P. Yu, S. Hu, Z. Liu and L. Chen, J. Computational Phys., 220, 498-510, 2006.

Recent progress in robust and quality Delaunay mesh generation, with D. Wang, J. Computational Applied Mathematics, 195, 8-23, 2006. (was a top download after publication)

Mesh and Solver Co-adaptation in Finite Element Methods for Anisotropic Problems, with Z. Huang and D. Wang, Numerical Methods for Partial Differential Equations, 21, 859-874, 2005

Mesh Optimization Based on the Centroidal Voronoi Tessellation, with D. Wang, International Journal of Numerical Analysis and Modeling, 2, Supp, 100-113, 2005

Finite Volume Methods on Spheres and Spherical Centroidal Voronoi Meshes, with L. Ju, SIAM J. Numer. Anal., 43, 1673-1692, 2005

An iterative-perturbation scheme for treating inhomogeneous elasticity in phase-field models, with Longqing Chen, S. Hu and P. Yu, J. Computational Phys., 208, 34-50, 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, 537-548, 2005

A phase field formulation of the Willmore problem, with C. Liu, R. Ryham and X. Wang, Nonlinearity, 18, 1249-1267, 2005.

The optimal centroidal Voronoi tessellations and the Gersho conjecture in the three-dimensional space, with D. Wang, Computers and Mathematics with Applications, 49, 1355-1373, 2005. (ScienceDirect Top 25 hottest articles)

Retrieving Topological Information for Phase Field Models, with C. Liu and X. Wang, SIAM J. Appl. Math, 65, 1913-1932, 2005

FENE Dumbbell Model and Its Several Linear and Nonlinear Closure Approximations, with P. Yu and C. Liu, SIAM Multiscale Modelling and Simulations, 4, 709-731, 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, 895-917, 2005

A preliminary investigation of the pseudo-spectral 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, 325-335, 2005

Anisotropic Centroidal Voronoi Tessellations and Their Applications, with D. Wang, SIAM J. Sci Comp., 26, 737-761, 2005

Analysis and Applications of the Exponential Time Differencing Schemes and Their Contour Integration Modifications, with W. Zhu, BIT, Numerical Mathematics, 45, no2, pp307-328, 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, 325-333, Seoul, Korea, Oct, 2005

Optimization-based methods for multidisciplinary simulation and optimization, with J. Lee and M. Gunzburger, Journal of Proceedings of the Korean SIAM, 177-182, 2005

Numerical approximations of the Ginzburg-Landau Models for Superconductivity, Journal of Mathematical Physics, 46, 095109(1-22), 2005       (an invited survey article)

2000-2004 (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, pp257-268.

Boundary recovery for three dimensional conforming Delaunay triangulation, with D. Wang, Comp. Meth. Appl. Mech. Engr, 193, no23-26, 2547-2563, 2004

Constrained boundary recovery for three dimensional Delaunay triangulations, with D. Wang, Int. J. Numer. Meth. Eng., 61, pp1471-1500, 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, pp450-468, 2004

Centroidal Voronoi tessellation based algorithms for vector fields visualization and segmentation, with X. Wang, IEEE Proceedings of Visualization 2004 (VIS2004), IEEE, pp43-50, Austin, TX, 2004.

Semidiscrete Finite Element Approximations of a Linear Fluid-Structure Interaction Problem, with M. Gunzburger, L. Hou, and J. Lee, SIAM J. Numer. Anal., 42, 1-29, 2004.

Stability analysis and applications of the exponential time differencing schemes, with W. Zhu, J. Computational Math., 22, pp200-209, 2004.

Computing the Ground State Solution of Bose--Einstein Condensates by a Normalized Gradient Flow, with W. Bao, SIAM J. Scientific Comp., 25, 1674-1697, 2004

Numerical simulations of the quantized vortices on a thin superconducting hollow sphere, with L. Ju, J. Computational Phys., 201, 511-530, 2004

Approximations of a Ginzburg-Landau model for superconducting hollow spheres based on spherical centroidal Voronoi tessellations, with L. Ju, Mathematics of Computation, 74, 1257-1280, 2004.

An integrated framework for multi-scale materials simulation and design, with Z. Liu, L. Chen, P. Raghavan, J. Sofo, S. Langer and C. Wolverton, J. Computer Aided Materials Design, 11, 183-199, 2004

Existence of Weak Solutions to Some Vortex Density Models, with P. Zhang, SIAM J. Math. Anal., 34, 1278-1298, 2003

Voronoi-based finite volume methods, optimal Voronoi meshes, and PDEs on the sphere, with M. Gunzburger and L. Ju, Comput. Meth. Appl. Mech. Engrg. , 192, 3933-3957, 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, 29-38.

Diverse vortex dynamics in superfluids, Current trends in scientific computing, Contemporary Mathematics, 329, pp105-117, 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, 1355-1373, 2003

Constrained Centroidal Voronoi Tessellations for Surfaces, with M. Gunzburger and L. Ju, SIAM Journal on Scientific Computing, 24, No.5, pp1488-1506, 2003.

Analysis of a fluid elastic structure interaction model , with M. Gunzburger, S.Hou and J. Lee, Dis. Cont. Dyn. Systems A., 9, 633--650, 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, 37-63, 2003

Grid generation and optimization based on centroidal Voronoi tessellations, with M. Gunzburger, Appl. Math. Comp., 133, No. 2-3, 591-607, 2002

Numerical studies of MacQueen's k-means algorithm for computing the centroidal voronoi tessellations, with T. Wong, Comp. Math. Appl., 44, 511-523, 2002.

Limiting Models for Josephson Junctions and Superconducting Weak Links, with J. Remski, J. Math Anal Appl, 266, pp357-382, 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, 1349-1366, 2002

Centroidal Voronoi Tessellation Based Proper Orthogonal Decomposition Analysis, with M. Gunzburger, International series of Numerical Mathematics, 143, 137-150, Birkhauser, 2002

Probabilistic methods for centroidal Voronoi tessellations and their parallel implementations, with M. Gunzburger, L. Ju, Parallel Computing, 28, 1477-1500, 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, 1421-1445, 2002

Model reduction by proper orthogonal decomposition coupled with centroidal Voronoi tessellation, with M. Gunzburger, Proc. Fluids Engineering Division Summer Meeting, FEDSM2002-31051, ASME, 2002

Numerical computations of quantized vortices in Bose-Einstein 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, 155-168, 2002.

The Global Minimizers and vortex solutions to a Ginzburg-Landau model of superconducting films, with S.  Ding, Comm on Pure and Applied Analysis, 1, No.3, pp327-340, 2002.

Modeling and Computation of Random Thermal Fluctuations and Material Defects in the Ginzburg-Landau Model for Superconductivity, with J. Deang, M.Gunzburger, J. Computational Physics, 181, no.1, p.45-67, 2002

Critical Magnetic Field and Asymptotic Behavior of Superconducting Thin Films, with S. Ding, SIAM Math. Anal., 34, 239-256, 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, 735-762, 2001

Stochastic dynamics of Ginzburg-Landau vortices in superconductors, with J. Deang, M.Gunzburger, Physical Review B, 64, 52506-52510, 2001

Optimization Based Nonoverlapping Domain Decomposition Algorithms and Their Convergence, SIAM J. Numer. Analysis, 39, pp1056-1077, 2001

Vortices in a rotating Bose-Einstein condensate: Critical angular velocities and energy diagrams in the Thomas-Fermi regime, with A. Aftalion, Physical Review A, 64, 063603(1-11), 2001

Efficient Parallel Algorithms for Parabolic Problems, with M. Mu and Z. Wu, SIAM J. Numer. Anal., 39, 1469-1487, 2001

The bifurcation diagrams for the Ginzburg-Landau system of superconductivity, with A. Aftalion, Physica D, 163, 94-105, 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, 687-706, 2000.

Optimization-based 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, 689-694, 2000.

Convergence Analysis of a Numerical Method for a Mean Field Model of Superconducting Vortices, SIAM J. Numer. Anal, 37, 911-926, 2000;

A Gradient Method Approach to Optimization-Based Multidisciplinary Simulations and Nonoverlapping Domain Decomposition Algorithms, with M. Gunzburger, SIAM J. Numer. Anal , 37, 1513-1541, 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, 1542-1570, 2000.


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, 1-14, 1997;

Vortices in superconductors: modelling and computer simulations , with J. Deang, M. Gunzburger and J. Peterson, Philos. Trans. Roy. Soc. London Ser. A, 355, 1957-1968, 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;


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;


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
    CVTs, Meshes and Geometry
    Numerical PDE
    Rare events and transition states
    Nonlocal models
    Numerical algebra
    Biological membranes
    Complex fluids and materials
    Scientific but nontechnical publicaitons
    Presentations in other media

  Our Research Group

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