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In this paper, we proposed two new types of edge multiscale methods motivated by \cite{GL18} to solve Partial Differential Equations (PDEs) with high-contrast heterogeneous coefficients: Edge spectral multiscale Finte Element method…

Numerical Analysis · Mathematics 2019-09-04 Shubin Fu , Eric Chung , Guanglian Li

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

This paper presents and analyses a Constraint Energy Minimization Generalized Multiscale Finite Element Method (CEM-GMsFEM) for solving single-phase non-linear compressible flows in highly heterogeneous media. The construction of CEM-GMsFEM…

Numerical Analysis · Mathematics 2023-03-31 Leonardo A. Poveda , Shubin Fu , Eric T. Chung , Lina Zhao

In this paper, we apply the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) to first solving a nonlinear poroelasticity problem. The arising system consists of a nonlinear pressure equation and a…

Numerical Analysis · Mathematics 2022-05-31 Shubin Fu , Eric Chung , Tina Mai

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 develop the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) for convection-diffusion equations with inhomogeneous Dirichlet, Neumann and Robin boundary conditions, along with…

Numerical Analysis · Mathematics 2024-08-02 Po Chai Wong , Eric T. Chung , Changqing Ye , Lina Zhao

In this paper, we address the numerical homogenization approximation of a free-boundary dam problem posed in a heterogeneous media. More precisely, we propose a generalized multiscale finite element (GMsFEM) method for the heterogeneous dam…

Numerical Analysis · Mathematics 2019-02-19 Juan Galvis , Carlos Vásquez , Luis F. Contreras

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

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 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

In this paper, we present a Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for parabolic equations with multiscale coefficients, arising from applications in porous media. We will present the…

Numerical Analysis · Mathematics 2018-06-14 Mengnan Li , Eric Chung , Lijian Jiang

In this paper, we develop the constraint energy minimization generalized multiscale finite element method (CEM-GMsFEM) in mixed formulation applied to parabolic equations with heterogeneous diffusion coefficients. The construction of the…

Numerical Analysis · Mathematics 2020-10-01 Yiran Wang , Eric Chung , Lina Zhao

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

In this paper, we derive an a-posteriori error indicator for the Generalized Multiscale Finite Element Method (GMsFEM) framework. This error indicator is further used to develop an adaptive enrichment algorithm for the linear elliptic…

Numerical Analysis · Mathematics 2015-06-17 Eric T. Chung , Yalchin Efendiev , Guanliang Li

In this paper, we propose oversampling strategies in the Generalized Multiscale Finite Element Method (GMsFEM) framework. The GMsFEM, which has been recently introduced in [12], allows solving multiscale parameter-dependent problems at a…

Analysis of PDEs · Mathematics 2013-04-18 Yalchin Efendiev , Juan Galvis , Guanglian Li , Michael Presho

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

In this paper, we study the Schr\"{o}dinger equation in the semiclassical regime and with multiscale potential function. We develop the so-called constraint energy minimization generalized multiscale finite element method (CEM-GMsFEM), in…

Numerical Analysis · Mathematics 2025-07-21 Xingguang Jin , Liu Liu , Xiang Zhong , Eric T. Chung

We consider in this paper a challenging problem of simulating fluid flows, in complex multiscale media possessing multi-continuum background. As an effort to handle this obstacle, model reduction is employed. In \cite{rh2}, homogenization…

Numerical Analysis · Mathematics 2022-05-31 Jun Sur Richard Park , Siu Wun Cheung , Tina Mai , Viet Ha Hoang

In this work, we develop an online adaptive enrichment method within the framework of the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) for solving the linear heterogeneous poroelasticity models with…

Numerical Analysis · Mathematics 2023-05-17 Xin Su , Sai-Mang Pun

A novel multi-scale finite element formulation for contact mechanics between nominally smooth but microscopically rough surfaces is herein proposed. The approach integrates the interface finite element method (FEM) for modelling interface…

Computational Engineering, Finance, and Science · Computer Science 2025-04-03 Jacopo Bonari , Maria R. Marulli , Nora Hagmeyer , Matthias Mayr , Alexander Popp , Marco Paggi