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Xiaochuan Tian
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2020 – today
- 2024
- [i15]Qiang Du, James M. Scott, Xiaochuan Tian:
Asymptotically compatible schemes for nonlinear variational models via Gamma-convergence and applications to nonlocal problems. CoRR abs/2402.07749 (2024) - [i14]Qihao Ye, Xiaochuan Tian, Dong Wang:
A Fast and Accurate Solver for the Fractional Fokker-Planck Equation with Dirac-Delta Initial Conditions. CoRR abs/2407.15315 (2024) - [i13]Qiang Du, Lili Ju, Jianfang Lu, Xiaochuan Tian:
Numerical analysis of a class of penalty discontinuous Galerkin methods for nonlocal diffusion problems. CoRR abs/2408.07261 (2024) - 2023
- [j19]Qihao Ye
, Xiaochuan Tian
Monotone Meshfree Methods for Linear Elliptic Equations in Non-divergence Form via Nonlocal Relaxation. J. Sci. Comput. 96(3): 85 (2023) - [j18]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): 46 (2023) - [i12]Yimeng Zhang, Alexander Cloninger, Bo Li, Xiaochuan Tian:
A neural network kernel decomposition for learning multiple steady states in parameterized dynamical systems. CoRR abs/2312.10315 (2023) - [i11]Xiaochuan Tian, Yixuan Wu
Gaussian radial basis functions collocation for fractional PDEs: methodology and error analysis. CoRR abs/2312.17461 (2023) - 2022
- [j17]Yu Leng
A Petrov-Galerkin method for nonlocal convection-dominated diffusion problems. J. Comput. Phys. 452: 110919 (2022) - [j16]Yiming Fan
An asymptotically compatible probabilistic collocation method for randomly heterogeneous nonlocal problems. J. Comput. Phys. 465: 111376 (2022) - [i10]Marco Pasetto, Zhaoxiang Shen, Marta D'Elia, Xiaochuan Tian, Nathaniel Trask, David Kamensky:
Efficient optimization-based quadrature for variational discretization of nonlocal problems. CoRR abs/2201.12391 (2022) - [i9]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 abs/2202.06578 (2022) - [i8]Qiang Du, Xiaochuan Tian, Zhi Zhou:
Nonlocal diffusion models with consistent local and fractional limits. CoRR abs/2203.00167 (2022) - [i7]Qihao Ye, Xiaochuan Tian:
Minimal positive stencils in meshfree finite difference methods for linear elliptic equations in non-divergence form. CoRR abs/2211.12490 (2022) - 2021
- [j15]Leszek F. Demkowicz, Thomas Führer
The double adaptivity paradigm: (How to circumvent the discrete inf-sup conditions of Babuška and Brezzi). Comput. Math. Appl. 95: 41-66 (2021) - [j14]Yu Leng, Xiaochuan Tian
Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion. SIAM J. Numer. Anal. 59(1): 88-118 (2021) - [i6]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 abs/2107.01386 (2021) - [i5]Yu Leng, Xiaochuan Tian, Leszek F. Demkowicz, Hector Gomez, John T. Foster:
A Petrov-Galerkin method for nonlocal convection-dominated diffusion problems. CoRR abs/2107.07080 (2021) - 2020
- [j13]Marta D'Elia, Qiang Du
Numerical methods for nonlocal and fractional models. Acta Numer. 29: 1-124 (2020) - [j12]Qiang Du
Mathematics of Smoothed Particle Hydrodynamics: A Study via Nonlocal Stokes Equations. Found. Comput. Math. 20(4): 801-826 (2020) - [j11]Xiaochuan Tian
Asymptotically Compatible Schemes for Robust Discretization of Parametrized Problems with Applications to Nonlocal Models. SIAM Rev. 62(1): 199-227 (2020) - [j10]Marta D'Elia, Xiaochuan Tian
A Physically Consistent, Flexible, and Efficient Strategy to Convert Local Boundary Conditions into Nonlocal Volume Constraints. SIAM J. Sci. Comput. 42(4): A1935-A1949 (2020) - [p1]Qiang Du, Björn Engquist, Xiaochuan Tian:
Multiscale modeling, homogenization and nonlocal effects: Mathematical and computational issues. 75 Years of Mathematics of Computation 2020 - [i4]Yu Leng, Xiaochuan Tian, Nathaniel A. Trask, John T. Foster:
Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation. CoRR abs/2001.00649 (2020) - [i3]Marta D'Elia, Qiang Du, Christian Glusa, Max D. Gunzburger, Xiaochuan Tian, Zhi Zhou:
Numerical methods for nonlocal and fractional models. CoRR abs/2002.01401 (2020)
2010 – 2019
- 2019
- [j9]Yunzhe Tao, Xiaochuan Tian
Nonlocal Models with Heterogeneous Localization and Their Application to Seamless Local-Nonlocal Coupling. Multiscale Model. Simul. 17(3): 1052-1075 (2019) - [i2]Yu Leng, Xiaochuan Tian, Nathaniel Trask, John T. Foster:
Asymptotically compatible reproducing kernel collocation and meshfree integration for nonlocal diffusion. CoRR abs/1907.12031 (2019) - [i1]Qiang Du, Björn Engquist, Xiaochuan Tian:
Multiscale Modeling, Homogenization and Nonlocal Effects: Mathematical and Computational Issues. CoRR abs/1909.00708 (2019) - 2018
- [j8]Qiang Du
Stability of Nonlocal Dirichlet Integrals and Implications for Peridynamic Correspondence Material Modeling. SIAM J. Appl. Math. 78(3): 1536-1552 (2018) - [j7]Qiang Du
A Quasi-nonlocal Coupling Method for Nonlocal and Local Diffusion Models. SIAM J. Numer. Anal. 56(3): 1386-1404 (2018) - 2017
- [j6]Yunzhe Tao, Xiaochuan Tian
Nonlocal diffusion and peridynamic models with Neumann type constraints and their numerical approximations. Appl. Math. Comput. 305: 282-298 (2017) - [j5]Xiaochuan Tian
Trace Theorems for some Nonlocal Function Spaces with Heterogeneous Localization. SIAM J. Math. Anal. 49(2): 1621-1644 (2017) - 2016
- [j4]Xiaochuan Tian
Asymptotically compatible schemes for the approximation of fractional Laplacian and related nonlocal diffusion problems on bounded domains. Adv. Comput. Math. 42(6): 1363-1380 (2016) - 2015
- [j3]Xiaochuan Tian
Nonconforming Discontinuous Galerkin Methods for Nonlocal Variational Problems. SIAM J. Numer. Anal. 53(2): 762-781 (2015) - 2014
- [j2]Xiaochuan Tian
Asymptotically Compatible Schemes and Applications to Robust Discretization of Nonlocal Models. SIAM J. Numer. Anal. 52(4): 1641-1665 (2014) - 2013
- [j1]Xiaochuan Tian
Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations. SIAM J. Numer. Anal. 51(6): 3458-3482 (2013)
Coauthor Index
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