6 citations · 8 across the 6 of their papers we have counts for
6 papers
Nonlocal problems with local boundary conditions II: Green's identities and regularity of solutions
James M. Scott, Qiang Du
We study nonlocal integral equations on bounded domains with finite-range nonlocal interactions that are localized at the boundary. We establish a Green's identity for the nonlocal…
Nonlocal problems with local boundary conditions I: function spaces and variational principles
James M. Scott, Qiang Du
We present a systematic study on a class of nonlocal integral functionals for functions defined on a bounded domain and the naturally induced function spaces. The function spaces a…
Discontinuous Galerkin methods for a first-order semi-linear hyperbolic continuum model of a topological resonator dimer array
Qiang Du, Huaiyu Li, Michael Weinstein +1
We present discontinuous Galerkin (DG) methods for solving a first-order semi-linear hyperbolic system, which was originally proposed as a continuum model for a one-dimensional dim…
Convergence analysis for a nonlocal gradient descent method via directional Gaussian smoothing
Hoang Tran, Qiang Du, Guannan Zhang
We analyze the convergence of a nonlocal gradient descent method for minimizing a class of high-dimensional non-convex functions, where a directional Gaussian smoothing (DGS) is pr…
Nonlocal boundary-value problems with local boundary conditions
James M. Scott, Qiang Du
We describe and analyze nonlocal integro-differential equations with classical local boundary conditions. The interaction kernel of the nonlocal operator has horizon parameter depe…
Discovering State Variables Hidden in Experimental Data
Boyuan Chen, Kuang Huang, Sunand Raghupathi +3
All physical laws are described as relationships between state variables that give a complete and non-redundant description of the relevant system dynamics. However, despite the pr…