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In this paper, we consider an online basis enrichment mixed generalized multiscale method with oversampling, for solving flow problems in highly heterogeneous porous media. This is an exten- sion of the online mixed generalized multiscale…

Numerical Analysis · Mathematics 2018-07-03 Yanfang Yang , Shubin Fu , Eric T Chung

Simulating complex processes in fractured media requires some type of model reduction. Well-known approaches include multi-continuum techniques, which have been commonly used in approximating subgrid effects for flow and transport in…

Numerical Analysis · Mathematics 2017-02-24 Eric T. Chung , Yalchin Efendiev , 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 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 paper, we propose offline and online adaptive enrichment algorithms for the generalized multiscale approximation of a mixed finite element method with velocity elimination to solve the subsurface flow problem in high-contrast and…

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

We develop a new coarse-scale approximation strategy for the nonlinear single-continuum Richards equation as an unsaturated flow over heterogeneous non-periodic media, using the online generalized multiscale finite element method (online…

Numerical Analysis · Mathematics 2024-03-22 Denis Spiridonov , Sergei Stepanov , Tina Mai

In fluid flow simulation, the multi-continuum model is a useful strategy. When the heterogeneity and contrast of coefficients are high, the system becomes multiscale, and some kinds of reduced-order methods are demanded. Combining these…

Numerical Analysis · Mathematics 2023-02-08 Tina Mai , Siu Wun Cheung , Jun Sur Richard Park

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

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

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

In this research, an online basis enrichment strategy for the constraint energy minimizing generalized multiscale finite element method in mixed formulation is proposed. The online approach is based on the technique of oversampling. One…

Numerical Analysis · Mathematics 2019-10-01 Eric T. Chung , Sai-Mang Pun

In this paper, we consider an approximation method, and a novel general analysis, for second-order elliptic differential equations with heterogeneous multiscale coefficients. We obtain convergence of the Generalized Multi-scale Finite…

Numerical Analysis · Mathematics 2024-12-20 Eduardo Abreu , Ciro Diaz , Juan Galvis

In this paper, we present a residual-driven multiscale method for simulating Darcy flow in perforated domains, where complex geometries and highly heterogeneous permeability make direct simulations computationally expensive. To address…

Numerical Analysis · Mathematics 2026-03-11 Wei Xie , Shubin Fu , Yin Yang , Yunqing Huang

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 local model reduction approach for subsurface flow problems in stochastic and highly heterogeneous media. To guarantee the mass conservation, we consider the mixed formulation of the flow problem and aim to solve…

Numerical Analysis · Mathematics 2022-03-23 Yiran Wang , Eric Chung , Shubin Fu

In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. Mixed generalized multiscale finite element method (GMsFEM)…

Numerical Analysis · Mathematics 2017-04-05 Lijian Jiang , Qiuqi Li

In this paper, we develop an online basis enrichment method with the mortar mixed finite element method, using the oversampling technique, to solve for flow problems in highly heterogeneous media. We first compute a coarse grid solution…

Numerical Analysis · Mathematics 2017-10-05 Yanfang Yang , Eric T. Chung , Shubin Fu

In energy science, Darcy flow in heterogeneous porous media is a central problem in reservoir sim-ulation. However, the pronounced multiscale characteristics of such media pose significant challenges to conventional numerical methods in…

Numerical Analysis · Mathematics 2025-11-27 Peiqi Li , Jie Chen

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