3 citations · 3 across the 6 of their papers we have counts for
4 papers · 1 filter
Weighted nonlocal operators and their applications in semi-supervised learning
Qiang Du, James M. Scott
Motivated by problems in machine learning, we study a class of variational problems characterized by nonlocal operators. These operators are characterized by power-type weights, wh…
Numerical analysis of a class of penalty discontinuous Galerkin methods for nonlocal diffusion problems
Qiang Du, Lili Ju, Jianfang Lu +1
In this paper, we consider a class of discontinuous Galerkin (DG) methods for one-dimensional nonlocal diffusion (ND) problems. The nonlocal models, which are integral equations, a…
Asymptotically compatible schemes for nonlinear variational models via Gamma-convergence and applications to nonlocal problems
Qiang Du, James M. Scott, Xiaochuan Tian
We present a study on asymptotically compatible Galerkin discretizations for a class of parametrized nonlinear variational problems. The abstract analytical framework is based on v…
Ohta-Kawasaki energy for amphiphiles: asymptotics and phase-field simulations
Qiang Du, James M. Scott, Zirui Xu
We study the minimizers of a degenerate case of the Ohta-Kawasaki energy, defined as the sum of the perimeter and a Coulombic nonlocal term. We start by investigating radially symm…