209 citations · 348 across the 22 of their papers we have counts for
5 papers · 1 filter
A review of Local-to-Nonlocal coupling methods in nonlocal diffusion and nonlocal mechanics
Marta D'Elia, Xingjie Li, Pablo Seleson +2
Local-to-Nonlocal (LtN) coupling refers to a class of methods aimed at combining nonlocal and local modeling descriptions of a given system into a unified coupled representation. T…
Multiscale Modeling, Homogenization and Nonlocal Effects: Mathematical and Computational Issues
Qiang Du, Bjorn Engquist, Xiaochuan Tian
In this work, we review the connection between the subjects of homogenization and nonlocal modeling and discuss the relevant computational issues. By further exploring this connect…
Asymptotically compatible reproducing kernel collocation and meshfree integration for nonlocal diffusion
Yu Leng, Xiaochuan Tian, Nathaniel Trask +1
Reproducing kernel (RK) approximations are meshfree methods that construct shape functions from sets of scattered data. We present an asymptotically compatible (AC) RK collocation…
A physically-consistent, flexible and efficient strategy to convert local boundary conditions into nonlocal volume constraints
Marta D'Elia, Xiaochuan Tian, Yue Yu
Nonlocal models provide exceptional simulation fidelity for a broad spectrum of scientific and engineering applications. However, wider deployment of nonlocal models is hindered by…
Fast algorithm for computing nonlocal operators with finite interaction distance
Xiaochuan Tian, Bjorn Engquist
Developments of nonlocal operators for modeling processes that traditionally have been described by local differential operators have been increasingly active during the last few y…