Xiaochuan Tian
Orcid: 0000-0002-4539-6702
According to our database1,
Xiaochuan Tian
authored at least 29 papers
between 2013 and 2024.
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Bibliography
2024
Asymptotically compatible schemes for nonlinear variational models via Gamma-convergence and applications to nonlocal problems.
CoRR, 2024
2023
Correction to: Monotone Meshfree Methods for Linear Elliptic Equations in Non-divergence Form via Nonlocal Relaxation.
J. Sci. Comput., November, 2023
Monotone Meshfree Methods for Linear Elliptic Equations in Non-divergence Form via Nonlocal Relaxation.
J. Sci. Comput., September, 2023
Gaussian radial basis functions collocation for fractional PDEs: methodology and error analysis.
CoRR, 2023
A neural network kernel decomposition for learning multiple steady states in parameterized dynamical systems.
CoRR, 2023
2022
J. Comput. Phys., 2022
An asymptotically compatible probabilistic collocation method for randomly heterogeneous nonlocal problems.
J. Comput. Phys., 2022
Minimal positive stencils in meshfree finite difference methods for linear elliptic equations in non-divergence form.
CoRR, 2022
A Meshfree Peridynamic Model for Brittle Fracture in Randomly Heterogeneous Materials.
CoRR, 2022
Efficient optimization-based quadrature for variational discretization of nonlocal problems.
CoRR, 2022
2021
Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion.
SIAM J. Numer. Anal., 2021
The double adaptivity paradigm: (How to circumvent the discrete inf-sup conditions of Babuška and Brezzi).
Comput. Math. Appl., 2021
2020
A Physically Consistent, Flexible, and Efficient Strategy to Convert Local Boundary Conditions into Nonlocal Volume Constraints.
SIAM J. Sci. Comput., 2020
Asymptotically Compatible Schemes for Robust Discretization of Parametrized Problems with Applications to Nonlocal Models.
SIAM Rev., 2020
Mathematics of Smoothed Particle Hydrodynamics: A Study via Nonlocal Stokes Equations.
Found. Comput. Math., 2020
Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation.
CoRR, 2020
Multiscale modeling, homogenization and nonlocal effects: Mathematical and computational issues.
Proceedings of the 75 Years of Mathematics of Computation, 2020
2019
Nonlocal Models with Heterogeneous Localization and Their Application to Seamless Local-Nonlocal Coupling.
Multiscale Model. Simul., 2019
Multiscale Modeling, Homogenization and Nonlocal Effects: Mathematical and Computational Issues.
CoRR, 2019
2018
SIAM J. Numer. Anal., 2018
Stability of Nonlocal Dirichlet Integrals and Implications for Peridynamic Correspondence Material Modeling.
SIAM J. Appl. Math., 2018
2017
SIAM J. Math. Anal., 2017
Nonlocal diffusion and peridynamic models with Neumann type constraints and their numerical approximations.
Appl. Math. Comput., 2017
2016
Asymptotically compatible schemes for the approximation of fractional Laplacian and related nonlocal diffusion problems on bounded domains.
Adv. Comput. Math., 2016
2015
SIAM J. Numer. Anal., 2015
2014
Asymptotically Compatible Schemes and Applications to Robust Discretization of Nonlocal Models.
SIAM J. Numer. Anal., 2014
2013
Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations.
SIAM J. Numer. Anal., 2013