719 citations · 2.3k across the 72 of their papers we have counts for
80 papers
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…
Dynamic nonlinear multicontinuum homogenization of systems with intrinsically evolving microstructure
Mohammed Al-Kobaisi, Dmitry Ammosov, Yalchin Efendiev +2
In this paper, we propose a multicontinuum homogenization approach for nonlinear problems involving dynamically evolving multiscale media. The main idea of the proposed approach is…
Multicontinuum splitting scheme for multiscale flow problems
Yalchin Efendiev, Wing Tat Leung, Buzheng Shan +1
In this paper, we propose multicontinuum splitting schemes for multiscale problems, focusing on a parabolic equation with a high-contrast coefficient. Using the framework of multic…
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…
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…
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…
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…
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…
Computational multiscale methods for parabolic wave approximations in heterogeneous media
Eric Chung, Yalchin Efendiev, Sai-Mang Pun +1
In this paper, we develop a computational multiscale to solve the parabolic wave approximation with heterogeneous and variable media. Parabolic wave approximation is a technique to…
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…
Temporal Splitting algorithms for non-stationary multiscale problems
Yalchin Efendiev, Sai-Mang Pun, Petr N. Vabishchevich
In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multisca…
Multiscale dimension reduction for flow and transport problems in thin domain with reactive boundaries
Maria Vasilyeva, Valentin Alekseev, Eric T. Chung +1
In this paper, we consider flow and transport problems in thin domains. The mathematical model considered in the paper is described by a system of equations for velocity, pressure,…
Explicit and Energy-Conserving Constraint Energy Minimizing Generalized Multiscale Discontinuous Galerkin Method for Wave Propagation in Heterogeneous Media
Siu Wun Cheung, Eric T. Chung, Yalchin Efendiev +1
In this work, we propose a local multiscale model reduction approach for the time-domain scalar wave equation in a heterogenous media. A fine mesh is used to capture the heterogene…
Computational multiscale methods for quasi-gas dynamic equations
Boris Chetverushkin, Eric Chung, Yalchin Efendiev +2
In this paper, we consider the quasi-gas-dynamic (QGD) model in a multiscale environment. The model equations can be regarded as a hyperbolic regularization and are derived from ki…
Splitting methods for solution decomposition in nonstationary problems
Yalchin Efendiev, Petr N. Vabishchevich
In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these a…
Learning Algorithms for Coarsening Uncertainty Space and Applications to Multiscale Simulations
Zecheng Zhang, Eric Chung, Yalchin Efendiev +1
In this paper, we investigate and design multiscale simulations for stochastic multiscale PDEs. As for the space, we consider a coarse grid and a known multiscale method, the Gener…