Asymptotically compatible discretization of multidimensional nonlocal diffusion models and approximation of nonlocal Green’s functions

Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications

(2017) Qiang Du et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Robust a posteriori stress analysis for quadrature collocation approximations of nonlocal models via nonlocal gradients

(2016) Qiang Du et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Analysis of a nonlocal-in-time parabolic equation

(2016) Qiang Du et al.   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B

Static and Dynamic Green’s Functions in Peridynamics

(2016) Linjuan Wang et al.   JOURNAL OF ELASTICITY

The Green’s functions for peridynamic non-local diffusion

(2016) L. J. Wang et al.   PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

Asymptotically Compatible Fourier Spectral Approximations of Nonlocal Allen--Cahn Equations

(2016) Qiang Du et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

A meshfree unification: reproducing kernel peridynamics

(2014) M. A. Bessa et al.   COMPUTATIONAL MECHANICS

Critical thresholds in flocking hydrodynamics with non-local alignment

(2014) E. Tadmor et al.   PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

Asymptotically Compatible Schemes and Applications to Robust Discretization of Nonlocal Models

(2014) Xiaochuan Tian et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Nonlocal Constrained Value Problems for a Linear Peridynamic Navier Equation

(2013) Tadele Mengesha et al.   JOURNAL OF ELASTICITY

Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations

(2013) Xiaochuan Tian et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Local and global minimizers for a variational energy involving a fractional norm

(2012) Giampiero Palatucci et al.   ANNALI DI MATEMATICA PURA ED APPLICATA

A NONLOCAL VECTOR CALCULUS, NONLOCAL VOLUME-CONSTRAINED PROBLEMS, AND NONLOCAL BALANCE LAWS

(2012) QIANG DU et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

Continuous and discontinuous finite element methods for a peridynamics model of mechanics

(2010) X. Chen et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Mathematical analysis for the peridynamic nonlocal continuum theory

(2010) Qiang Du et al.   ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE

Crack nucleation in a peridynamic solid

(2010) S. A. Silling et al.   INTERNATIONAL JOURNAL OF FRACTURE

The peridynamic formulation for transient heat conduction

(2010) Florin Bobaru et al.   INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER

Coupling of peridynamic theory and the finite element method

(2010) Bahattin Kilic et al.   Journal of Mechanics of Materials and Structures

Mathematical and Numerical Analysis of Linear Peridynamic Models with Nonlocal Boundary Conditions

(2010) Kun Zhou et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Image Denoising Methods. A New Nonlocal Principle

(2010) A. Buades et al.   SIAM REVIEW

Image Recovery via Nonlocal Operators

(2009) Yifei Lou et al.   JOURNAL OF SCIENTIFIC COMPUTING

Convergence, adaptive refinement, and scaling in 1D peridynamics

(2008) Florin Bobaru et al.   INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

Nonlocal Operators with Applications to Image Processing

(2008) Guy Gilboa et al.   MULTISCALE MODELING & SIMULATION