12 citations · 27 across the 13 of their papers we have counts for
7 papers · 1 filter
Discovery of Dynamics Using Linear Multistep Methods
Rachael Keller, Qiang Du
Linear multistep methods (LMMs) are popular time discretization techniques for the numerical solution of differential equations. Traditionally they are applied to solve for the sta…
Variational Phase Field Formulations of Polarization and Phase Transition in Ferroelectric Thin Films
Qiang Du, Ruotai Li, Lei Zhang
Electric field plays an important role in ferroelectric phase transition. There have been numerous phase field formulations attempting to account for electrostatic interactions sub…
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…
Time-Fractional Allen-Cahn Equations: Analysis and Numerical Methods
Qiang Du, Jiang Yang, Zhi Zhou
In this work, we consider a time-fractional Allen-Cahn equation, where the conventional first order time derivative is replaced by a Caputo fractional derivative with order $α\in(0…
Nonlocal gradient operators with a nonspherical interaction neighborhood and their applications
Hwi Lee, Qiang Du
Nonlocal gradient operators are prototypical nonlocal differential operators thatare very important in the studies of nonlocal models. One of the simplest variational settings for…
A cooperative game for automated learning of elasto-plasticity knowledge graphs and models with AI-guided experimentation
Kun Wang, WaiChing Sun, Qiang Du
We introduce a multi-agent meta-modeling game to generate data, knowledge, and models that make predictions on constitutive responses of elasto-plastic materials. We introduce a ne…