Results 21 to 30 of about 27,923 (223)

DG-GMsFEM for Problems in Perforated Domains with Non-Homogeneous Boundary Conditions

Computation, 2021
Problems in perforated media are complex and require high resolution grid construction to capture complex irregular perforation boundaries leading to the large discrete system of equations. In this paper, we develop a multiscale model reduction technique
Valentin Alekseev, Maria Vasilyeva, Uygulaana Kalachikova, Eric T. Chung   +3 more
doaj   +1 more source

Multiscale Model Reduction of the Unsaturated Flow Problem in Heterogeneous Porous Media with Rough Surface Topography

Mathematics, 2020
In this paper, we consider unsaturated filtration in heterogeneous porous media with rough surface topography. The surface topography plays an important role in determining the flow process and includes multiscale features.
Denis Spiridonov, Maria Vasilyeva, Eric T. Chung, Yalchin Efendiev, Raghavendra Jana   +4 more
doaj   +1 more source

Randomized Oversampling for Generalized Multiscale Finite Element Methods [PDF]

Multiscale Modeling & Simulation, 2016
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 space locally using a few multiscale basis functions.
Calo, Victor M., Efendiev, Yalchin R., Galvis, Juan, Li, Guanglian   +3 more
openaire   +4 more sources

Mixed Generalized Multiscale Finite Element Method for a Simplified Magnetohydrodynamics Problem in Perforated Domains

Computation, 2020
In this paper, we consider a coupled system of equations that describes simplified magnetohydrodynamics (MHD) problem in perforated domains. We construct a fine grid that resolves the perforations on the grid level in order to use a traditional ...
Valentin Alekseev, Qili Tang, Maria Vasilyeva, Eric T. Chung, Yalchin Efendiev   +4 more
doaj   +1 more source

Review of Wind-Induced Effects Estimation through Nonlinear Analysis of Tall Buildings, High-Rise Structures, Flexible Bridges and Transmission Lines

Buildings, 2023
The nonlinear effects exhibited by structures under the action of wind loads have gradually stepped into the vision of wind-resistant researchers. By summarizing the prominent wind-induced nonlinear problems of four types of wind-sensitive structures ...
Shuang Zhao, Chengtao Zhang, Xianxing Dai, Zhitao Yan   +3 more
doaj   +1 more source

Residual-driven online generalized multiscale finite element methods [PDF]

Journal of Computational Physics, 2015
The construction of local reduced-order models via multiscale basis functions has been an area of active research. In this paper, we propose online multiscale basis functions which are constructed using the offline space and the current residual. Online multiscale basis functions are constructed adaptively in some selected regions based on our error ...
Chung, Eric T., Efendiev, Yalchin R., Leung, Wing Tat   +2 more
openaire   +4 more sources

A convergence analysis of Generalized Multiscale Finite Element Methods [PDF]

Journal of Computational Physics, 2019
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 Element Method (GMsFEM) method that uses local eigenvectors in its construction.
Eduardo Abreu, Ciro Díaz, Juan Galvis
openaire   +3 more sources

Generalized multiscale finite element method. Symmetric interior penalty coupling [PDF]

Journal of Computational Physics, 2013
Motivated by applications to numerical simulation of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose three different finite element spaces on the
Efendiev, Yalchin R., Galvis, Juan, Lazarov, Raytcho D., Moon, M., Sarkis, Marcus V.   +4 more
openaire   +4 more sources

Learning Algorithms for Coarsening Uncertainty Space and Applications to Multiscale Simulations

Mathematics, 2020
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).
Zecheng Zhang, Eric T. Chung, Yalchin Efendiev, Wing Tat Leung   +3 more
doaj   +1 more source

Generalized Multiscale Finite Element Method for Highly Heterogeneous Compressible Flow

Multiscale Modeling & Simulation, 2022
In this paper, we study the generalized multiscale finite element method (GMsFEM) for single phase compressible flow in highly heterogeneous porous media. We follow the major steps of the GMsFEM to construct permeability dependent offline basis for fast coarse-grid simulation.
Shubin Fu, Eric Chung, Lina Zhao
openaire   +3 more sources