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In this paper, we consider local multiscale model reduction for problems with multiple scales in space and time. We developed our approaches within the framework of the Generalized Multiscale Finite Element Method (GMsFEM) using space-time…

Numerical Analysis · Mathematics 2016-05-26 Eric T. Chung , Yalchin Efendiev , Wing Tat Leung , Shuai Ye

The main goal of this paper is to design multiscale basis functions within GMsFEM framework such that the convergence of method is independent of the contrast and linearly decreases with respect to mesh size if oversampling size is…

Numerical Analysis · Mathematics 2018-07-04 Eric T. Chung , Yalchin Efendiev , Wing Tat Leung

In this paper, we consider the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with discontinuous Galerkin (DG) coupling for the linear elasticity equations in highly heterogeneous and high contrast…

Numerical Analysis · Mathematics 2022-11-09 Zhongqian Wang , Shubin Fu , Eric Chung

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 of linear poroelasticity with high contrast. Firstly,…

Numerical Analysis · Mathematics 2023-10-26 Xin Su , Wing Tat Leung , Wenyuan Li , Sai-Mang Pun

Accurate numerical simulations of interaction between fluid and solid play an important role in applications. The task is challenging in practical scenarios as the media are usually highly heterogeneous with very large contrast. To overcome…

Numerical Analysis · Mathematics 2020-05-15 Xia Wang , Eric Chung , Shubin Fu , Zhaoqin Huang

In this paper, we consider the incompressible Stokes flow problem in a perforated domain and employ the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) to solve this problem. The proposed method…

Numerical Analysis · Mathematics 2020-07-08 Eric Chung , Jiuhua Hu , Sai-Mang Pun

The oversampling multiscale finite element method (MsFEM) is one of the most popular methods for simulating composite materials and flows in porous media which may have many scales. But the method may be inapplicable or inefficient in some…

Numerical Analysis · Mathematics 2012-11-16 Weibing Deng , Haijun Wu

In this paper we consider the numerical upscaling of the Brinkman equation in the presence of high-contrast permeability fields. We develop and analyze a robust and efficient Generalized Multiscale Finite Element Method (GMsFEM) for the…

Numerical Analysis · Mathematics 2014-04-22 Guanglian Li , Juan Galvis , Ke Shi

In this paper, we present a mixed Generalized Multiscale Finite Element Method (GMsFEM) for solving flow in heterogeneous media. Our approach constructs multiscale basis functions following a GMsFEM framework and couples these basis…

Numerical Analysis · Mathematics 2014-06-05 Eric T. Chung , Yalchin Efendiev , Chak Shing Lee

In this paper, we propose a multiscale method for the Darcy-Forchheimer model in highly heterogeneous porous media. The problem is solved in the framework of generalized multiscale finite element methods (GMsFEM) combined with a multipoint…

Numerical Analysis · Mathematics 2020-07-20 Zhengkang He , Eric T. Chung , Jie Chen , Zhangxin Chen

This work is concerned with the rigorous analysis on the Generalized Multiscale Finite Element Methods (GMsFEMs) for elliptic problems with high-contrast heterogeneous coefficients. GMsFEMs are popular numerical methods for solving flow…

Numerical Analysis · Mathematics 2018-02-27 Guanglian Li

In this paper, we propose a general approach called Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations for problems without scale separation over a complex input space. As in multiscale finite…

Numerical Analysis · Mathematics 2015-06-12 Yalchin Efendiev , Juan Galvis , Thomas Y. Hou

We present a multiscale mixed finite element method for solving second order elliptic equations with general $L^{\infty}$-coefficients arising from flow in highly heterogeneous porous media. Our approach is based on a multiscale spectral…

Numerical Analysis · Mathematics 2024-04-05 Christian Alber , Chupeng Ma , Robert Scheichl

The dual continuum model serves as a powerful tool in the modeling of subsurface applications. It allows a systematic coupling of various components of the solutions. The system is of multiscale nature as it involves high heterogeneous and…

Numerical Analysis · Mathematics 2018-07-31 Siu Wun Cheung , Eric T. Chung , Yalchin Efendiev , Wing Tat Leung , Maria Vasilyeva

In this paper, we propose a method for the construction of locally conservative flux fields through a variation of the Generalized Multiscale Finite Element Method (GMsFEM). The flux values are obtained through the use of a Ritz formulation…

Numerical Analysis · Mathematics 2015-04-09 Michael Presho , Juan Galvis

In this paper, we consider a poroelasticity problem in heterogeneous multicontinuum media that is widely used in simulations of the unconventional hydrocarbon reservoirs and geothermal fields. Mathematical model contains a coupled system of…

Numerical Analysis · Mathematics 2019-08-07 Aleksei Tyrylgin , Maria Vasilyeva , Denis Spiridonov , Eric T. Chung

In this paper we propose a method for the construction of locally conservative flux fields from Generalized Multiscale Finite Element Method (GMsFEM) pressure solutions. The flux values are obtained from an element-based postprocessing…

Analysis of PDEs · Mathematics 2013-04-24 Lawrence Bush , Victor Ginting , Michael Presho

In this paper, we propose a local-global multiscale method for highly heterogeneous stochastic groundwater flow problems under the framework of reduced basis method and the generalized multiscale finite element method (GMsFEM). Due to…

Numerical Analysis · Mathematics 2022-03-02 Yiran Wang , Eric Chung , Shubin Fu

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 kinetic equations. So far, the research on QGD models has been…

Numerical Analysis · Mathematics 2021-06-30 Boris Chetverushkin , Eric Chung , Yalchin Efendiev , Sai-Mang Pun , Zecheng Zhang

The coupling effects in multiphysics processes are often neglected in designing multiscale methods. The coupling may be described by a non-positive definite operator, which in turn brings significant challenges in multiscale simulations. In…

Numerical Analysis · Mathematics 2024-01-05 Xiaofei Guan , Lijian Jiang , Yajun Wang