Xiaochuan Tian

Publication Activity (10 Years)

Years Active: 2013-2024
Publications (10 Years): 30

Top Topics

Basis Functions

Numerical Methods

Top Venues

SIAM J. Numer. Anal.

J. Sci. Comput.

J. Comput. Phys.

Publications

Qiang Du, James M. Scott, Xiaochuan Tian
Asymptotically compatible schemes for nonlinear variational models via Gamma-convergence and applications to nonlocal problems. CoRR (2024)
Qihao Ye, Xiaochuan Tian, Dong Wang
A Fast and Accurate Solver for the Fractional Fokker-Planck Equation with Dirac-Delta Initial Conditions. CoRR (2024)
Qihao Ye, Xiaochuan Tian
Correction to: Monotone Meshfree Methods for Linear Elliptic Equations in Non-divergence Form via Nonlocal Relaxation. J. Sci. Comput. 97 (2) (2023)
Xiaochuan Tian, Yixuan Wu, Yanzhi Zhang
Gaussian radial basis functions collocation for fractional PDEs: methodology and error analysis. CoRR (2023)
Qihao Ye, Xiaochuan Tian
Monotone Meshfree Methods for Linear Elliptic Equations in Non-divergence Form via Nonlocal Relaxation. J. Sci. Comput. 96 (3) (2023)
Yimeng Zhang, Alexander Cloninger, Bo Li, Xiaochuan Tian
A neural network kernel decomposition for learning multiple steady states in parameterized dynamical systems. CoRR (2023)
Qiang Du, Xiaochuan Tian, Zhi Zhou
Nonlocal diffusion models with consistent local and fractional limits. CoRR (2022)
Yu Leng, Xiaochuan Tian, Leszek F. Demkowicz, Hector Gomez, John T. Foster
A Petrov-Galerkin method for nonlocal convection-dominated diffusion problems. J. Comput. Phys. 452 (2022)
Marco Pasetto, Zhaoxiang Shen, Marta D'Elia, Xiaochuan Tian, Nathaniel Trask, David Kamensky
Efficient optimization-based quadrature for variational discretization of nonlocal problems. CoRR (2022)
Qihao Ye, Xiaochuan Tian
Minimal positive stencils in meshfree finite difference methods for linear elliptic equations in non-divergence form. CoRR (2022)
Yiming Fan, Xiaochuan Tian, Xiu Yang, Xingjie Helen Li, Clayton Webster, Yue Yu
An asymptotically compatible probabilistic collocation method for randomly heterogeneous nonlocal problems. J. Comput. Phys. 465 (2022)
Yiming Fan, Huaiqian You, Xiaochuan Tian, Xiu Yang, Xingjie Helen Li, Naveen Prakash, Yue Yu
A Meshfree Peridynamic Model for Brittle Fracture in Randomly Heterogeneous Materials. CoRR (2022)
Yiming Fan, Xiaochuan Tian, Xiu Yang, Xingjie Helen Li, Clayton Webster, Yue Yu
An asymptotically compatible probabilistic collocation method for randomly heterogeneous nonlocal problems. CoRR (2021)
Yu Leng, Xiaochuan Tian, Leszek F. Demkowicz, Hector Gomez, John T. Foster
A Petrov-Galerkin method for nonlocal convection-dominated diffusion problems. CoRR (2021)
Leszek F. Demkowicz, Thomas Führer, Norbert Heuer, Xiaochuan Tian
The double adaptivity paradigm: (How to circumvent the discrete inf-sup conditions of Babuška and Brezzi). Comput. Math. Appl. 95 (2021)
Yu Leng, Xiaochuan Tian, Nathaniel Trask, John T. Foster
Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion. SIAM J. Numer. Anal. 59 (1) (2021)
Marta D'Elia, Xiaochuan Tian, Yue Yu
A Physically Consistent, Flexible, and Efficient Strategy to Convert Local Boundary Conditions into Nonlocal Volume Constraints. SIAM J. Sci. Comput. 42 (4) (2020)
Qiang Du, Xiaochuan Tian
Mathematics of Smoothed Particle Hydrodynamics: A Study via Nonlocal Stokes Equations. Found. Comput. Math. 20 (4) (2020)
Marta D'Elia, Qiang Du, Christian A. Glusa, Max D. Gunzburger, Xiaochuan Tian, Zhi Zhou
Numerical methods for nonlocal and fractional models. CoRR (2020)
Marta D'Elia, Qiang Du, Christian A. Glusa, Max D. Gunzburger, Xiaochuan Tian, Zhi Zhou
Numerical methods for nonlocal and fractional models. Acta Numer. 29 (2020)
Yu Leng, Xiaochuan Tian, Nathaniel A. Trask, John T. Foster
Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation. CoRR (2020)
Xiaochuan Tian, Qiang Du
Asymptotically Compatible Schemes for Robust Discretization of Parametrized Problems with Applications to Nonlocal Models. SIAM Rev. 62 (1) (2020)
Yunzhe Tao, Xiaochuan Tian, Qiang Du
Nonlocal Models with Heterogeneous Localization and Their Application to Seamless Local-Nonlocal Coupling. Multiscale Model. Simul. 17 (3) (2019)
Yu Leng, Xiaochuan Tian, Nathaniel Trask, John T. Foster
Asymptotically compatible reproducing kernel collocation and meshfree integration for nonlocal diffusion. CoRR (2019)
Qiang Du, Björn Engquist, Xiaochuan Tian
Multiscale Modeling, Homogenization and Nonlocal Effects: Mathematical and Computational Issues. CoRR (2019)
Qiang Du, Xiaochuan Tian
Stability of Nonlocal Dirichlet Integrals and Implications for Peridynamic Correspondence Material Modeling. SIAM J. Appl. Math. 78 (3) (2018)
Qiang Du, Xingjie Helen Li, Jianfeng Lu, Xiaochuan Tian
A Quasi-nonlocal Coupling Method for Nonlocal and Local Diffusion Models. SIAM J. Numer. Anal. 56 (3) (2018)
Xiaochuan Tian, Qiang Du
Trace Theorems for some Nonlocal Function Spaces with Heterogeneous Localization. SIAM J. Math. Anal. 49 (2) (2017)
Yunzhe Tao, Xiaochuan Tian, Qiang Du
Nonlocal diffusion and peridynamic models with Neumann type constraints and their numerical approximations. Appl. Math. Comput. 305 (2017)
Xiaochuan Tian, Qiang Du, Max D. Gunzburger
Asymptotically compatible schemes for the approximation of fractional Laplacian and related nonlocal diffusion problems on bounded domains. Adv. Comput. Math. 42 (6) (2016)
Xiaochuan Tian, Qiang Du
Nonconforming Discontinuous Galerkin Methods for Nonlocal Variational Problems. SIAM J. Numer. Anal. 53 (2) (2015)
Xiaochuan Tian, Qiang Du
Asymptotically Compatible Schemes and Applications to Robust Discretization of Nonlocal Models. SIAM J. Numer. Anal. 52 (4) (2014)
Xiaochuan Tian, Qiang Du
Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations. SIAM J. Numer. Anal. 51 (6) (2013)