Xiaochuan Tian

41 papers Journal 40

Year	Rank	Type	Title / Venue / Authors
2026	J	`jnl`	Sparse RBF Networks for PDEs and nonlocal equations: function space theory, operator calculus, and training algorithms. CoRR Zihan Shao, Konstantin Pieper, Xiaochuan Tian
2025	J	`jnl`	A Robust Model-Based Approach for Continuous-Time Policy Evaluation with Unknown Lévy Process Dynamics. CoRR Qihao Ye, Xiaochuan Tian, Yuhua Zhu
2025	J	`jnl`	Asymptotically compatible schemes for nonlinear variational models via Gamma-convergence and applications to nonlocal problems. Math. Comput. Qiang Du, James M. Scott, Xiaochuan Tian
2025	J	`jnl`	Design of crowd counting system based on improved CSRNet. Artif. Life Robotics Xiaochuan Tian, Hironori Hiraishi
2025	J	`jnl`	Monotone Peridynamic Neural Operator for Nonlinear Material Modeling with Conditionally Unique Solutions. CoRR Jihong Wang, Xiaochuan Tian, Zhongqiang Zhang, Stewart Silling, Siavash Jafarzadeh, Yue Yu
2025	J	`jnl`	Solving Nonlinear PDEs with Sparse Radial Basis Function Networks. CoRR Zihan Shao, Konstantin Pieper, Xiaochuan Tian
2024	J	`jnl`	A Fast and Accurate Solver for the Fractional Fokker-Planck Equation with Dirac-Delta Initial Conditions. CoRR Qihao Ye, Xiaochuan Tian, Dong Wang
2024	J	`jnl`	Asymptotically compatible schemes for nonlinear variational models via Gamma-convergence and applications to nonlocal problems. CoRR Qiang Du, James M. Scott, Xiaochuan Tian
2024	J	`jnl`	Numerical analysis of a class of penalty discontinuous Galerkin methods for nonlocal diffusion problems. CoRR Qiang Du, Lili Ju, Jianfang Lu, Xiaochuan Tian
2023	J	`jnl`	A neural network kernel decomposition for learning multiple steady states in parameterized dynamical systems. CoRR Yimeng Zhang, Alexander Cloninger, Bo Li, Xiaochuan Tian
2023	J	`jnl`	Correction to: Monotone Meshfree Methods for Linear Elliptic Equations in Non-divergence Form via Nonlocal Relaxation. J. Sci. Comput. Qihao Ye, Xiaochuan Tian
2023	J	`jnl`	Gaussian radial basis functions collocation for fractional PDEs: methodology and error analysis. CoRR Xiaochuan Tian, Yixuan Wu, Yanzhi Zhang
2023	J	`jnl`	Monotone Meshfree Methods for Linear Elliptic Equations in Non-divergence Form via Nonlocal Relaxation. J. Sci. Comput. Qihao Ye, Xiaochuan Tian
2022	J	`jnl`	A Meshfree Peridynamic Model for Brittle Fracture in Randomly Heterogeneous Materials. CoRR Yiming Fan, Huaiqian You, Xiaochuan Tian, Xiu Yang, Xingjie Li, Naveen Prakash, Yue Yu
2022	J	`jnl`	A Petrov-Galerkin method for nonlocal convection-dominated diffusion problems. J. Comput. Phys. Yu Leng, Xiaochuan Tian, Leszek F. Demkowicz, Héctor Gómez, John T. Foster
2022	J	`jnl`	An asymptotically compatible probabilistic collocation method for randomly heterogeneous nonlocal problems. J. Comput. Phys. Yiming Fan, Xiaochuan Tian, Xiu Yang, Xingjie Li, Clayton Webster, Yue Yu
2022	J	`jnl`	Efficient optimization-based quadrature for variational discretization of nonlocal problems. CoRR Marco Pasetto, Zhaoxiang Shen, Marta D'Elia, Xiaochuan Tian, Nathaniel Trask, David Kamensky
2022	J	`jnl`	Minimal positive stencils in meshfree finite difference methods for linear elliptic equations in non-divergence form. CoRR Qihao Ye, Xiaochuan Tian
2022	J	`jnl`	Nonlocal diffusion models with consistent local and fractional limits. CoRR Qiang Du, Xiaochuan Tian, Zhi Zhou
2021	J	`jnl`	A Petrov-Galerkin method for nonlocal convection-dominated diffusion problems. CoRR Yu Leng, Xiaochuan Tian, Leszek F. Demkowicz, Héctor Gómez, John T. Foster
2021	J	`jnl`	An asymptotically compatible probabilistic collocation method for randomly heterogeneous nonlocal problems. CoRR Yiming Fan, Xiaochuan Tian, Xiu Yang, Xingjie Li, Clayton Webster, Yue Yu
2021	J	`jnl`	Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion. SIAM J. Numer. Anal. Yu Leng, Xiaochuan Tian, Nathaniel Trask, John T. Foster
2021	J	`jnl`	The double adaptivity paradigm: (How to circumvent the discrete inf-sup conditions of Babuška and Brezzi). Comput. Math. Appl. Leszek F. Demkowicz, Thomas Führer, Norbert Heuer, Xiaochuan Tian
2020	J	`jnl`	A Physically Consistent, Flexible, and Efficient Strategy to Convert Local Boundary Conditions into Nonlocal Volume Constraints. SIAM J. Sci. Comput. Marta D'Elia, Xiaochuan Tian, Yue Yu
2020	J	`jnl`	Asymptotically Compatible Schemes for Robust Discretization of Parametrized Problems with Applications to Nonlocal Models. SIAM Rev. Xiaochuan Tian, Qiang Du
2020	J	`jnl`	Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation. CoRR Yu Leng, Xiaochuan Tian, Nathaniel A. Trask, John T. Foster
2020	J	`jnl`	Mathematics of Smoothed Particle Hydrodynamics: A Study via Nonlocal Stokes Equations. Found. Comput. Math. Qiang Du, Xiaochuan Tian
2020	—	`ch.`	Multiscale modeling, homogenization and nonlocal effects: Mathematical and computational issues. 75 Years of Mathematics of Computation Qiang Du, Björn Engquist, Xiaochuan Tian
2020	J	`jnl`	Numerical methods for nonlocal and fractional models. Acta Numer. Marta D'Elia, Qiang Du, Christian Glusa, Max D. Gunzburger, Xiaochuan Tian, Zhi Zhou
2020	J	`jnl`	Numerical methods for nonlocal and fractional models. CoRR Marta D'Elia, Qiang Du, Christian Glusa, Max D. Gunzburger, Xiaochuan Tian, Zhi Zhou
2019	J	`jnl`	Asymptotically compatible reproducing kernel collocation and meshfree integration for nonlocal diffusion. CoRR Yu Leng, Xiaochuan Tian, Nathaniel Trask, John T. Foster
2019	J	`jnl`	Multiscale Modeling, Homogenization and Nonlocal Effects: Mathematical and Computational Issues. CoRR Qiang Du, Björn Engquist, Xiaochuan Tian
2019	J	`jnl`	Nonlocal Models with Heterogeneous Localization and Their Application to Seamless Local-Nonlocal Coupling. Multiscale Model. Simul. Yunzhe Tao, Xiaochuan Tian, Qiang Du
2018	J	`jnl`	A Quasi-nonlocal Coupling Method for Nonlocal and Local Diffusion Models. SIAM J. Numer. Anal. Qiang Du, Xingjie Helen Li, Jianfeng Lu, Xiaochuan Tian
2018	J	`jnl`	Stability of Nonlocal Dirichlet Integrals and Implications for Peridynamic Correspondence Material Modeling. SIAM J. Appl. Math. Qiang Du, Xiaochuan Tian
2017	J	`jnl`	Nonlocal diffusion and peridynamic models with Neumann type constraints and their numerical approximations. Appl. Math. Comput. Yunzhe Tao, Xiaochuan Tian, Qiang Du
2017	J	`jnl`	Trace Theorems for some Nonlocal Function Spaces with Heterogeneous Localization. SIAM J. Math. Anal. Xiaochuan Tian, Qiang Du
2016	J	`jnl`	Asymptotically compatible schemes for the approximation of fractional Laplacian and related nonlocal diffusion problems on bounded domains. Adv. Comput. Math. Xiaochuan Tian, Qiang Du, Max D. Gunzburger
2015	J	`jnl`	Nonconforming Discontinuous Galerkin Methods for Nonlocal Variational Problems. SIAM J. Numer. Anal. Xiaochuan Tian, Qiang Du
2014	J	`jnl`	Asymptotically Compatible Schemes and Applications to Robust Discretization of Nonlocal Models. SIAM J. Numer. Anal. Xiaochuan Tian, Qiang Du
2013	J	`jnl`	Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations. SIAM J. Numer. Anal. Xiaochuan Tian, Qiang Du