| Analysis and comparison of different approximations to nonlocal diffusion and linear peridynamic equations X Tian, Q Du SIAM Journal on Numerical Analysis 51 (6), 3458-3482, 2013 | 242 | 2013 |
| Numerical methods for nonlocal and fractional models M D’Elia, Q Du, C Glusa, M Gunzburger, X Tian, Z Zhou Acta Numerica 29, 1-124, 2020 | 220 | 2020 |
| Asymptotically compatible schemes and applications to robust discretization of nonlocal models X Tian, Q Du SIAM Journal on Numerical Analysis 52 (4), 1641-1665, 2014 | 217 | 2014 |
| Nonlocal diffusion and peridynamic models with Neumann type constraints and their numerical approximations Y Tao, X Tian, Q Du Applied Mathematics and Computation 305, 282-298, 2017 | 71 | 2017 |
| A review of local-to-nonlocal coupling methods in nonlocal diffusion and nonlocal mechanics M D’Elia, X Li, P Seleson, X Tian, Y Yu Journal of Peridynamics and Nonlocal Modeling, 1-50, 2021 | 69 | 2021 |
| A peridynamic model of fracture mechanics with bond-breaking Q Du, Y Tao, X Tian Journal of Elasticity 132, 197-218, 2018 | 60 | 2018 |
| A physically consistent, flexible, and efficient strategy to convert local boundary conditions into nonlocal volume constraints M D'Elia, X Tian, Y Yu SIAM Journal on Scientific Computing 42 (4), A1935-A1949, 2020 | 45 | 2020 |
| Trace theorems for some nonlocal function spaces with heterogeneous localization X Tian, Q Du SIAM Journal on Mathematical Analysis 49 (2), 1621-1644, 2017 | 45 | 2017 |
| Nonconforming discontinuous Galerkin methods for nonlocal variational problems X Tian, Q Du SIAM Journal on Numerical Analysis 53 (2), 762-781, 2015 | 45 | 2015 |
| Asymptotically compatible reproducing kernel collocation and meshfree integration for nonlocal diffusion Y Leng, X Tian, N Trask, JT Foster SIAM Journal on Numerical Analysis 59 (1), 88-118, 2021 | 40 | 2021 |
| Asymptotically compatible schemes for the approximation of fractional Laplacian and related nonlocal diffusion problems on bounded domains X Tian, Q Du, M Gunzburger Advances in Computational Mathematics 42, 1363-1380, 2016 | 40 | 2016 |
| Asymptotically compatible discretization of multidimensional nonlocal diffusion models and approximation of nonlocal Green’s functions Q Du, Y Tao, X Tian, J Yang IMA Journal of numerical analysis 39 (2), 607-625, 2019 | 38 | 2019 |
| A quasi-nonlocal coupling method for nonlocal and local diffusion models Q Du, XH Li, J Lu, X Tian SIAM Journal on Numerical Analysis 56 (3), 1386-1404, 2018 | 38 | 2018 |
| Stability of nonlocal Dirichlet integrals and implications for peridynamic correspondence material modeling Q Du, X Tian SIAM Journal on Applied Mathematics 78 (3), 1536-1552, 2018 | 37 | 2018 |
| Mathematics of smoothed particle hydrodynamics: A study via nonlocal stokes equations Q Du, X Tian Foundations of Computational Mathematics 20 (4), 801-826, 2020 | 36 | 2020 |
| Asymptotically compatible schemes for robust discretization of parametrized problems with applications to nonlocal models X Tian, Q Du SIAM Review 62 (1), 199-227, 2020 | 36 | 2020 |
| Robust a posteriori stress analysis for quadrature collocation approximations of nonlocal models via nonlocal gradients Q Du, Y Tao, X Tian, J Yang Computer Methods in Applied Mechanics and Engineering 310, 605-627, 2016 | 34 | 2016 |
| Nonlocal models with heterogeneous localization and their application to seamless local-nonlocal coupling Y Tao, X Tian, Q Du Multiscale Modeling & Simulation 17 (3), 1052-1075, 2019 | 32 | 2019 |
| The double adaptivity paradigm:(How to circumvent the discrete inf–sup conditions of Babuška and Brezzi) L Demkowicz, T Führer, N Heuer, X Tian Computers & Mathematics with Applications 95, 41-66, 2021 | 25 | 2021 |
| A meshfree peridynamic model for brittle fracture in randomly heterogeneous materials Y Fan, H You, X Tian, X Yang, X Li, N Prakash, Y Yu Computer Methods in Applied Mechanics and Engineering 399, 115340, 2022 | 24 | 2022 |
Qiang DuFu Foundation Professor of Applied Mathematics, Columbia University確認したメール アドレス: columbia.edu