Fetching the paper…
Reading the bibliography…
In this paper we present an asymptotically compatible meshfree method for solving nonlocal equations with random coefficients, describing diffusion in heterogeneous media.
K. Dayal, K. Bhattacharya, A real-space non-local phase-field model of ferroelectric domain patterns in complex geometries, Acta Materialia 55 (6) (2007) 1907–1917
1917
Earlier work this paper cites.
G. Zhang, M. Gunzburger, Error analysis of a stochastic collocation method for parabolic partial differential equations with random input data, SIAM Journal on Numerical Analysis 50 (4) (2012) 1922–1940
1940
Earlier work this paper cites.
S. A. Smolyak, Quadrature and interpolation formulas for tensor products of certain classes of functions, in: Doklady Akademii Nauk, Vol. 148, Russian Academy of Sciences, 1963, pp. 1042–1045
1963
Earlier work this paper cites.
M. Stein, Large sample properties of simulations using latin hypercube sampling, Technometrics 29 (2) (1987) 143–151
1987
Earlier work this paper cites.
H. Niederreiter, Random number generation and quasi-Monte Carlo methods, SIAM, 1992
1992
Earlier work this paper cites.
E. Novak, K. Ritter, High dimensional integration of smooth functions over cubes, Numerische Mathematik 75 (1) (1996) 79–97
1996
Earlier work this paper cites.
I. Podlubny, Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Vol. 198, Academic Press, 1998
1998
Earlier work this paper cites.
G. Dagan, Comment on “renormalization group analysis of macrodispersion in a directed random flow” by u. jaekel and h. vereecken, Water resources research 34 (11) (1998) 3197–3198
1998
Earlier work this paper cites.
B. L. Fox, Strategies for Quasi-Monte Carlo, Vol. 22, Springer Science & Business Media, 1999
1999
Earlier work this paper cites.
E. Novak, K. Ritter, Simple cubature formulas with high polynomial exactness, Constructive approximation 15 (4) (1999) 499–522
1999
Earlier work this paper cites.
S. A. Silling, Reformulation of elasticity theory for discontinuities and long-range forces, Journal of the Mechanics and Physics of Solids 48 (1) (2000) 175–209
2000
Earlier work this paper cites.
Z. P. Baz̆ant, M. Jirásek, Nonlocal integral formulations of plasticity and damage: survey of progress, Journal of Engineering Mechanics 128 (11) (2002) 1119–1149
2002
Earlier work this paper cites.
2002
Earlier work this paper cites.
D. Xiu, G. E. Karniadakis, The wiener–askey polynomial chaos for stochastic differential equations, SIAM journal on scientific computing 24 (2) (2002) 619–644
2002
Earlier work this paper cites.
L. C. Evans, Partial Differential Equations (Graduate Studies in Mathematics, Vol. 19), American Mathematical Society, Providence, Rhode Island, 2002
2002
Earlier work this paper cites.
R. G. Ghanem, P. D. Spanos, Stochastic finite elements: a spectral approach, Courier Corporation, 2003
2003
Earlier work this paper cites.
I. Babuska, R. Tempone, G. E. Zouraris, Galerkin finite element approximations of stochastic elliptic partial differential equations, SIAM Journal on Numerical Analysis 42 (2) (2004) 800–825
2004
Earlier work this paper cites.
O. Le Maıtre, O. Knio, H. Najm, R. Ghanem, Uncertainty propagation using wiener–haar expansions, Journal of computational Physics 197 (1) (2004) 28–57
2004
Earlier work this paper cites.
H. Wendland, Scattered data approximation, Vol. 17, Cambridge university press, 2004
2004
Earlier work this paper cites.
M. Zimmermann, A continuum theory with long-range forces for solids, Ph.D. thesis, Massachusetts Institute of Technology (2005)
2005
Earlier work this paper cites.
X. Antoine, H. Barucq, Approximation by generalized impedance boundary conditions of a transmission problem in acoustic scattering, ESAIM: Mathematical Modelling and Numerical Analysis 39 (5) (2005) 1041–1059
2005
Earlier work this paper cites.
S. A. Silling, E. Askari, A meshfree method based on the peridynamic model of solid mechanics, Computers & structures 83 (17-18) (2005) 1526–1535
2005
Earlier work this paper cites.
I. Babuška, R. Tempone, G. E. Zouraris, Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation, Computer methods in applied mechanics and engineering 194 (12-16) (2005) 1251–1294
2005
Earlier work this paper cites.
H. G. Matthies, A. Keese, Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations, Computer methods in applied mechanics and engineering 194 (12-16) (2005) 1295–1331
2005
Earlier work this paper cites.
X. Wan, G. E. Karniadakis, An adaptive multi-element generalized polynomial chaos method for stochastic differential equations, Journal of Computational Physics 209 (2) (2005) 617–642
2005
Cited alongside, same era.
D. Xiu, J. S. Hesthaven, High-order collocation methods for differential equations with random inputs, SIAM Journal on Scientific Computing 27 (3) (2005) 1118–1139
2005
Cited alongside, same era.
R. L. Magin, Fractional calculus in bioengineering, Begell House Publishers Inc., Redding, CT, 2006
2006
Cited alongside, same era.
E. Emmrich, O. Weckner, Analysis and numerical approximation of an integro-differential equation modeling non-local effects in linear elasticity, Mathematics and Mechanics of Solids 12 (4) (2007) 363–384
2007
Cited alongside, same era.
E. Emmrich, O. Weckner, et al., On the well-posedness of the linear peridynamic model and its convergence towards the navier equation of linear elasticity, Communications in Mathematical Sciences 5 (4) (2007) 851–864
T. Mengesha, Q. Du, The bond-based peridynamic system with dirichlet-type volume constraint, Proc. Roy. Soc. Edinburgh Sect. A 144 (1) (2014) 161–186
2014
Later among the works it cites.
O. Defterli, M. D’Elia, Q. Du, M. Gunzburger, R. Lehoucq, M. M. Meerschaert, Fractional diffusion on bounded domains, Fractional Calculus and Applied Analysis 18 (2) (2015) 342–360
2015
Later among the works it cites.
Q. Du, R. Lipton, T. Mengesha, Multiscale analysis of linear evolution equations with applications to nonlocal models for heterogeneous media, ESAIM: Mathematical Modelling and Numerical Analysis 50 (5) (2016) 1425–1455
2016
Later among the works it cites.
C. Bucur, E. Valdinoci, Nonlocal diffusion and applications, Vol. 20, Springer, 2016
2016
Later among the works it cites.
P. Seleson, D. J. Littlewood, Convergence studies in meshfree peridynamic simulations, Computers & Mathematics with Applications 71 (11) (2016) 2432–2448
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2007
Cited alongside, same era.
G. Rozza, D. B. P. Huynh, A. T. Patera, Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations, Archives of Computational Methods in Engineering 15 (3) (2007) 1
2007
Cited alongside, same era.
G. Rozza, K. Veroy, On the stability of the reduced basis method for stokes equations in parametrized domains, Computer methods in applied mechanics and engineering 196 (7) (2007) 1244–1260
2007
Cited alongside, same era.
F. Nobile, R. Tempone, C. G. Webster, An anisotropic sparse grid stochastic collocation method for partial differential equations with random input data, SIAM Journal on Numerical Analysis 46 (5) (2008) 2411–2442
2008
Cited alongside, same era.
X. Ma, N. Zabaras, An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations, Journal of Computational Physics 228 (8) (2009) 3084–3113
2009
Cited alongside, same era.
G. Lin, A. M. Tartakovsky, An efficient, high-order probabilistic collocation method on sparse grids for three-dimensional flow and solute transport in randomly heterogeneous porous media, Advances in Water Resources 32 (5) (2009) 712–722
2009
Cited alongside, same era.
F. Bobaru, M. Yang, L. F. Alves, S. A. Silling, E. Askari, J. Xu, Convergence, adaptive refinement, and scaling in 1d peridynamics, International Journal for Numerical Methods in Engineering 77 (6) (2009) 852–877
2009
Cited alongside, same era.
K. Zhou, Q. Du, Mathematical and numerical analysis of linear peridynamic models with nonlocal boundary conditions, SIAM Journal on Numerical Analysis 48 (5) (2010) 1759–1780
2010
Cited alongside, same era.
2016
Later among the works it cites.
Q. Du, Local limits and asymptotically compatible discretizations, Handbook of peridynamic modeling (2016) 87–108
2016
Later among the works it cites.
Y. Tao, X. Tian, Q. Du, Nonlocal diffusion and peridynamic models with neumann type constraints and their numerical approximations, Applied Mathematics and Computation 305 (2017) 282–298
2017
Later among the works it cites.
Q. Guan, M. Gunzburger, C. G. Webster, G. Zhang, Reduced basis methods for nonlocal diffusion problems with random input data, Computer Methods in Applied Mechanics and Engineering 317 (2017) 746–770
2017
Later among the works it cites.
H. Tran, C. G. Webster, G. Zhang, Analysis of quasi-optimal polynomial approximations for parameterized pdes with deterministic and stochastic coefficients, Numerische Mathematik 137 (2) (2017) 451–493
2017
Later among the works it cites.
F. A. Chiarello, P. Goatin, Global entropy weak solutions for general non-local traffic flow models with anisotropic kernel, ESAIM: Mathematical Modelling and Numerical Analysis 52 (1) (2018) 163–180
2018
Later among the works it cites.
H. A. Erbay, S. Erbay, A. Erkip, Convergence of a semi-discrete numerical method for a class of nonlocal nonlinear wave equations, ESAIM: Mathematical Modelling and Numerical Analysis 52 (3) (2018) 803–826
2018
Later among the works it cites.
Y. Yu, F. F. Bargos, H. You, M. L. Parks, M. L. Bittencourt, G. E. Karniadakis, A partitioned coupling framework for peridynamics and classical theory: Analysis and simulations, Computer Methods in Applied Mechanics and Engineering 340 (2018) 905–931
2018
Later among the works it cites.
M. Pasetto, Y. Leng, J.-S. Chen, J. T. Foster, P. Seleson, A reproducing kernel enhanced approach for peridynamic solutions, Computer Methods in Applied Mechanics and Engineering 340 (2018) 1044–1078
2018
Later among the works it cites.
N. Trask, H. You, Y. Yu, M. L. Parks, An asymptotically compatible meshfree quadrature rule for nonlocal problems with applications to peridynamics, Computer Methods in Applied Mechanics and Engineering 343 (2019) 151–165
2019
Later among the works it cites.
M. Hillman, M. Pasetto, G. Zhou, Generalized reproducing kernel peridynamics: unification of local and non-local meshfree methods, non-local derivative operations, and an arbitrary-order state-based peridynamic formulation, Computational Particle Mechanics 7 (2) (2020) 435–469
2020
Later among the works it cites.
H. You, X. Lu, N. Task, Y. Yu, An asymptotically compatible approach for neumann-type boundary condition on nonlocal problems, ESAIM: Mathematical Modelling and Numerical Analysis 54 (4) (2020) 1373–1413
2020
Later among the works it cites.
H. You, Y. Yu, D. Kamensky, An asymptotically compatible formulation for local-to-nonlocal coupling problems without overlapping regions, Computer Methods in Applied Mechanics and Engineering 366 (2020) 113038
2020
Later among the works it cites.
J. Zhao, Z. Chen, J. Mehrmashhadi, F. Bobaru, A stochastic multiscale peridynamic model for corrosion-induced fracture in reinforced concrete, Engineering Fracture Mechanics (2020) 106969
2020
Later among the works it cites.
H. You, Y. Yu, N. Trask, M. Gulian, M. D’Elia, Data-driven learning of nonlocal physics from high-fidelity synthetic data, Computer Methods in Applied Mechanics and Engineering 374 (2021) 113553
2021
Closest in time.
Y. Leng, X. Tian, N. Trask, J. T. Foster, Asymptotically compatible reproducing kernel collocation and meshfree integration for nonlocal diffusion, SIAM Journal on Numerical Analysis 59 (1) (2021) 88–118
2021
Closest in time.
Y. Yu, H. You, N. Trask, An asymptotically compatible treatment of traction loading in linearly elastic peridynamic fracture, Computer Methods in Applied Mechanics and Engineering 377 (2021) 113691
2021
Closest in time.
S. A. Silling, Propagation of a stress pulse in a heterogeneous elastic bar, Journal of Peridynamics and Nonlocal Modeling (2021) 1–21
2021
Closest in time.
W.-L. Loh, et al., On latin hypercube sampling, Annals of statistics 24 (5) (1996) 2058–2080
2080
Closest in time.