English
Related papers

Related papers: A Generalized Multiscale Finite Element Method for…

200 papers

For nonlinear Cosserat elasticity, we consider multiscale methods in this paper. In particular, we explore the generalized multiscale finite element method (GMsFEM) to solve an isotropic Cosserat problem with strain-limiting property…

Numerical Analysis · Mathematics 2024-03-22 Dmitry Ammosov , Tina Mai , Juan Galvis

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 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

In this paper, we discuss the application of Generalized Multiscale Finite Element Method (GMsFEM) to elasticity equation in heterogeneous media. Our applications are motivated by elastic wave propagation in subsurface where the subsurface…

Numerical Analysis · Mathematics 2014-08-27 Eric T. Chung , Yalchin Efendiev , Shubin Fu

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 multiscale method for simulations of the multicontinua unsaturated flow problems in heterogeneous fractured porous media. The mathematical model is described by the system of Richards equations for each continuum…

Numerical Analysis · Mathematics 2019-08-02 Denis Spiridonov , Maria Vasilyeva , Eric T. Chung

In this paper, we construct a class of Mixed Generalized Multiscale Finite Element Methods for the approximation on a coarse grid for an elliptic problem in thin two-dimensional domains. We consider the elliptic equation with homogeneous…

Numerical Analysis · Mathematics 2021-10-13 Denis Spiridonov , Maria Vasilyeva , Min Wang , Eric T. Chung

In this paper, we propose a randomized generalized multiscale finite element method (Randomized GMsFEM) for flow problems with parameterized inputs and high-contrast heterogeneous media. The method employs a data-driven predictor to…

Numerical Analysis · Mathematics 2025-08-05 Wing Tat Leung , Qiuqi Li , Songwei Liu

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling…

Geophysics · Physics 2015-05-20 Kai Gao , Shubin Fu , Richard L. Gibson , Eric T. Chung , Yalchin Efendiev

In this paper, we consider multiscale methods for nonlinear elasticity. In particular, we investigate the Generalized Multiscale Finite Element Method (GMsFEM) for a strain-limiting elasticity problem. Being a special case of the naturally…

Numerical Analysis · Mathematics 2022-05-24 Shubin Fu , Eric Chung , Tina Mai

The Multiscale Finite Element Method (MsFEM) is developed in the vein of Crouzeix-Raviart element for solving viscous incompressible flows in genuine heterogeneous media. Such flows are relevant in many branches of engineering, often at…

Numerical Analysis · Mathematics 2014-04-11 Bagus Putra Muljadi , Jacek Narski , Alexei Lozinski , Pierre Degond

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

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

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 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 develop the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with mixed boundary conditions (Dirichlet and Neumann) for the elasticity equations in high contrast media. By a special…

Numerical Analysis · Mathematics 2022-10-21 Zhongqian Wang , Changqing Ye , Eric T. Chung

In this paper, we propose a multiscale empirical interpolation method for solving nonlinear multiscale partial differential equations. The proposed method combines empirical interpolation techniques and local multiscale methods, such as the…

Numerical Analysis · Mathematics 2014-07-02 Victor Calo , Yalchin Efendiev , Juan Galvis , Mehdi Ghommem

In this paper, we propose a novel multiscale model reduction strategy tailored to address the Poisson equation within heterogeneous perforated domains. The numerical simulation of this intricate problem is impeded by its multiscale…

Numerical Analysis · Mathematics 2024-04-29 Wei Xie , Yin Yang , Eric Chung , Yunqing Huang

In this work, we introduce a time memory formalism in poroelasticity model that couples the pressure and displacement. We assume this multiphysics process occurs in multicontinuum media. The mathematical model contains a coupled system of…

Numerical Analysis · Mathematics 2022-01-20 Aleksei Tyrylgin , Maria Vasilyeva , Anatoly Alikhanov , Dongwoo Sheen

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 Generalized Multiscale Finite Element Method (GMsFEM). In order…

Numerical Analysis · Mathematics 2020-04-10 Zecheng Zhang , Eric Chung , Yalchin Efendiev , Wing Tat Leung