Analysis and Approximation of the Ginzburg-Landau Model of Superconductivity. - Qiang Du 001; Max D. Gunzburger; Janet S. Peterson (SIAM Rev., 1992)

Modeling and Analysis of a Periodic Ginzburg-Landau Model for Type-II Superconductors. - Qiang Du 001; Max D. Gunzburger; Janet S. Peterson (SIAM J. Appl. Math., 1993)

On the Lawrence-Doniach and Anisotropic Ginzburg-Landau Models for Layered Superconductors. - S. Jonathan Chapman; Qiang Du 001; Max D. Gunzburger (SIAM J. Appl. Math., 1995)

High-Kappa Limits of the Time-Dependent Ginzburg-Landau Model. - Qiang Du 001; Paul Gray (SIAM J. Appl. Math., 1996)

Quasi-Laguerre Iteration in Solving Symmetric Tridiagonal Eigenvalue Problems. - Qiang Du 001; Ming Jin; Tien-Yien Li; Zhonggang Zeng (SIAM J. Sci. Comput., 1996)

The quasi-Laguerre iteration. - Qiang Du 001; Ming Jin; Tien-Yien Li; Zhonggang Zeng (Math. Comput., 1997)

Impulsive Stretching of a Surface in a Viscous Fluid. - Chien-Cheng Chang; Chang-Yi Wang; Milan Miklavcic; Qiang Du 001 (SIAM J. Appl. Math., 1997)

Discrete gauge invariant approximations of a time dependent Ginzburg-Landau model of superconductivity. - Qiang Du 001 (Math. Comput., 1998)

Analysis and computation of a mean-field model for superconductivity. - Qiang Du 001; Max D. Gunzburger; Hyesuk K. Lee (Numerische Mathematik, 1999)

Studies of a Ginzburg-Landau Model for d-Wave Superconductors. - Qiang Du 001 (SIAM J. Appl. Math., 1999)

Centroidal Voronoi Tessellations: Applications and Algorithms. - Qiang Du 001; Vance Faber; Max D. Gunzburger (SIAM Rev., 1999)

Numerical Algorithms of the Lawrence-Doniach Model for Layered Superconductors and their Parallel Implementation. - Qiang Du 001; Paul Gray (SIAM J. Sci. Comput., 1999)

Finite Element Methods with Matching and Nonmatching Meshes for Maxwell Equations with Discontinuous Coefficients. - Zhiming Chen; Qiang Du 001; Jun Zou 003 (SIAM J. Numer. Anal., 2000)

Convergence Analysis of a Numerical Method for a Mean Field Model of Superconducting Vortices. - Qiang Du 001 (SIAM J. Numer. Anal., 2000)

A Gradient Method Approach to Optimization-Based Multidisciplinary Simulations and Nonoverlapping Domain Decomposition Algorithms. - Qiang Du 001; Max D. Gunzburger (SIAM J. Numer. Anal., 2000)

Optimization Based Nonoverlapping Domain Decomposition Algorithms and Their Convergence. - Qiang Du 001 (SIAM J. Numer. Anal., 2001)

Fourier Spectral Approximation to a Dissipative System Modeling the Flow of Liquid Crystals. - Qiang Du 001; Ben-yu Guo; Jie Shen 001 (SIAM J. Numer. Anal., 2001)

Grid generation and optimization based on centroidal Voronoi tessellations. - Qiang Du 001; Max D. Gunzburger (Appl. Math. Comput., 2002)

Probabilistic methods for centroidal Voronoi tessellations and their parallel implementations. - Lili Ju; Qiang Du 001; Max D. Gunzburger (Parallel Comput., 2002)

Critical Magnetic Field and Asymptotic Behavior of Superconducting Thin Films. - Shijin Ding; Qiang Du 001 (SIAM J. Math. Anal., 2002)

Efficient Parallel Algorithms for Parabolic Problems. - Qiang Du 001; Mo Mu; Zi-Niu Wu (SIAM J. Numer. Anal., 2002)

Numerical Approximation of Some Linear Stochastic Partial Differential Equations Driven by Special Additive Noises. - Qiang Du 001; Tianyu Zhang (SIAM J. Numer. Anal., 2002)

Existence of Weak Solutions to Some Vortex Density Models. - Qiang Du 001; Ping Zhang (SIAM J. Math. Anal., 2003)

Convergence Analysis of a Finite Volume Method for Maxwell's Equations in Nonhomogeneous Media. - Eric T. Chung 001; Qiang Du 001; Jun Zou 003 (SIAM J. Numer. Anal., 2003)

Corrigendum: Fourier Spectral Approximation to a Dissipative System Modeling the Flow of Liquid Crystals. - Qiang Du 001; Ben-yu Guo; Jie Shen 001 (SIAM J. Numer. Anal., 2003)

Constrained Centroidal Voronoi Tessellations for Surfaces. - Qiang Du 001; Max D. Gunzburger; Lili Ju (SIAM J. Sci. Comput., 2003)

Tesselation and Clustering by Mixture Models and Their Parallel Implementations. - Qiang Du 001; Xiaoqiang Wang 002 (SDM, 2004)

Centroidal Voronoi Tessellation Based Algorithms for Vector Fields Visualization and Segmentation. - Qiang Du 001; Xiaoqiang Wang 002 (IEEE Visualization, 2004)

Semidiscrete Finite Element Approximations of a Linear Fluid-Structure Interaction Problem. - Qiang Du 001; Max D. Gunzburger; L. Steven Hou; J. Lee (SIAM J. Numer. Anal., 2004)

Computing the Ground State Solution of Bose-Einstein Condensates by a Normalized Gradient Flow. - Weizhu Bao; Qiang Du 001 (SIAM J. Sci. Comput., 2004)

FENE Dumbbell Model and Its Several Linear and Nonlinear Closure Approximations. - Qiang Du 001; Chun Liu 009; Peng Yu (Multiscale Model. Simul., 2005)

From Micro to Macro Dynamics via a New Closure Approximation to the FENE Model of Polymeric Fluids. - Peng Yu; Qiang Du 001; Chun Liu 009 (Multiscale Model. Simul., 2005)

Approximations of a Ginzburg-Landau model for superconducting hollow spheres based on spherical centroidal Voronoi tessellations. - Qiang Du 001; Lili Ju (Math. Comput., 2005)

Retrieving Topological Information for Phase Field Models. - Qiang Du 001; Chun Liu 009; Xiaoqiang Wang 002 (SIAM J. Appl. Math., 2005)

Finite Volume Methods on Spheres and Spherical Centroidal Voronoi Meshes. - Qiang Du 001; Lili Ju (SIAM J. Numer. Anal., 2005)

Anisotropic Centroidal Voronoi Tessellations and Their Applications. - Qiang Du 001; Desheng Wang (SIAM J. Sci. Comput., 2005)

Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions. - Qiang Du 001; Chun Liu 009; Xiaoqiang Wang 002 (J. Comput. Phys., 2006)

Spectral implementation of an adaptive moving mesh method for phase-field equations. - Weiming Feng 002; Peng Yu; Shenyang Hu; Zi-Kui Liu; Qiang Du 001; Long-Qing Chen (J. Comput. Phys., 2006)

Centroidal Voronoi Tessellation Algorithms for Image Compression, Segmentation, and Multichannel Restoration. - Qiang Du 001; Max D. Gunzburger; Lili Ju; Xiaoqiang Wang 002 (J. Math. Imaging Vis., 2006)

Acceleration schemes for computing centroidal Voronoi tessellations. - Qiang Du 001; Maria Emelianenko (Numer. Linear Algebra Appl., 2006)

Dynamics of Rotating Bose-Einstein Condensates and its Efficient and Accurate Numerical Computation. - Weizhu Bao; Qiang Du 001; Yanzhi Zhang (SIAM J. Appl. Math., 2006)

Convergence of the Lloyd Algorithm for Computing Centroidal Voronoi Tessellations. - Qiang Du 001; Maria Emelianenko; Lili Ju (SIAM J. Numer. Anal., 2006)

The Dynamics and Interaction of Quantized Vortices in the Ginzburg-Landau-Schrödinger Equation. - Yanzhi Zhang; Weizhu Bao; Qiang Du 001 (SIAM J. Appl. Math., 2007)

Mathematical and Numerical Aspects of a Phase-field Approach to Critical Nuclei Morphology in Solids. - Lei Zhang 017; Long-Qing Chen; Qiang Du 001 (J. Sci. Comput., 2008)

An Enhanced Macroscopic Closure Approximation to the Micro-Macro FENE Model for Polymeric Materials. - YunKyong Hyon; Qiang Du 001; Chun Liu 009 (Multiscale Model. Simul., 2008)

Uniform Convergence of a Nonlinear Energy-Based Multilevel Quantization Scheme. - Qiang Du 001; Maria Emelianenko (SIAM J. Numer. Anal., 2008)

Adaptive Finite Element Method for a Phase Field Bending Elasticity Model of Vesicle Membrane Deformations. - Qiang Du 001; Jian Zhang 070 (SIAM J. Sci. Comput., 2008)

A phase field model for vesicle-substrate adhesion. - Jian Zhang 070; Sovan Das; Qiang Du 001 (J. Comput. Phys., 2009)

On Mesh Geometry and Stiffness Matrix Conditioning for General Finite Element Spaces. - Qiang Du 001; Desheng Wang; Liyong Zhu (SIAM J. Numer. Anal., 2009)

Numerical Studies of Discrete Approximations to the Allen–Cahn Equation in the Sharp Interface Limit. - Jian Zhang 070; Qiang Du 001 (SIAM J. Sci. Comput., 2009)

Diffuse-interface approach to predicting morphologies of critical nucleus and equilibrium structure for cubic to tetragonal transformations. - Lei Zhang 017; Long-Qing Chen; Qiang Du 001 (J. Comput. Phys., 2010)

Vortex Solutions of the High-κ High-Field Ginzburg-Landau Model with an Applied Current. - Qiang Du 001; Juncheng Wei; Chunyi Zhao (SIAM J. Math. Anal., 2010)

Mathematical and Numerical Analysis of Linear Peridynamic Models with Nonlocal Boundary Conditions. - Kun Zhou; Qiang Du 001 (SIAM J. Numer. Anal., 2010)

Adaptive finite element methods for elliptic equations over hierarchical T-meshes. - Li Tian; Falai Chen; Qiang Du 001 (J. Comput. Appl. Math., 2011)

Mesh-dependent stability for finite element approximations of parabolic equations with mass lumping. - Liyong Zhu; Qiang Du 001 (J. Comput. Appl. Math., 2011)

Constrained shrinking dimer dynamics for saddle point search with constraints. - Jingyan Zhang; Qiang Du 001 (J. Comput. Phys., 2012)

A Hybrid Implicit-Explicit Adaptive Multirate Numerical Scheme for Time-Dependent Equations. - Brandon Chabaud; Qiang Du 001 (J. Sci. Comput., 2012)

Motion of Interfaces Governed by the Cahn-Hilliard Equation with Highly Disparate Diffusion Mobility. - Shibin Dai; Qiang Du 001 (SIAM J. Appl. Math., 2012)

A New Approach for a Nonlocal, Nonlinear Conservation Law. - Qiang Du 001; James R. Kamm; Richard B. Lehoucq; Michael L. Parks (SIAM J. Appl. Math., 2012)

Shrinking Dimer Dynamics and Its Applications to Saddle Point Search. - Jingyan Zhang; Qiang Du 001 (SIAM J. Numer. Anal., 2012)

Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints. - Qiang Du 001; Max D. Gunzburger; Richard B. Lehoucq; Kun Zhou (SIAM Rev., 2012)

Robust modeling of constant mean curvature surfaces. - Hao Pan 001; Yi-King Choi; Yang Liu 014; Wenchao Hu; Qiang Du 001; Konrad Polthier; Caiming Zhang 001; Wenping Wang 001 (ACM Trans. Graph., 2012)

A posteriori error analysis of finite element method for linear nonlocal diffusion and peridynamic models. - Qiang Du 001; Lili Ju; Li Tian; Kun Zhou (Math. Comput., 2013)

A Convergent Adaptive Finite Element Algorithm for Nonlocal Diffusion and Peridynamic Models. - Qiang Du 001; Li Tian; Xuying Zhao (SIAM J. Numer. Anal., 2013)

Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations. - Xiaochuan Tian; Qiang Du 001 (SIAM J. Numer. Anal., 2013)

A variance-estimation-based stopping rule for symbolic dynamic filtering. - Yicheng Wen; Asok Ray; Qiang Du 001 (Signal Image Video Process., 2013)

On balanced moving mesh methods. - Joan Remski; Jingyan Zhang; Qiang Du 001 (J. Comput. Appl. Math., 2014)

Constraint-Free Adaptive FEMs on Quadrilateral Nonconforming Meshes. - Xuying Zhao; Zhong-Ci Shi; Qiang Du 001 (J. Sci. Comput., 2014)

Coarsening Mechanism for Systems Governed by the Cahn-Hilliard Equation with Degenerate Diffusion Mobility. - Shibin Dai; Qiang Du 001 (Multiscale Model. Simul., 2014)

Linear finite element superconvergence on simplicial meshes. - Jie Chen; Desheng Wang; Qiang Du 001 (Math. Comput., 2014)

Mesh dependent stability and condition number estimates for finite element approximations of parabolic problems. - Liyong Zhu; Qiang Du 001 (Math. Comput., 2014)

Asymptotically Compatible Schemes and Applications to Robust Discretization of Nonlocal Models. - Xiaochuan Tian; Qiang Du 001 (SIAM J. Numer. Anal., 2014)

Optimization of Subdivision Invariant Tetrahedra. - David J. T. Liu; Qiang Du 001 (Int. J. Comput. Geom. Appl., 2015)

Fast Explicit Integration Factor Methods for Semilinear Parabolic Equations. - Lili Ju; Jian Zhang 070; Liyong Zhu; Qiang Du 001 (J. Sci. Comput., 2015)

Nonconforming Discontinuous Galerkin Methods for Nonlocal Variational Problems. - Xiaochuan Tian; Qiang Du 001 (SIAM J. Numer. Anal., 2015)

Extreme-scale phase field simulations of coarsening dynamics on the sunway taihulight supercomputer. - Jian Zhang 070; Chunbao Zhou; Yangang Wang; Lili Ju; Qiang Du 001; Xuebin Chi; Dongsheng Xu; Dexun Chen; Yong Liu; Zhao Liu (SC, 2016)

Asymptotically compatible schemes for the approximation of fractional Laplacian and related nonlocal diffusion problems on bounded domains. - Xiaochuan Tian; Qiang Du 001; Max D. Gunzburger (Adv. Comput. Math., 2016)

Generalized local and nonlocal master equations for some stochastic processes. - Yanxiang Zhao; Jiakou Wang; Yanping Ma; Qiang Du 001 (Comput. Math. Appl., 2016)

Computational studies of coarsening rates for the Cahn-Hilliard equation with phase-dependent diffusion mobility. - Shibin Dai; Qiang Du 001 (J. Comput. Phys., 2016)

Efficient and stable exponential time differencing Runge-Kutta methods for phase field elastic bending energy models. - Xiaoqiang Wang 002; Lili Ju; Qiang Du 001 (J. Comput. Phys., 2016)

A Multiscale Implementation Based on Adaptive Mesh Refinement for the Nonlocal Peridynamics Model in One Dimension. - Feifei Xu; Max D. Gunzburger; John V. Burkardt; Qiang Du 001 (Multiscale Model. Simul., 2016)

Asymptotically Compatible Fourier Spectral Approximations of Nonlocal Allen-Cahn Equations. - Qiang Du 001; Jiang Yang (SIAM J. Numer. Anal., 2016)

Optimization-based Shrinking Dimer Method for Finding Transition States. - Lei Zhang 017; Qiang Du 001; Zhenzhen Zheng (SIAM J. Sci. Comput., 2016)

Nonlocal diffusion and peridynamic models with Neumann type constraints and their numerical approximations. - Yunzhe Tao; Xiaochuan Tian; Qiang Du 001 (Appl. Math. Comput., 2017)

Nonlocal Convection-Diffusion Problems on Bounded Domains and Finite-Range Jump Processes. - Marta D'Elia; Qiang Du 001; Max D. Gunzburger; Richard B. Lehoucq (Comput. Methods Appl. Math., 2017)

Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications. - Qiang Du 001; Jiang Yang (J. Comput. Phys., 2017)

Trace Theorems for some Nonlocal Function Spaces with Heterogeneous Localization. - Xiaochuan Tian; Qiang Du 001 (SIAM J. Math. Anal., 2017)

Nonlocal Conservation Laws. A New Class of Monotonicity-Preserving Models. - Qiang Du 001; Zhan Huang; Philippe G. LeFloch (SIAM J. Numer. Anal., 2017)

Numerical Solution of the Nonlocal Diffusion Equation on the Real Line. - Chunxiong Zheng; Jiashun Hu; Qiang Du 001; Jiwei Zhang 002 (SIAM J. Sci. Comput., 2017)

A Reinforced Topic-Aware Convolutional Sequence-to-Sequence Model for Abstractive Text Summarization. - Li Wang 092; Junlin Yao; Yunzhe Tao; Li Zhong; Wei Liu 005; Qiang Du 001 (IJCAI, 2018)

Nonlocal Neural Networks, Nonlocal Diffusion and Nonlocal Modeling. - Yunzhe Tao; Qi Sun; Qiang Du 001; Wei Liu 005 (NeurIPS, 2018)

Hierarchical Attention-Based Recurrent Highway Networks for Time Series Prediction. - Yunzhe Tao; Lin Ma 002; Weizhong Zhang; Jian Liu; Wei Liu 005; Qiang Du 001 (CoRR, 2018)

Stochastic Training of Residual Networks: a Differential Equation Viewpoint. - Qi Sun; Yunzhe Tao; Qiang Du 001 (CoRR, 2018)

Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation. - Qiang Du 001; Lili Ju; Xiao Li; Zhonghua Qiao (J. Comput. Phys., 2018)

Data-driven compressive sensing and applications in uncertainty quantification. - Hong Liang; Qi Sun; Qiang Du 001 (J. Comput. Phys., 2018)

A spectral method for nonlocal diffusion operators on the sphere. - Richard Mikaël Slevinsky; Hadrien Montanelli; Qiang Du 001 (J. Comput. Phys., 2018)

Stability of Nonlocal Dirichlet Integrals and Implications for Peridynamic Correspondence Material Modeling. - Qiang Du 001; Xiaochuan Tian (SIAM J. Appl. Math., 2018)

A Quasi-nonlocal Coupling Method for Nonlocal and Local Diffusion Models. - Qiang Du 001; Xingjie Helen Li 001; Jianfeng Lu 001; Xiaochuan Tian (SIAM J. Numer. Anal., 2018)

Asymptotically Compatible Schemes for Stochastic Homogenization. - Qi Sun; Qiang Du 001; Ju Ming (SIAM J. Numer. Anal., 2018)

Erratum: Asymptotically Compatible Schemes for Stochastic Homogenization. - Qi Sun; Qiang Du 001; Ju Ming (SIAM J. Numer. Anal., 2018)

Numerical Solution of a Two-Dimensional Nonlocal Wave Equation on Unbounded Domains. - Qiang Du 001; Houde Han; Jiwei Zhang 002; Chunxiong Zheng (SIAM J. Sci. Comput., 2018)

Stabilizing Traffic via Autonomous Vehicles: A Continuum Mean Field Game Approach. - Kuang Huang; Xuan Di; Qiang Du 001; Xi Chen (ITSC, 2019)

A Game-Theoretic Framework for Autonomous Vehicles Velocity Control: Bridging Microscopic Differential Games and Macroscopic Mean Field Games. - Kuang Huang; Xuan Di; Qiang Du 001; Xi Chen (CoRR, 2019)

Multiscale Modeling, Homogenization and Nonlocal Effects: Mathematical and Computational Issues. - Qiang Du 001; Björn Engquist; Xiaochuan Tian (CoRR, 2019)

Analysis of Fully Discrete Approximations for Dissipative Systems and Application to Time-Dependent Nonlocal Diffusion Problems. - Qiang Du 001; Lili Ju; Jianfang Lu (J. Sci. Comput., 2019)

A Conforming DG Method for Linear Nonlocal Models with Integrable Kernels. - Qiang Du 001; Xiaobo Yin (J. Sci. Comput., 2019)

Nonlocal Models with Heterogeneous Localization and Their Application to Seamless Local-Nonlocal Coupling. - Yunzhe Tao; Xiaochuan Tian; Qiang Du 001 (Multiscale Model. Simul., 2019)

A discontinuous Galerkin method for one-dimensional time-dependent nonlocal diffusion problems. - Qiang Du 001; Lili Ju; Jianfang Lu (Math. Comput., 2019)

Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen-Cahn Equation. - Qiang Du 001; Lili Ju; Xiao Li; Zhonghua Qiao (SIAM J. Numer. Anal., 2019)

Asymptotically Compatible SPH-Like Particle Discretizations of One Dimensional Linear Advection Models. - Hwi Lee; Qiang Du 001 (SIAM J. Numer. Anal., 2019)

New Error Bounds for Deep ReLU Networks Using Sparse Grids. - Hadrien Montanelli; Qiang Du 001 (SIAM J. Math. Data Sci., 2019)

Multiscale modeling, homogenization and nonlocal effects: Mathematical and computational issues. - Qiang Du 001; Björn Engquist; Xiaochuan Tian (75 Years of Mathematics of Computation, 2020)

Numerical methods for nonlocal and fractional models. - Marta D'Elia; Qiang Du 001; Christian Glusa; Max D. Gunzburger; Xiaochuan Tian; Zhi Zhou 002 (Acta Numer., 2020)

Nonlocal-in-time dynamics and crossover of diffusive regimes. - Qiang Du 001; Zhi Zhou 002 (CoRR, 2020)

Driving and Routing Game for Autonomous Vehicles on a Network. - Kuang Huang; Xu Chen; Xuan Di; Qiang Du 001 (CoRR, 2020)

Mathematics of Smoothed Particle Hydrodynamics: A Study via Nonlocal Stokes Equations. - Qiang Du 001; Xiaochuan Tian (Found. Comput. Math., 2020)

Time-Fractional Allen-Cahn Equations: Analysis and Numerical Methods. - Qiang Du 001; Jiang Yang; Zhi Zhou 002 (J. Sci. Comput., 2020)

Variational Phase Field Formulations of Polarization and Phase Transition in Ferroelectric Thin Films. - Qiang Du 001; Ruotai Li; Lei Zhang 061 (SIAM J. Appl. Math., 2020)

Energy Decaying Phase-Field Model for Fluid-Particle Interaction in Two-Phase Flow. - Xiang Li; Qiang Du 001; Xiao-Ping Wang 002 (SIAM J. Appl. Math., 2020)

Stability and Error Analysis for a Second-Order Fast Approximation of the Local and Nonlocal Diffusion Equations on the Real Line. - Chunxiong Zheng; Qiang Du 001; Xiang Ma; Jiwei Zhang 002 (SIAM J. Numer. Anal., 2020)

Asymptotically Compatible Schemes for Robust Discretization of Parametrized Problems with Applications to Nonlocal Models. - Xiaochuan Tian; Qiang Du 001 (SIAM Rev., 2020)

Physics-Informed Deep Learning for Traffic State Estimation. - Rongye Shi; Zhaobin Mo; Kuang Huang; Xuan Di; Qiang Du 001 (CoRR, 2021)

A Physics-Informed Deep Learning Paradigm for Traffic State Estimation and Fundamental Diagram Discovery. - Rongye Shi; Zhaobin Mo; Kuang Huang; Xuan Di; Qiang Du 001 (CoRR, 2021)

On some nonlocal models with radially symmetric interaction domains and the effect of domain truncation. - Qiang Du 001; Hehu Xie; Xiaobo Yin (CoRR, 2021)

Discovering State Variables Hidden in Experimental Data. - Boyuan Chen 001; Kuang Huang; Sunand Raghupathi; Ishaan Chandratreya; Qiang Du 001; Hod Lipson (CoRR, 2021)

An energy-stable scheme for a 2D simple fluid-particle interaction problem. - Xiang Li; Qiang Du 001; Li Luo 003; Xiao-Ping Wang 002 (J. Comput. Phys., 2021)

Discovery of Dynamics Using Linear Multistep Methods. - Rachael T. Keller; Qiang Du 001 (SIAM J. Numer. Anal., 2021)

Maximum Bound Principles for a Class of Semilinear Parabolic Equations and Exponential Time-Differencing Schemes. - Qiang Du 001; Lili Ju; Xiao Li; Zhonghua Qiao (SIAM Rev., 2021)

Nonlocal diffusion models with consistent local and fractional limits. - Qiang Du 001; Xiaochuan Tian; Zhi Zhou 002 (CoRR, 2022)

On the Ternary Ohta-Kawasaki Free Energy and Its One-dimensional Global Minimizers. - Zirui Xu; Qiang Du 001 (J. Nonlinear Sci., 2022)

Numerical Simulation of Singularity Propagation Modeled by Linear Convection Equations with Spatially Heterogeneous Nonlocal Interactions. - Xiaoxuan Yu; Yan Xu 008; Qiang Du 001 (J. Sci. Comput., 2022)

Automated discovery of fundamental variables hidden in experimental data. - Boyuan Chen 001; Kuang Huang; Sunand Raghupathi; Ishaan Chandratreya; Qiang Du 001; Hod Lipson (Nat. Comput. Sci., 2022)

Stability of a Nonlocal Traffic Flow Model for Connected Vehicles. - Kuang Huang; Qiang Du 001 (SIAM J. Appl. Math., 2022)

The Average Distance Problem with Perimeter-to-Area Ratio Penalization. - Qiang Du 001; Xin Yang Lu; Chong Wang 025 (SIAM J. Math. Anal., 2022)

A Physics-Informed Deep Learning Paradigm for Traffic State and Fundamental Diagram Estimation. - Rongye Shi; Zhaobin Mo; Kuang Huang; Xuan Di; Qiang Du 001 (IEEE Trans. Intell. Transp. Syst., 2022)

The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimation. - Qiang Du 001; Yiqi Gu; Haizhao Yang; Chao Zhou 010 (SIAM J. Numer. Anal., 2022)

On the Convergence to Local Limit of Nonlocal Models with Approximated Interaction Neighborhoods. - Qiang Du 001; Hehu Xie; Xiaobo Yin (SIAM J. Numer. Anal., 2022)

Asymptotically compatibility of a class of numerical schemes for a nonlocal traffic flow model. - Kuang Huang; Qiang Du 001 (CoRR, 2023)

Minimizing Optimal Transport for Functions with Fixed-Size Nodal Sets. - Qiang Du 001; Amir Sagiv (J. Nonlinear Sci., 2023)

Asymptotically compatible schemes for nonlinear variational models via Gamma-convergence and applications to nonlocal problems. - Qiang Du 001; James M. Scott; Xiaochuan Tian (CoRR, 2024)

Nonlocal Stokes equation with relaxation on the divergence free equation. - Yajie Zhang; Qiang Du 001; Zuoqiang Shi (CoRR, 2024)

Numerical analysis of a class of penalty discontinuous Galerkin methods for nonlocal diffusion problems. - Qiang Du 001; Lili Ju; Jianfang Lu; Xiaochuan Tian (CoRR, 2024)

Error estimates of finite element methods for nonlocal problems using exact or approximated interaction neighborhoods. - Qiang Du 001; Hehu Xie; Xiaobo Yin; Jiwei Zhang 002 (CoRR, 2024)

({ varGamma } )-Convergence of Nonlocal Dirichlet Energies with Penalty Formulations of Dirichlet Boundary Data. - Weiye Gan; Qiang Du 001; Zuoqiang Shi (SIAM J. Math. Anal., 2024)

Nonlocal Problems with Local Boundary Conditions I: Function Spaces and Variational Principles. - James M. Scott; Qiang Du 001 (SIAM J. Math. Anal., 2024)

Asymptotic Compatibility of a Class of Numerical Schemes for a Nonlocal Traffic Flow Model. - Kuang Huang; Qiang Du 001 (SIAM J. Numer. Anal., 2024)

Discontinuous Galerkin Methods for a First-Order Semi-Linear Hyperbolic Continuum Model of a Topological Resonator Dimer Array. - Qiang Du 001; Huaiyu Li; Michael I. Weinstein; Lu Zhang (J. Sci. Comput., 2024)

Nonlocal Problems with Local Boundary Conditions II: Green's Identities and Regularity of Solutions. - James M. Scott; Qiang Du 001 (SIAM J. Math. Anal., 2025)

Convergence analysis for a nonlocal gradient descent method via directional Gaussian smoothing. - Hoang Tran; Qiang Du 001; Guannan Zhang (Comput. Optim. Appl., 2025)