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

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

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

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)

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

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

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)

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

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)

Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation. - Yu Leng; Xiaochuan Tian; Nathaniel A. Trask; John T. Foster (CoRR, 2020)

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

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

A Physically Consistent, Flexible, and Efficient Strategy to Convert Local Boundary Conditions into Nonlocal Volume Constraints. - Marta D'Elia; Xiaochuan Tian; Yue Yu (SIAM J. Sci. Comput., 2020)

The double adaptivity paradigm: (How to circumvent the discrete inf-sup conditions of Babuška and Brezzi). - Leszek F. Demkowicz; Thomas Führer; Norbert Heuer; Xiaochuan Tian (Comput. Math. Appl., 2021)

Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion. - Yu Leng; Xiaochuan Tian; Nathaniel Trask; John T. Foster (SIAM J. Numer. Anal., 2021)

Efficient optimization-based quadrature for variational discretization of nonlocal problems. - Marco Pasetto; Zhaoxiang Shen; Marta D'Elia; Xiaochuan Tian; Nathaniel Trask; David Kamensky (CoRR, 2022)

A Meshfree Peridynamic Model for Brittle Fracture in Randomly Heterogeneous Materials. - Yiming Fan; Huaiqian You; Xiaochuan Tian; Xiu Yang; Xingjie Li 001; Naveen Prakash; Yue Yu (CoRR, 2022)

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

Minimal positive stencils in meshfree finite difference methods for linear elliptic equations in non-divergence form. - Qihao Ye; Xiaochuan Tian (CoRR, 2022)

An asymptotically compatible probabilistic collocation method for randomly heterogeneous nonlocal problems. - Yiming Fan; Xiaochuan Tian; Xiu Yang; Xingjie Li 001; Clayton Webster; Yue Yu (J. Comput. Phys., 2022)

A Petrov-Galerkin method for nonlocal convection-dominated diffusion problems. - Yu Leng; Xiaochuan Tian; Leszek F. Demkowicz; Héctor Gómez; John T. Foster (J. Comput. Phys., 2022)

A neural network kernel decomposition for learning multiple steady states in parameterized dynamical systems. - Yimeng Zhang; Alexander Cloninger; Bo Li; Xiaochuan Tian (CoRR, 2023)

Gaussian radial basis functions collocation for fractional PDEs: methodology and error analysis. - Xiaochuan Tian; Yixuan Wu; Yanzhi Zhang (CoRR, 2023)

Monotone Meshfree Methods for Linear Elliptic Equations in Non-divergence Form via Nonlocal Relaxation. - Qihao Ye; Xiaochuan Tian (J. Sci. Comput., 2023)

Correction to: Monotone Meshfree Methods for Linear Elliptic Equations in Non-divergence Form via Nonlocal Relaxation. - Qihao Ye; Xiaochuan Tian (J. Sci. Comput., 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)

A Fast and Accurate Solver for the Fractional Fokker-Planck Equation with Dirac-Delta Initial Conditions. - Qihao Ye; Xiaochuan Tian; Dong Wang (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)

Design of crowd counting system based on improved CSRNet. - Xiaochuan Tian; Hironori Hiraishi (Artif. Life Robotics, 2025)

A Robust Model-Based Approach for Continuous-Time Policy Evaluation with Unknown Lévy Process Dynamics. - Qihao Ye; Xiaochuan Tian; Yuhua Zhu (CoRR, 2025)

Monotone Peridynamic Neural Operator for Nonlinear Material Modeling with Conditionally Unique Solutions. - Jihong Wang; Xiaochuan Tian; Zhongqiang Zhang; Stewart Silling; Siavash Jafarzadeh; Yue Yu (CoRR, 2025)

Solving Nonlinear PDEs with Sparse Radial Basis Function Networks. - Zihan Shao; Konstantin Pieper; Xiaochuan Tian (CoRR, 2025)