Fetching the paper…
Reading the bibliography…
We develop and analyze an optimization-based method for the coupling of a static peri-dynamic (PD) model and a static classical elasticity model.
Application of a fractional advection-dispersion equation
D.A. Benson, S.W. Wheatcraft, and M.M. Meerschaert · 2000
Earlier work this paper cites.
The random walk’s guide to anomalous diffusion: a fractional dynamics approach
R. Metzler and J. Klafter · 2000
Earlier work this paper cites.
Reformulation of elasticity theory for discontinuities and long-range forces
S.A. Silling · 2000
Earlier work this paper cites.
Reformulation of elasticity theory for discontinuities and long-range forces
S.A. Silling · 2000
Earlier work this paper cites.
Eulerian derivation of the fractional advection-dispersion equation
R. Schumer, D.A. Benson, M.M. Meerschaert, and S.W. Wheatcraft · 2001
Earlier work this paper cites.
Some nonclassical trends in parabolic and parabolic-like evolutions
P. Fife · 2003
Earlier work this paper cites.
Multiscaling fractional advection-dispersion equations and their solutions
R. Schumer, D.A. Benson, M.M. Meerschaert, and B. Baeumer · 2003
Earlier work this paper cites.
A meshfree method based on the peridynamic model of solid mechanics
S. A Silling and E. Askari · 2005
Earlier work this paper cites.
A meshfree method based on the peridynamic model of solid mechanics
S.A. Silling and E. Askari · 2005
Earlier work this paper cites.
Nonlocal linear image regularization and supervised segmentation
G. Gilboa and S. Osher · 2007
Earlier work this paper cites.
Peridynamic states and constitutive modeling
S. Silling, M. Epton, O. Weckner, J. Xu, and E. Askari · 2007
Earlier work this paper cites.
Image denoising methods. a new nonlocal principle
A. A. Buades, B. Coll, and J.M. Morel · 2010
Earlier work this paper cites.
A direct 𝒪 ( N log 2 N ) \mathcal{O}(N\log^{2}\!N) finite difference method for fractional diffusion equations
H. Wang, K. Wang, and T. Sircar · 2010
Earlier work this paper cites.
Continuous and discontinuous finite element methods for a peridynamics model of mechanics
Xi Chen and Max Gunzburger · 2011
Earlier work this paper cites.
Characteristics of dynamic brittle fracture captured with peridynamics
Youn Doh Ha and Florin Bobaru · 2011
Earlier work this paper cites.
On the role of the influence function in the peridynamic theory
P. Seleson and M.L. Parks · 2011
Earlier work this paper cites.
Coupling of nonlocal and local continuum models by the Arlequin approach
Fei Han and Gilles Lubineau · 2012
Earlier work this paper cites.
A morphing strategy to couple non-local to local continuum mechanics
G. Lubineau, Y. Azdoud, F. Han, C. Rey, and A. Askari · 2012
Earlier work this paper cites.
Stochastic models for fractional calculus
M.M. Meerschaert and A. Sikorskii · 2012
Earlier work this paper cites.
Peridigm Users’ Guide v1.0.0
M.L. Parks, D.J. Littlewood, J.A. Mitchell, and S.A. Silling · 2012
Earlier work this paper cites.
Albany: A component–based partial differential equation code built on Trilinos
A.G. Salinger, R.A. Bartlett, Q. Chen, X. Gao, G.A. Hansen, I. Kalashnikova, A. Mota, R.P. Muller, E. Nielsen, J.T. Ostien, R.P. Pawlowski, E.T. Phipps, and W. Sun · 2013
Earlier work this paper cites.
A force-based coupling scheme for peridynamics and classical elasticity
P. Seleson, S. Beneddine, and S. Prudhomme · 2013
Earlier work this paper cites.
Interface problems in nonlocal diffusion and sharp transitions between local and nonlocal domains
Pablo Seleson, Max Gunzburger, and Michael L Parks · 2013
Earlier work this paper cites.
The exit-time problem for a markov jump process
N. Burch, M. D’Elia, and R. Lehoucq · 2014
Cited alongside, same era.
Optimization-based coupling of nonlocal and local diffusion models
M. D’Elia and P. Bochev · 2014
Cited alongside, same era.
Peridynamics and material interfaces
B. Alali and M. Gunzburger · 2015
Cited alongside, same era.
Fractional diffusion on bounded domains
O. Defterli, M D’Elia, Q. Du, M. Gunzburger, R. Lehoucq, and M. M. Meerschaert · 2015
Cited alongside, same era.
Non-local formulation for multiscale flow in porous media
A.H. Delgoshaie, D.W. Meyer, P. Jenny, and H. Tchelepi · 2015
Cited alongside, same era.
Roadmap for peridynamic software implementation
D.J. Littlewood · 2015
Cited alongside, same era.
An asymptotically compatible meshfree quadrature rule for nonlocal problems with applications to peridynamics
Nathaniel Trask, Huaiqian You, Yue Yu, and Michael L Parks · 2019
Later among the works it cites.
Concurrent coupling of peridynamics and classical elasticity for elastodynamic problems
X. Wang, S.S. Kulkarni, and A. Tabarraei · 2019
Later among the works it cites.
Numerical methods for nonlocal and fractional models
M. D’Elia, Q. Du, C. Glusa, M. Gunzburger, X. Tian, and Z. Zhou · 2020
Later among the works it cites.
Helmholtz-Hodge decompositions in the nonlocal framework. well-posedness analysis and applications
M. D’Elia, C. Flores, X. Li, P. Radu, and Y. Yu · 2020
Later among the works it cites.
A unified theory of fractional, nonlocal, and weighted nonlocal vector calculus
M. D’Elia, M. Gulian, H. Olson, and G. E. Karniadakis · 2020
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Concurrent coupling of bond-based peridynamics and the navier equation of classical elasticity by blending
P. Seleson, Y.-D. Ha, and S. Beneddine · 2015
Cited alongside, same era.
Variable horizon in a peridynamic medium
S. Silling, D. Littlewood, and P. Seleson · 2015
Cited alongside, same era.
A coupling strategy for nonlocal and local diffusion models with mixed volume constraints and boundary conditions
M. D’Elia, M. Perego, P. Bochev, and D.J. Littlewood · 2016
Cited alongside, same era.
An effective way to couple FEM meshes and peridynamics grids for the solution of static equilibrium problems
U. Galvanetto, T. Mudric, A. Shojaei, and M. Zaccariotto · 2016
Cited alongside, same era.
A morphing approach to couple state-based peridynamics with classical continuum mechanics
F. Han, G. Lubineau, Y. Azdoud, and A. Askari · 2016
Cited alongside, same era.
Convergence studies in meshfree peridynamic simulations
P. Seleson and D.J. Littlewood · 2016
Cited alongside, same era.
A cookbook for finite element methods for nonlocal problems, including quadrature rule choices and the use of approximate neighborhoods
M. D’Elia, M. Gunzburger, and C. Vollman · 2020
Later among the works it cites.
A physically-consistent, flexible and efficient strategy to convert local boundary conditions into nonlocal volume constraints
M. D’Elia, X. Tian, and Y. Yu · 2020
Later among the works it cites.
nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications
G. Pang, M. D’Elia, M. Parks, and G. E. Karniadakis · 2020
Later among the works it cites.
An asymptotically compatible formulation for local-to-nonlocal coupling problems without overlapping regions
H. You, Y. Yu, and D. Kamensky · 2020
Later among the works it cites.
An asymptotically compatible approach for neumann-type boundary condition on nonlocal problems
Huaiqian You, XinYang Lu, Nathaniel Task, and Yue Yu · 2020
Later among the works it cites.
Efficient quadrature rules for finite element discretizations of nonlocal equations
E. Aulisa, G. Capodaglio, A. Chierici, and M. D’Elia · 2021
Closest in time.
On a nonlocal Cahn-Hilliard model permitting sharp interfaces
O. Burkovska and M. Gunzburger · 2021
Closest in time.
G. Capodaglio, M. D’Elia, M. Gunzburger, P. Bochev, M. Klar, and C. Vollmann · 2021
Closest in time.
Two-point stress–strain-rate correlation structure and non-local eddy viscosity in turbulent flows
Patricio Clark Di Leoni, Tamer A. Zaki, George Karniadakis, and Charles Meneveau · 2021
Closest in time.
M. D’Elia and M. Gulian · 2021
Closest in time.
Bilevel parameter optimization for nonlocal image denoising model
M. D’Elia, J.C. De los Reyes, and A. Trujillo · 2021
Closest in time.
On the prescription of boundary conditions for nonlocal poisson’s and peridynamics models
Marta D’Elia and Yue Yu · 2021
Closest in time.
Formulation, analysis and computation of an optimization-based local-to-nonlocal coupling method
Marta D’Elia and Pavel Bochev · 2021
Closest in time.
An asymptotically compatible probabilistic collocation method for randomly heterogeneous nonlocal problems
Yiming Fan, Xiaochuan Tian, Xiu Yang, Xingjie Li, Clayton Webster, and Yue Yu · 2021
Closest in time.
Convergence analysis and numerical studies for linearly elastic peridynamics with dirichlet-type boundary conditions
Mikil Foss, Petronela Radu, and Yue Yu · 2021
Closest in time.
A feti approach to domain decomposition for meshfree discretizations of nonlocal problems
X. Xu, C. Glusa, M. D’Elia, and J.T. Foster · 2021
Closest in time.
An asymptotically compatible treatment of traction loading in linearly elastic peridynamic fracture
Yue Yu, Huaiqian You, and Nathaniel Trask · 2021
Closest in time.