Qiang Du

Orcid: 0000-0002-1067-8937

Affiliations:
  • Columbia University, Department of Applied Physics and Applied Mathematics, NY, USA


According to our database1, Qiang Du authored at least 138 papers between 1992 and 2024.

Collaborative distances:
  • Dijkstra number2 of three.
  • Erdős number3 of two.

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Bibliography

2024
Asymptotically compatible schemes for nonlinear variational models via Gamma-convergence and applications to nonlocal problems.
CoRR, 2024

2023
Asymptotically compatibility of a class of numerical schemes for a nonlocal traffic flow model.
CoRR, 2023

2022
On the Convergence to Local Limit of Nonlocal Models with Approximated Interaction Neighborhoods.
SIAM J. Numer. Anal., August, 2022

The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimation.
SIAM J. Numer. Anal., August, 2022

A Physics-Informed Deep Learning Paradigm for Traffic State and Fundamental Diagram Estimation.
IEEE Trans. Intell. Transp. Syst., 2022

The Average Distance Problem with Perimeter-to-Area Ratio Penalization.
SIAM J. Math. Anal., 2022

Stability of a Nonlocal Traffic Flow Model for Connected Vehicles.
SIAM J. Appl. Math., 2022

Numerical Simulation of Singularity Propagation Modeled by Linear Convection Equations with Spatially Heterogeneous Nonlocal Interactions.
J. Sci. Comput., 2022

On the Ternary Ohta-Kawasaki Free Energy and Its One-dimensional Global Minimizers.
J. Nonlinear Sci., 2022

Nonlocal diffusion models with consistent local and fractional limits.
CoRR, 2022

2021
Maximum Bound Principles for a Class of Semilinear Parabolic Equations and Exponential Time-Differencing Schemes.
SIAM Rev., 2021

Discovery of Dynamics Using Linear Multistep Methods.
SIAM J. Numer. Anal., 2021

An energy-stable scheme for a 2D simple fluid-particle interaction problem.
J. Comput. Phys., 2021

Discovering State Variables Hidden in Experimental Data.
CoRR, 2021

On some nonlocal models with radially symmetric interaction domains and the effect of domain truncation.
CoRR, 2021

A Physics-Informed Deep Learning Paradigm for Traffic State Estimation and Fundamental Diagram Discovery.
CoRR, 2021

Physics-Informed Deep Learning for Traffic State Estimation.
CoRR, 2021

2020
Asymptotically Compatible Schemes for Robust Discretization of Parametrized Problems with Applications to Nonlocal Models.
SIAM Rev., 2020

Stability and Error Analysis for a Second-Order Fast Approximation of the Local and Nonlocal Diffusion Equations on the Real Line.
SIAM J. Numer. Anal., 2020

Energy Decaying Phase-Field Model for Fluid-Particle Interaction in Two-Phase Flow.
SIAM J. Appl. Math., 2020

Variational Phase Field Formulations of Polarization and Phase Transition in Ferroelectric Thin Films.
SIAM J. Appl. Math., 2020

Time-Fractional Allen-Cahn Equations: Analysis and Numerical Methods.
J. Sci. Comput., 2020

Mathematics of Smoothed Particle Hydrodynamics: A Study via Nonlocal Stokes Equations.
Found. Comput. Math., 2020

Driving and Routing Game for Autonomous Vehicles on a Network.
CoRR, 2020

Nonlocal-in-time dynamics and crossover of diffusive regimes.
CoRR, 2020

Numerical methods for nonlocal and fractional models.
Acta Numer., 2020

Multiscale modeling, homogenization and nonlocal effects: Mathematical and computational issues.
Proceedings of the 75 Years of Mathematics of Computation, 2020

2019
New Error Bounds for Deep ReLU Networks Using Sparse Grids.
SIAM J. Math. Data Sci., 2019

Asymptotically Compatible SPH-Like Particle Discretizations of One Dimensional Linear Advection Models.
SIAM J. Numer. Anal., 2019

Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen-Cahn Equation.
SIAM J. Numer. Anal., 2019

A discontinuous Galerkin method for one-dimensional time-dependent nonlocal diffusion problems.
Math. Comput., 2019

Nonlocal Models with Heterogeneous Localization and Their Application to Seamless Local-Nonlocal Coupling.
Multiscale Model. Simul., 2019

A Conforming DG Method for Linear Nonlocal Models with Integrable Kernels.
J. Sci. Comput., 2019

Analysis of Fully Discrete Approximations for Dissipative Systems and Application to Time-Dependent Nonlocal Diffusion Problems.
J. Sci. Comput., 2019

Multiscale Modeling, Homogenization and Nonlocal Effects: Mathematical and Computational Issues.
CoRR, 2019

A Game-Theoretic Framework for Autonomous Vehicles Velocity Control: Bridging Microscopic Differential Games and Macroscopic Mean Field Games.
CoRR, 2019

Stabilizing Traffic via Autonomous Vehicles: A Continuum Mean Field Game Approach.
Proceedings of the 2019 IEEE Intelligent Transportation Systems Conference, 2019

2018
Numerical Solution of a Two-Dimensional Nonlocal Wave Equation on Unbounded Domains.
SIAM J. Sci. Comput., 2018

Erratum: Asymptotically Compatible Schemes for Stochastic Homogenization.
SIAM J. Numer. Anal., 2018

Asymptotically Compatible Schemes for Stochastic Homogenization.
SIAM J. Numer. Anal., 2018

A Quasi-nonlocal Coupling Method for Nonlocal and Local Diffusion Models.
SIAM J. Numer. Anal., 2018

Stability of Nonlocal Dirichlet Integrals and Implications for Peridynamic Correspondence Material Modeling.
SIAM J. Appl. Math., 2018

A spectral method for nonlocal diffusion operators on the sphere.
J. Comput. Phys., 2018

Data-driven compressive sensing and applications in uncertainty quantification.
J. Comput. Phys., 2018

Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation.
J. Comput. Phys., 2018

Stochastic Training of Residual Networks: a Differential Equation Viewpoint.
CoRR, 2018

Hierarchical Attention-Based Recurrent Highway Networks for Time Series Prediction.
CoRR, 2018

Nonlocal Neural Networks, Nonlocal Diffusion and Nonlocal Modeling.
Proceedings of the Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems 2018, 2018

A Reinforced Topic-Aware Convolutional Sequence-to-Sequence Model for Abstractive Text Summarization.
Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, 2018

2017
Numerical Solution of the Nonlocal Diffusion Equation on the Real Line.
SIAM J. Sci. Comput., 2017

Nonlocal Conservation Laws. A New Class of Monotonicity-Preserving Models.
SIAM J. Numer. Anal., 2017

Trace Theorems for some Nonlocal Function Spaces with Heterogeneous Localization.
SIAM J. Math. Anal., 2017

Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications.
J. Comput. Phys., 2017

Nonlocal Convection-Diffusion Problems on Bounded Domains and Finite-Range Jump Processes.
Comput. Methods Appl. Math., 2017

Nonlocal diffusion and peridynamic models with Neumann type constraints and their numerical approximations.
Appl. Math. Comput., 2017

2016
Optimization-based Shrinking Dimer Method for Finding Transition States.
SIAM J. Sci. Comput., 2016

Asymptotically Compatible Fourier Spectral Approximations of Nonlocal Allen-Cahn Equations.
SIAM J. Numer. Anal., 2016

A Multiscale Implementation Based on Adaptive Mesh Refinement for the Nonlocal Peridynamics Model in One Dimension.
Multiscale Model. Simul., 2016

Efficient and stable exponential time differencing Runge-Kutta methods for phase field elastic bending energy models.
J. Comput. Phys., 2016

Computational studies of coarsening rates for the Cahn-Hilliard equation with phase-dependent diffusion mobility.
J. Comput. Phys., 2016

Generalized local and nonlocal master equations for some stochastic processes.
Comput. Math. Appl., 2016

Asymptotically compatible schemes for the approximation of fractional Laplacian and related nonlocal diffusion problems on bounded domains.
Adv. Comput. Math., 2016

Extreme-scale phase field simulations of coarsening dynamics on the sunway taihulight supercomputer.
Proceedings of the International Conference for High Performance Computing, 2016

2015
Nonconforming Discontinuous Galerkin Methods for Nonlocal Variational Problems.
SIAM J. Numer. Anal., 2015

Fast Explicit Integration Factor Methods for Semilinear Parabolic Equations.
J. Sci. Comput., 2015

Optimization of Subdivision Invariant Tetrahedra.
Int. J. Comput. Geom. Appl., 2015

2014
Asymptotically Compatible Schemes and Applications to Robust Discretization of Nonlocal Models.
SIAM J. Numer. Anal., 2014

Mesh dependent stability and condition number estimates for finite element approximations of parabolic problems.
Math. Comput., 2014

Linear finite element superconvergence on simplicial meshes.
Math. Comput., 2014

Coarsening Mechanism for Systems Governed by the Cahn-Hilliard Equation with Degenerate Diffusion Mobility.
Multiscale Model. Simul., 2014

Constraint-Free Adaptive FEMs on Quadrilateral Nonconforming Meshes.
J. Sci. Comput., 2014

On balanced moving mesh methods.
J. Comput. Appl. Math., 2014

2013
A variance-estimation-based stopping rule for symbolic dynamic filtering.
Signal Image Video Process., 2013

Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations.
SIAM J. Numer. Anal., 2013

A Convergent Adaptive Finite Element Algorithm for Nonlocal Diffusion and Peridynamic Models.
SIAM J. Numer. Anal., 2013

A posteriori error analysis of finite element method for linear nonlocal diffusion and peridynamic models.
Math. Comput., 2013

2012
Robust modeling of constant mean curvature surfaces.
ACM Trans. Graph., 2012

Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints.
SIAM Rev., 2012

Shrinking Dimer Dynamics and Its Applications to Saddle Point Search.
SIAM J. Numer. Anal., 2012

A New Approach for a Nonlocal, Nonlinear Conservation Law.
SIAM J. Appl. Math., 2012

Motion of Interfaces Governed by the Cahn-Hilliard Equation with Highly Disparate Diffusion Mobility.
SIAM J. Appl. Math., 2012

A Hybrid Implicit-Explicit Adaptive Multirate Numerical Scheme for Time-Dependent Equations.
J. Sci. Comput., 2012

Constrained shrinking dimer dynamics for saddle point search with constraints.
J. Comput. Phys., 2012

2011
Mesh-dependent stability for finite element approximations of parabolic equations with mass lumping.
J. Comput. Appl. Math., 2011

Adaptive finite element methods for elliptic equations over hierarchical T-meshes.
J. Comput. Appl. Math., 2011

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

Vortex Solutions of the High-κ High-Field Ginzburg-Landau Model with an Applied Current.
SIAM J. Math. Anal., 2010

Diffuse-interface approach to predicting morphologies of critical nucleus and equilibrium structure for cubic to tetragonal transformations.
J. Comput. Phys., 2010

2009
Numerical Studies of Discrete Approximations to the Allen--Cahn Equation in the Sharp Interface Limit.
SIAM J. Sci. Comput., 2009

On Mesh Geometry and Stiffness Matrix Conditioning for General Finite Element Spaces.
SIAM J. Numer. Anal., 2009

A phase field model for vesicle-substrate adhesion.
J. Comput. Phys., 2009

2008
Adaptive Finite Element Method for a Phase Field Bending Elasticity Model of Vesicle Membrane Deformations.
SIAM J. Sci. Comput., 2008

Uniform Convergence of a Nonlinear Energy-Based Multilevel Quantization Scheme.
SIAM J. Numer. Anal., 2008

An Enhanced Macroscopic Closure Approximation to the Micro-Macro FENE Model for Polymeric Materials.
Multiscale Model. Simul., 2008

Mathematical and Numerical Aspects of a Phase-field Approach to Critical Nuclei Morphology in Solids.
J. Sci. Comput., 2008

2007
The Dynamics and Interaction of Quantized Vortices in the Ginzburg-Landau-Schrödinger Equation.
SIAM J. Appl. Math., 2007

2006
Convergence of the Lloyd Algorithm for Computing Centroidal Voronoi Tessellations.
SIAM J. Numer. Anal., 2006

Dynamics of Rotating Bose-Einstein Condensates and its Efficient and Accurate Numerical Computation.
SIAM J. Appl. Math., 2006

Acceleration schemes for computing centroidal Voronoi tessellations.
Numer. Linear Algebra Appl., 2006

Centroidal Voronoi Tessellation Algorithms for Image Compression, Segmentation, and Multichannel Restoration.
J. Math. Imaging Vis., 2006

Spectral implementation of an adaptive moving mesh method for phase-field equations.
J. Comput. Phys., 2006

Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions.
J. Comput. Phys., 2006

2005
Anisotropic Centroidal Voronoi Tessellations and Their Applications.
SIAM J. Sci. Comput., 2005

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

Retrieving Topological Information for Phase Field Models.
SIAM J. Appl. Math., 2005

Approximations of a Ginzburg-Landau model for superconducting hollow spheres based on spherical centroidal Voronoi tessellations.
Math. Comput., 2005

From Micro to Macro Dynamics via a New Closure Approximation to the FENE Model of Polymeric Fluids.
Multiscale Model. Simul., 2005

FENE Dumbbell Model and Its Several Linear and Nonlinear Closure Approximations.
Multiscale Model. Simul., 2005

2004
Computing the Ground State Solution of Bose-Einstein Condensates by a Normalized Gradient Flow.
SIAM J. Sci. Comput., 2004

Semidiscrete Finite Element Approximations of a Linear Fluid-Structure Interaction Problem.
SIAM J. Numer. Anal., 2004

Centroidal Voronoi Tessellation Based Algorithms for Vector Fields Visualization and Segmentation.
Proceedings of the 15th IEEE Visualization Conference, 2004

Tesselation and Clustering by Mixture Models and Their Parallel Implementations.
Proceedings of the Fourth SIAM International Conference on Data Mining, 2004

2003
Constrained Centroidal Voronoi Tessellations for Surfaces.
SIAM J. Sci. Comput., 2003

Corrigendum: Fourier Spectral Approximation to a Dissipative System Modeling the Flow of Liquid Crystals.
SIAM J. Numer. Anal., 2003

Convergence Analysis of a Finite Volume Method for Maxwell's Equations in Nonhomogeneous Media.
SIAM J. Numer. Anal., 2003

Existence of Weak Solutions to Some Vortex Density Models.
SIAM J. Math. Anal., 2003

2002
Numerical Approximation of Some Linear Stochastic Partial Differential Equations Driven by Special Additive Noises.
SIAM J. Numer. Anal., 2002

Efficient Parallel Algorithms for Parabolic Problems.
SIAM J. Numer. Anal., 2002

Critical Magnetic Field and Asymptotic Behavior of Superconducting Thin Films.
SIAM J. Math. Anal., 2002

Probabilistic methods for centroidal Voronoi tessellations and their parallel implementations.
Parallel Comput., 2002

Grid generation and optimization based on centroidal Voronoi tessellations.
Appl. Math. Comput., 2002

2001
Fourier Spectral Approximation to a Dissipative System Modeling the Flow of Liquid Crystals.
SIAM J. Numer. Anal., 2001

Optimization Based Nonoverlapping Domain Decomposition Algorithms and Their Convergence.
SIAM J. Numer. Anal., 2001

2000
A Gradient Method Approach to Optimization-Based Multidisciplinary Simulations and Nonoverlapping Domain Decomposition Algorithms.
SIAM J. Numer. Anal., 2000

Convergence Analysis of a Numerical Method for a Mean Field Model of Superconducting Vortices.
SIAM J. Numer. Anal., 2000

Finite Element Methods with Matching and Nonmatching Meshes for Maxwell Equations with Discontinuous Coefficients.
SIAM J. Numer. Anal., 2000

1999
Numerical Algorithms of the Lawrence-Doniach Model for Layered Superconductors and their Parallel Implementation.
SIAM J. Sci. Comput., 1999

Centroidal Voronoi Tessellations: Applications and Algorithms.
SIAM Rev., 1999

Studies of a Ginzburg-Landau Model for <i>d</i>-Wave Superconductors.
SIAM J. Appl. Math., 1999

Analysis and computation of a mean-field model for superconductivity.
Numerische Mathematik, 1999

1998
Discrete gauge invariant approximations of a time dependent Ginzburg-Landau model of superconductivity.
Math. Comput., 1998

1997
Impulsive Stretching of a Surface in a Viscous Fluid.
SIAM J. Appl. Math., 1997

The quasi-Laguerre iteration.
Math. Comput., 1997

1996
Quasi-Laguerre Iteration in Solving Symmetric Tridiagonal Eigenvalue Problems.
SIAM J. Sci. Comput., 1996

High-Kappa Limits of the Time-Dependent Ginzburg-Landau Model.
SIAM J. Appl. Math., 1996

1995
On the Lawrence-Doniach and Anisotropic Ginzburg-Landau Models for Layered Superconductors.
SIAM J. Appl. Math., 1995

1993
Modeling and Analysis of a Periodic Ginzburg-Landau Model for Type-II Superconductors.
SIAM J. Appl. Math., 1993

1992
Analysis and Approximation of the Ginzburg-Landau Model of Superconductivity.
SIAM Rev., 1992


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