73 citations · 253 across the 29 of their papers we have counts for
30 papers
Towards a unified nonlocal, peridynamics framework for the coarse-graining of molecular dynamics data with fractures
Huaiqian You, Xiao Xu, Yue Yu +3
Molecular dynamics (MD) has served as a powerful tool for designing materials with reduced reliance on laboratory testing. However, the use of MD directly to treat the deformation…
OBMeshfree: An optimization-based meshfree solver for nonlocal diffusion and peridynamics models
Yiming Fan, Huaiqian You, Yue Yu
We present OBMeshfree, an Optimization-Based Meshfree solver for compactly supported nonlocal integro-differential equations (IDEs) that can describe material heterogeneity and bri…
Bayesian Nonlocal Operator Regression (BNOR): A Data-Driven Learning Framework of Nonlocal Models with Uncertainty Quantification
Yiming Fan, Marta D'Elia, Yue Yu +2
We consider the problem of modeling heterogeneous materials where micro-scale dynamics and interactions affect global behavior. In the presence of heterogeneities in material micro…
Hybrid mixed discontinuous Galerkin finite element method for incompressible wormhole propagation problem
Jiansong Zhang, Yun Yu, Jiang Zhu +2
Wormhole propagation plays a very important role in the product enhancement of oil and gas reservoir. A new combined hybrid mixed finite element method is proposed to solve incompr…
Hybrid mixed discontinuous Galerkin finite element method for incompressible miscible displacement problem
Jiansong Zhang, Yun Yu, Jiang Zhu +3
A new hybrid mixed discontinuous Galerkin finite element (HMDGFE) method is constructed for incompressible miscible displacement problem. In this method, the hybrid mixed finite el…
Unified Implementation of Finite Element Methods involving Jumps and Averages in Matlab
Yue Yu
We provide unified implementations of the finite element methods involving jumps and averages in Maltab by combing the use of the software package varFEM, including the adaptive fi…
varFEM: variational formulation based programming for finite element methods in Matlab
Yue Yu
This paper summarizes the development of varFEM, which provides a realization of the programming style in FreeFEM by using the Matlab language.
The Sparse-Grid-Based Adaptive Spectral Koopman Method
Bian Li, Yue Yu, Xiu Yang
The adaptive spectral Koopman (ASK) method was introduced to numerically solve autonomous dynamical systems that lay the foundation of numerous applications across different fields…
Nonparametric learning of kernels in nonlocal operators
Fei Lu, Qingci An, Yue Yu
Nonlocal operators with integral kernels have become a popular tool for designing solution maps between function spaces, due to their efficiency in representing long-range dependen…
mVEM: A MATLAB Software Package for the Virtual Element Methods
Yue Yu
This paper summarizes the development of mVEM, a MATLAB software package containing efficient and easy-following codes for various virtual element methods (VEMs) published in the l…
A Meshfree Peridynamic Model for Brittle Fracture in Randomly Heterogeneous Materials
Yiming Fan, Huaiqian You, Xiaochuan Tian +4
In this work we aim to develop a unified mathematical framework and a reliable computational approach to model the brittle fracture in heterogeneous materials with variability in m…
Time complexity analysis of quantum difference methods for linear high dimensional and multiscale partial differential equations
Shi Jin, Nana Liu, Yue Yu
We investigate time complexities of finite difference methods for solving the high-dimensional linear heat equation, the high-dimensional linear hyperbolic equation and the multisc…
A novel locking-free virtual element method for linear elasticity problems
Jianguo Huang, Sen Lin, Yue Yu
This paper devises a novel lowest-order conforming virtual element method (VEM) for planar linear elasticity with the pure displacement/traction boundary condition. The main trick…
A lowest-order locking-free nonconforming virtual element method based on the reduced integration technique for linear elasticity problems
Yue Yu
We develop a lowest-order nonconforming virtual element method for planar linear elasticity, which can be viewed as an extension of the idea in Falk (1991) to the virtual element m…
An asymptotically compatible probabilistic collocation method for randomly heterogeneous nonlocal problems
Yiming Fan, Xiaochuan Tian, Xiu Yang +3
In this paper we present an asymptotically compatible meshfree method for solving nonlocal equations with random coefficients, describing diffusion in heterogeneous media. In parti…
Nonlocal Trace Spaces and Extension Results for Nonlocal Calculus
Qiang Du, Xiaochuan Tian, Cory Wright +1
For a given Lipschitz domain , it is a classical result that the trace space of is , namely any function has a well-defined $W^…
On the prescription of boundary conditions for nonlocal Poisson's and peridynamics models
Marta D'Elia, Yue Yu
We introduce a technique to automatically convert local boundary conditions into nonlocal volume constraints for nonlocal Poisson's and peridynamic models. The proposed strategy is…
Convergence Analysis and Numerical Studies for Linearly Elastic Peridynamics with Dirichlet-Type Boundary Conditions
Mikil Foss, Petronela Radu, Yue Yu
The nonlocal models of peridynamics have successfully predicted fractures and deformations for a variety of materials. In contrast to local mechanics, peridynamic boundary conditio…
Size-Sieving Separation of Hard-Sphere Mixtures through Cylindrical Pores
Yue Yu, Kai Zhang
The collision dynamics of hard spheres and cylindrical pores is solved exactly, which is the minimal model for a regularly porous membrane. Nonequilibrium event-driven molecular dy…
An asymptotically compatible treatment of traction loading in linearly elastic peridynamic fracture
Yue Yu, Huaiqian You, Nathaniel Trask
Meshfree discretizations of state-based peridynamic models are attractive due to their ability to naturally describe fracture of general materials. However, two factors conspire to…
A sparse grid discrete ordinate discontinuous Galerkin method for the radiative transfer equation
Jianguo Huang, Yue Yu
The radiative transfer equation is a fundamental equation in transport theory and applications, which is a 5-dimensional PDE in the stationary one-velocity case, leading to great d…
Data-driven learning of nonlocal models: from high-fidelity simulations to constitutive laws
Huaiqian You, Yue Yu, Stewart Silling +1
We show that machine learning can improve the accuracy of simulations of stress waves in one-dimensional composite materials. We propose a data-driven technique to learn nonlocal c…
Data-driven learning of robust nonlocal physics from high-fidelity synthetic data
Huaiqian You, Yue Yu, Nathaniel Trask +2
A key challenge to nonlocal models is the analytical complexity of deriving them from first principles, and frequently their use is justified a posteriori. In this work we extract…
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…