Results 11 to 20 of about 27,980 (243)

Generalized multiscale finite element methods (GMsFEM) [PDF]

Journal of Computational Physics, 2013
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.
Efendiev, Yalchin, Galvis, Juan, Hou, Thomas Y.   +2 more
core   +6 more sources

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

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   +2 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
Yalchin Efendiev, Juan Galvis, Raytcho Lazarov, Minam Moon, Marcus Sarkis   +4 more
openalex   +6 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
openalex   +5 more sources

Generalized Multiscale Finite Element Method for discrete network (graph) models [PDF]

Journal of Computational and Applied Mathematics
In this paper, we consider a time-dependent discrete network model with highly varying connectivity. The approximation by time is performed using an implicit scheme. We propose the coarse scale approximation construction of network models based on the Generalized Multiscale Finite Element Method.
Maria Vasilyeva
  +6 more sources

Cluster-based generalized multiscale finite element method for elliptic PDEs with random coefficients [PDF]

, 2018
We propose a generalized multiscale finite element method (GMsFEM) based on clustering algorithm to study the elliptic PDEs with random coefficients in the multi-query setting. Our method consists of offline and online stages.
Eric T. Chung, Yalchin Efendiev, Wing Tat Leung, Zhiwen Zhang   +3 more
openalex   +3 more sources

Fast Online Generalized Multiscale Finite Element Method using Constraint Energy Minimization [PDF]

Journal of Computational Physics, 2017
Local multiscale methods often construct multiscale basis functions in the offline stage without taking into account input parameters, such as source terms, boundary conditions, and so on.
Chung, Eric T., Efendiev, Yalchin, Leung, Wing Tat   +2 more
core   +2 more sources

Sparse Generalized Multiscale Finite Element Methods and their applications [PDF]

International Journal for Multiscale Computational Engineering, 2015
In a number of previous papers, local (coarse grid) multiscale model reduction techniques are developed using a Generalized Multiscale Finite Element Method.
Chung, Eric, Efendiev, Yalchin, Leung, Wing Tat, Li, Guanglian   +3 more
core   +2 more sources

Generalized Multiscale Finite Element Method for the poroelasticity\n problem in multicontinuum media [PDF]

Journal of Computational and Applied Mathematics, 2019
In this paper, we consider a poroelasticity problem in heterogeneous multicontinuum media that is widely used in simulations of the unconventional hydrocarbon reservoirs and geothermal fields. Mathematical model contains a coupled system of equations for pressures in each continuum and effective equation for displacement with volume force sources that ...
Aleksei Tyrylgin, Maria Vasilyeva, Denis Spiridonov, Eric T. Chung   +3 more
  +6 more sources

Generalized Multiscale Finite Element Methods with energy minimizing oversampling

International Journal for Numerical Methods in Engineering, 2018
SummaryIn this paper, we propose a general concept for constructing multiscale basis functions within Generalized Multiscale Finite Element Method, which uses oversampling and stable decomposition. The oversampling refers to using larger regions in constructing multiscale basis functions and stable decomposition allows estimating the local errors.
Eric T. Chung, Yalchin Efendiev, Wing Tat Leung   +2 more
openalex   +4 more sources