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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

A modeling of metasurfaces in the finite element method (FEM) based on generalized sheet transition conditions (GSTCs) is presented. The discontinuities in electromagnetic fields across a metasurface as represented by the GSTC are modeled…

Classical Physics · Physics 2017-05-24 Srikumar Sandeep , Jian Ming Jin , Christophe Caloz

In this paper, we combine discrete empirical interpolation techniques, global mode decomposition methods, and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM), to reduce the computational…

Numerical Analysis · Mathematics 2023-07-19 Manal Alotaibi , Victor M. Calo , Yalchin Efendiev , Juan Galvis , Mehdi Ghommem

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

Neural operators (NOs) struggle with high-contrast multiscale partial differential equations (PDEs), where fine-scale heterogeneities cause large errors. To address this, we use the Generalized Multiscale Finite Element Method (GMsFEM) that…

This paper presents a novel mass-conservative mixed multiscale method for solving flow equations in heterogeneous porous media. The media properties (the permeability) contain multiple scales and high contrast. The proposed method solves…

Numerical Analysis · Mathematics 2019-04-01 Eric Chung , Yalchin Efendiev , Wing Tat Leung

In this paper, we consider the numerical solution of poroelasticity problems that are of Biot type and develop a general algorithm for solving coupled systems. We discuss the challenges associated with mechanics and flow problems in…

Numerical Analysis · Mathematics 2015-08-11 Donald L. Brown , Maria Vasilyeva

In this paper, we study the development of efficient multiscale methods for flows in heterogeneous media. Our approach uses the Generalized Multiscale Finite Element (GMsFEM) framework. The main idea of GMsFEM is to approximate the solution…

Numerical Analysis · Mathematics 2014-09-26 Victor M. Calo , Y. Efendiev , Juan Galvis , Guanglian Li

In this paper, we consider the numerical solution of some nonlinear poroelasticity problems that are of Biot type and develop a general algorithm for solving nonlinear coupled systems. We discuss the difficulties associated with flow and…

Numerical Analysis · Mathematics 2015-08-11 Donald L. Brown , Maria Vasilyeva

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 work, we propose a generalized multiscale inversion algorithm for heterogeneous problems that aims at solving an inverse problem on a computational coarse grid. Previous inversion techniques for multiscale problems seek a…

Numerical Analysis · Mathematics 2017-07-27 Eric T. Chung , Yalchin Efendiev , Bangti Jin , Wing Tat Leung , Maria Vasilyeva

In this paper, we propose a novel iterative multiscale framework for solving high-contrast contact problems of Signorini type. The method integrates the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM)…

Numerical Analysis · Mathematics 2025-10-28 Zishang Li , Changqing Ye , Eric T. Chung

In this paper we use the GeneralizedMultiscale Finite ElementMethod (GMsFEM) framework, introduced in [20], in order to solve nonlinear elliptic equations with high-contrast coefficients. The proposed solution method involves linearizing…

Analysis of PDEs · Mathematics 2016-08-24 Yalchin Efendiev , Juan Galvis , Guanglian Li , Michael Presho

Numerical simulations of waves in highly heterogeneous media have important applications, but direct computations are prohibitively expensive. In this paper, we develop a new generalized multiscale finite element method with the aim of…

Numerical Analysis · Mathematics 2015-09-09 Eric T. Chung , Wing Tat Leung

Problems with sign-changing coefficients occur, for instance, in the study of transmission problems with metamaterials. In this work, we present and analyze a generalized finite element method in the spirit of the Localized Orthogonal…

Numerical Analysis · Mathematics 2020-08-28 Théophile Chaumont-Frelet , Barbara Verfürth

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 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

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

We analyse wave propagation in two-dimensional bianisotropic media with the Finite Element Method (FEM). We start from the Maxwell-Tellegen's equations in bianisotropic media, and derive some system of coupled Partial Difference Equations…

Optics · Physics 2016-12-21 Yan Liu , Boris Gralak , Sebastien Guenneau

This paper reviews standard oversampling strategies as performed in the Multiscale Finite Element Method (MsFEM). Common to those approaches is that the oversampling is performed in the full space restricted to a patch but including coarse…

Numerical Analysis · Mathematics 2014-04-16 Patrick Henning , Daniel Peterseim