(numerical/applied analysis, parallel/adaptive algorithms)
-Applications in physical/biological/materials sciences
(superfluids, complex fluids, biomembranes, phase transitions)
-Applications in information sciences
(data mining, model reduction, meshing, image analysis)
List of publications from Google Scholar
publisher sites by clicking on journal names, you may email me for
reprints if you don't have access)
(and to appear)
- Nonlocal diffusion and peridynamic models with Neumann type constraints and their numerical approximations, with Y. Tao and X. Tian, 2016.
- Trace theorems for some nonlocal energy spaces, with X. Tian, 2016.
- Multi-level Monte Carlo method for a stochastic optimal control problem, with Q. Sun and J. Ming, submitted, 2016.
- Finite range jump processes and volume-constrained diffusion problems, with M D'Elia, M Gunzburger, R Lehoucq, submitted, 2014.
- Modeling and segmentation of nuclei based on Morse-Smale complex, with F. Sun, K.-C. Cheng, submitted, 2013.
- On the consistency between nearest-neighbor peridynamic discretizations and discretized classical elasticity models, with M. Parks and P. Seleson, to appear in Comp. Meth. Applied Mech. and Eng., 2016.
- Analysis of a nonlocal-in-time parabolic equation, with J. Yang and Z. Zhou, to appear in Disc Cont Dyn Sys, 2016.
- A class of high order nonlocal operators, with X. Tian, to appear in Arch Rat. Mech. Anal., 2016.
- Asymptotically compatible schemes for the approximation of fractional Laplacian and related nonlocal diffusion problems on bounded domains, with X. Tian and M. Gunzburger, to appear in Advances in Computational Mathematics, 2016.
- Local limits of peridynamic models and asymptotically compatible discretizations, to appear in Handbook of Peridynamic Modeling, 2016.
- Nonlocal calculus of variations and well-posedness of peridynamics, to appear in Handbook of Peridynamic Modeling, 2016.
- 2015-present (please download directly from the publisher by clicking on journals, email me for reprints if you don't have access)
- Multiscale analysis of an abstract evolution equation with applications to nonlocal models for heterogeneous media, with R. Lipton and T. Mengesha, 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.
- 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 Lin's 80th birthday), 45, 939–952, 2015.
- 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. D'Elia, 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 diusion 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 don't 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. 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.
- 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, arxiv.org/abs/1209.1452, 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, ESIAM: 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 Variational 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, 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's 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, Contemp Math. 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
Analysis and Approximation of the Ginzburg-Landau Model of Superconductivity,
SIAM Review, 34, 54-81, 1992 (citation in google scholars)
Computational simulation of type-II superconductivity including pinning phenomena,
Phy. Rev. B, 51, 16194-16203, 1995
- Discrete gauge
invariant approximations of the Ginzburg-Landau models,
Mathematics of Computation, 67, 965-986, 1998
in a rotating Bose-Einstein condensate: Critical angular velocities and energy diagrams in the Thomas-Fermi regime,
Physical Review A, 64, 063603(1-11), 2001
Flow and Vortex Shedding in the Painleve Boundary Layer of a Bose-Einstein Condensate,
Phys. Rev. Lett., 91, 090407, 2003
Computing the ground state of the Bose-Einstein condensate
via normalized gradient flow,
SIAM J. Scientific Comp., 25, 1674-1697, 2004
approximations of the
Ginzburg-Landau Models for Superconductivity,
J. Mathematical Physics, 46, 095109(1-22), 2005
Tessellations: Applications and Algorithms,
SIAM Review, 41, 637-676, 1999 (citation in google scholars)
- Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations,
Int. J. Numer. Meth. in Eng., 56, 1355-1373, 2002
methods for centroidal Voronoi tessellations and their parallel implementations,
Parallel Computing, 28, 1477-1500, 2002
A Finite Difference Domain Decomposition Algorithm for Numerical Solution of the Heat Equation,
Mathematics of Computation, 57, 63-71, 1991
- Optimization based
nonoverlapping domain decomposition algorithms and their convergence,
SIAM J Numer. Anal., 39, 1056-1077, 2001
Implementation of An Adaptive Moving Mesh
Method for Phase-field Equations,
J. Computational Phys., 220, 498-510, 2006
Methods on Spheres
and Spherical Centroidal Voronoi Meshes,
SIAM J. Numer. Anal., 43, 1673-1692, 2005
On Mesh Geometry and Stiffness Matrix Conditioning
for General Finite Element Spaces,
SIAM J. Numer. Analy., 47, 1421-1444, 2009
- Linear finite element superconvergence on
Mathematics of Computation, 83, 2161-2185, 2014
Shrinking dimer dynamics and its applications to
saddle point search,
SIAM J. Numer. Anal. , 50, 1899-1921, 2012
critical nuclei in solid state phase transformations,
Physical Review Letters, 98, 265703, 2007
Analysis and approximation of nonlocal
diffusion problems with volume constraints,
SIAM Review, 54, 667-696, 2012
Asymptotically compatible schemes and applications to robust discretization of nonlocal models,
SIAM J. Numer. Anal., 52, 1641-1665, 2014
Mathematics of Computation, 66, 345-361, 1997
- A phase field approach in the numerical study of the elastic bending energy for vesicle membranes,
J. Comp. Phy., 198, 450-468, 2004
- Adhesion of Multi-component 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, 895-917, 2005
- Incorporating Diffuse Interface
Nuclei in Phase-field Simulations
Scripta Materialia, 63, 8-11, 2010
- Coarsening mechanism for systems governed by the
Cahn-Hilliard equation with degenerate diffusion
Multiscale Modeling and Simulation, 12, 1870–1889, 2014
- 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, 1-3, 2004