202 citations · 748 across the 55 of their papers we have counts for
60 papers
An Adaptive and Physics-Preserving Multiscale Method for Two-Phase Flow Simulations in High-Contrast Heterogeneous Porous Media
Junhao Huang, Eric Chung, Wing Tat Leung
In this paper, we propose an adaptive physics-preserving multiscale method for incompressible and immiscible two-phase flow in high-contrast porous media. The method couples a phys…
Multiscale modeling for problems with high contrast heterogeneous coefficients by the CEM-GMsFEM
Eric T. Chung, Yalchin Efendiev, Xingguang Jin +2
This review paper provides a comprehensive overview of the Constrained Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for solving elliptic PDEs charact…
Multicontinuum Generalized Multiscale Finite Element Method (MC-GMsFEM). Theory and applications to upscaling of two-phase flow
Mohammed Al Kobaisi, Dmitry Ammosov, Yalchin Efendiev +1
We develop a multicontinuum Generalized Multiscale Finite Element Method (MC-GMsFEM) for constructing coarse-scale models in heterogeneous media that simultaneously provide accurat…
Multicontinuum Homogenization for Coupled Flow and Transport Equations
Dmitry Ammosov, W. T. Leung, Buzheng Shan +1
In this paper, we present the derivation of a multicontinuum model for the coupled flow and transport equations by applying multicontinuum homogenization. We perform the multiconti…
Multicontinuum homogenization in perforated domains
Wei Xie, Yalchin Efendiev, Yunqing Huang +2
In this paper, we develop a general framework for multicontinuum homogenization in perforated domains. The simulations of problems in perforated domains are expensive and, in many…
Partially explicit splitting scheme with explicit-implicit-null method for nonlinear multiscale flow problems
Yating Wang, Wing Tat Leung
In this work, we present an efficient approach to solve nonlinear high-contrast multiscale diffusion problems. We incorporate the explicit-implicit-null (EIN) method to separate th…
Some convergence analysis for multicontinuum homogenization
Wing Tat Leung
In this paper, we provide an analysis of a recently proposed multicontinuum homogenization technique. The analysis differs from those used in classical homogenization methods for s…
Partially Explicit Generalized Multiscale Method for Poroelasticity Problem
Xin Su, Wing Tat Leung, Wenyuan Li +1
We develop a partially explicit time discretization based on the framework of constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) for the problem…
Multicontinuum homogenization. General theory and applications
E. Chung, Y. Efendiev, J. Galvis +1
In this paper, we discuss a general framework for multicontinuum homogenization. Multicontinuum models are widely used in many applications and some derivations for these models ar…
Bayesian deep operator learning for homogenized to fine-scale maps for multiscale PDE
Zecheng Zhang, Christian Moya, Wing Tat Leung +2
We present a new framework for computing fine-scale solutions of multiscale Partial Differential Equations (PDEs) using operator learning tools. Obtaining fine-scale solutions of m…
A discretization-invariant extension and analysis of some deep operator networks
Zecheng Zhang, Wing Tat Leung, Hayden Schaeffer
We present a generalized version of the discretization-invariant neural operator and prove that the network is a universal approximation in the operator sense. Moreover, by incorpo…
Hybrid explicit-implicit learning for multiscale problems with time dependent source
Yalchin Efendiev, Wing Tat Leung, Wenyuan Li +1
The splitting method is a powerful method for solving partial differential equations. Various splitting methods have been designed to separate different physics, nonlinearities, an…
Multicontinuum homogenization and its relation to nonlocal multicontinuum theories
Yalchin Efendiev, Wing Tat Leung
In this paper, we present a general derivation of multicontinuum equations and discuss cell problems. We present constraint cell problem formulations in a representative volume ele…
Nonlocal transport equations in multiscale media. Modeling, dememorization, and discretizations
Yalchin Efendiev, Wing Tat Leung, Wenyuan Li +2
In this paper, we consider a class of convection-diffusion equations with memory effects. These equations arise as a result of homogenization or upscaling of linear transport equat…
Partially Explicit Time Discretization for Nonlinear Time Fractional Diffusion Equations
Wenyuan Li, Anatoly Alikhanov, Yalchin Efendiev +1
Nonlinear time fractional partial differential equations are widely used in modeling and simulations. In many applications, there are high contrast changes in media properties. For…
Continuous data assimilation for two-phase flow: analysis and simulations
Yat Tin Chow, Wing Tat Leung, Ali Pakzad
We propose, analyze, and test a novel continuous data assimilation two-phase flow algorithm for reservoir simulation. We show that the solutions of the algorithm, constructed using…
HEI: hybrid explicit-implicit learning for multiscale problems
Yalchin Efendiev, Wing Tat Leung, Guang Lin +1
Splitting is a method to handle application problems by splitting physics, scales, domain, and so on. Many splitting algorithms have been designed for efficient temporal discretiza…
Partially Explicit Time Discretization for Time Fractional Diffusion Equation
Jiuhua Hu, Anatoly Alikhanov, Yalchin Efendiev +1
Time fractional PDEs have been used in many applications for modeling and simulations. Many of these applications are multiscale and contain high contrast variations in the media p…
NH-PINN: Neural homogenization based physics-informed neural network for multiscale problems
Wing Tat Leung, Guang Lin, Zecheng Zhang
Physics-informed neural network (PINN) is a data-driven approach to solve equations. It is successful in many applications; however, the accuracy of the PINN is not satisfactory wh…
Contrast-independent partially explicit time discretizations for nonlinear multiscale problems
Eric T. Chung, Yalchin Efendiev, Wing Tat Leung +1
This work continues a line of works on developing partially explicit methods for multiscale problems. In our previous works, we have considered linear multiscale problems, where th…
Space-time Non-local multi-continua upscaling for parabolic equations with moving channelized media
Jiuhua Hu, Wing Tat Leung, Eric Chung +2
In this paper, we consider a parabolic problem with time-dependent heterogeneous coefficients. Many applied problems have coupled space and time heterogeneities. Their homogenizati…
Contrast-independent partially explicit time discretizations for multiscale wave problems
Eric T. Chung, Yalchin Efendiev, Wing Tat Leung +1
In this work, we design and investigate contrast-independent partially explicit time discretizations for wave equations in heterogeneous high-contrast media. We consider multiscale…
Contrast-independent partially explicit time discretizations for multiscale flow problems
Eric T. Chung, Yalchin Efendiev, Wing Tat Leung +1
Many multiscale problems have a high contrast, which is expressed as a very large ratio between the media properties. The contrast is known to introduce many challenges in the desi…
Multi-agent Reinforcement Learning Accelerated MCMC on Multiscale Inversion Problem
Eric Chung, Yalchin Efendiev, Wing Tat Leung +2
In this work, we propose a multi-agent actor-critic reinforcement learning (RL) algorithm to accelerate the multi-level Monte Carlo Markov Chain (MCMC) sampling algorithms. The pol…