3 citations · 3 across the 6 of their papers we have counts for
7 papers
Improving Learning of Green's Functions Through Kernel Decomposition
Beiji Chen, Qiang Du, Kui Ren +1
This work analyzes a framework for learning the solution operator, or equivalently, the Green's function, of a general self-adjoint second-order elliptic operator $\cL$. Subtractin…
On parameterized nonlocal-fractional transmission problems and associated function spaces
Qiang Du, Zhaolong Han, Tadele Mengesha +2
In this paper, we consider a family of seamlessly coupled nonlocal models associated with transmission conditions across an interface. The models are derived from the variation of…
A discontinuous Galerkin method for one-dimensional nonlocal wave problems
Qiang Du, Kui Ren, Lu Zhang +1
This paper presents a fully discrete numerical scheme for one-dimensional nonlocal wave equations and provides a rigorous theoretical analysis. To facilitate the spatial discretiza…
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…