719 citations · 2.3k across the 72 of their papers we have counts for
11 papers · 1 filter
A multiscale HDG method for second order elliptic equations. Part I. Polynomial and homogenization-based multiscale spaces
Yalchin Efendiev, Raytcho Lazarov, Ke Shi
We introduce a finite element method for numerical upscaling of second order elliptic equations with highly heterogeneous coefficients. The method is based on a mixed formulation o…
An adaptive GMsFEM for high-contrast flow problems
Eric T. Chung, Yalchin Efendiev, Guanliang Li
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…
Generalized multiscale finite element methods for wave propagation in heterogeneous media
Eric T. Chung, Yalchin Efendiev, Wing Tat Leung
Numerical modeling of wave propagation in heterogeneous media is important in many applications. Due to the complex nature, direct numerical simulations on the fine grid are prohib…
Generalized Multiscale Finite Element Methods. Nonlinear Elliptic Equations
Yalchin Efendiev, Juan Galvis, Guanglian Li +1
In this paper we use the GeneralizedMultiscale Finite ElementMethod (GMsFEM) framework, introduced in [20], in order to solve nonlinear elliptic equations with high-contrast coeffi…
Generalized Multiscale Finite Element Methods. Oversampling Strategies
Yalchin Efendiev, Juan Galvis, Guanglian Li +1
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], al…
Upscaling of Nonlinear Forchheimer Flows
Eugenio Aulisa, Lidia Bloshanskaya, Yalchin Efendiev +1
In this work we propose upscaling method for nonlinear Forchheimer flow in highly heterogeneous porous media. The generalized Forchheimer law is considered for incompressible and s…
Generalized Multiscale Finite Element Method. Symmetric Interior Penalty Coupling
Y. Efendiev, J. Galvis, R. Lazarov +2
Motivated by applications to numerical simulation of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. W…
Mode Decomposition Methods for Flows in High-Contrast Porous Media. Part II. Local-Global Approach
Mehdi Ghommem, Michael Presho, Victor M. Calo +1
In this paper, we combine concepts of the generalized multiscale finite element method and mode decomposition methods to construct a robust local-global approach for model reductio…
Mode Decomposition Methods for Flows in High-Contrast Porous Media. Part I. Global Approach
Mehdi Ghommem, Victor M. Calo, Yalchin Efendiev
We apply dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD) methods to flows in highly-heterogeneous porous media to extract the dominant coherent structure…
Multi-Level Monte Carlo approaches for numerical homogenization
Yalchin Efendiev, Cornelia Kronsbein, Frederic Legoll
In this article, we study the application of Multi-Level Monte Carlo (MLMC) approaches to numerical random homogenization. Our objective is to compute the expectation of some funct…
Generalized Multiscale Finite Element Methods (GMsFEM)
Yalchin Efendiev, Juan Galvis, Thomas Y. Hou
In this paper, we propose a general approach called Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations for problems without scale separatio…