The Experts below are selected from a list of 50910 Experts worldwide ranked by ideXlab platform
Yalchin Efendiev - One of the best experts on this subject based on the ideXlab platform.
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deep Multiscale Model learning
Journal of Computational Physics, 2020Co-Authors: Yalchin Efendiev, Eric T Chung, Yating Wang, Siu Wun Cheung, Min WangAbstract:Abstract The objective of this paper is to design novel multi-layer neural networks for Multiscale simulations of flows taking into account the observed fine data and physical Modeling concepts. Our approaches use deep learning techniques combined with local Multiscale Model reduction methodologies to predict flow dynamics. Using reduced-order Model concepts is important for constructing robust deep learning architectures since the reduced-order Models provide fewer degrees of freedom. We consider flow dynamics in porous media as multi-layer networks in this work. More precisely, the solution (e.g., pressures and saturation) at the time instant n + 1 depends on the solution at the time instant n and input parameters, such as permeability fields, forcing terms, and initial conditions. One can regard the solution as a multi-layer network, where each layer, in general, is a nonlinear forward map and the number of layers relates to the internal time steps. We will rely on rigorous Model reduction concepts to define unknowns and connections between layers. It is critical to use reduced-order Models for this purpose, which will identify the regions of influence and the appropriate number of variables. Furthermore, due to the lack of available observed fine data, the reduced-order Model can provide us sufficient inexpensive data as needed. The designed deep neural network will be trained using both coarse simulation data which is obtained from the reduced-order Model and observed fine data. We will present the main ingredients of our approach and numerical examples. Numerical results show that using deep learning with data generated from Multiscale Models as well as available observed fine data, we can obtain an improved forward map which can better approximate the fine scale Model.
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deep Multiscale Model learning
arXiv: Numerical Analysis, 2018Co-Authors: Yalchin Efendiev, Eric T Chung, Yating Wang, Siu Wun Cheung, Min WangAbstract:The objective of this paper is to design novel multi-layer neural network architectures for Multiscale simulations of flows taking into account the observed data and physical Modeling concepts. Our approaches use deep learning concepts combined with local Multiscale Model reduction methodologies to predict flow dynamics. Using reduced-order Model concepts is important for constructing robust deep learning architectures since the reduced-order Models provide fewer degrees of freedom. Flow dynamics can be thought of as multi-layer networks. More precisely, the solution (e.g., pressures and saturations) at the time instant $n+1$ depends on the solution at the time instant $n$ and input parameters, such as permeability fields, forcing terms, and initial conditions. One can regard the solution as a multi-layer network, where each layer, in general, is a nonlinear forward map and the number of layers relates to the internal time steps. We will rely on rigorous Model reduction concepts to define unknowns and connections for each layer. In each layer, our reduced-order Models will provide a forward map, which will be modified ("trained") using available data. It is critical to use reduced-order Models for this purpose, which will identify the regions of influence and the appropriate number of variables. Because of the lack of available data, the training will be supplemented with computational data as needed and the interpolation between data-rich and data-deficient Models. We will also use deep learning algorithms to train the elements of the reduced Model discrete system. We will present main ingredients of our approach and numerical results. Numerical results show that using deep learning and Multiscale Models, we can improve the forward Models, which are conditioned to the available data.
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Multiscale Model reduction for shale gas transport in poroelastic fractured media
Journal of Computational Physics, 2018Co-Authors: Yucel I Akkutlu, Yalchin Efendiev, Maria V Vasilyeva, Yuhe WangAbstract:Abstract Inherently coupled flow and geomechanics processes in fractured shale media have implications for shale gas production. The system involves highly complex geo-textures comprised of a heterogeneous anisotropic fracture network spatially embedded in an ultra-tight matrix. In addition, nonlinearities due to viscous flow, diffusion, and desorption in the matrix and high velocity gas flow in the fractures complicates the transport. In this paper, we develop a Multiscale Model reduction approach to couple gas flow and geomechanics in fractured shale media. A Discrete Fracture Model (DFM) is used to treat the complex network of fractures on a fine grid. The coupled flow and geomechanics equations are solved using a fixed stress-splitting scheme by solving the pressure equation using a continuous Galerkin method and the displacement equation using an interior penalty discontinuous Galerkin method. We develop a coarse grid approximation and coupling using the Generalized Multiscale Finite Element Method (GMsFEM). GMsFEM constructs the Multiscale basis functions in a systematic way to capture the fracture networks and their interactions with the shale matrix. Numerical results and an error analysis is provided showing that the proposed approach accurately captures the coupled process using a few Multiscale basis functions, i.e. a small fraction of the degrees of freedom of the fine-scale problem.
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Multiscale Model reduction for shale gas transport in fractured media
Computational Geosciences, 2016Co-Authors: I Y Akkutlu, Yalchin Efendiev, Maria VasilyevaAbstract:In this paper, we develop a Multiscale Model reduction technique that describes shale gas transport in fractured media. Due to the pore-scale heterogeneities and processes, we use upscaled Models to describe the matrix. We follow our previous work (Akkutlu et al. Transp. Porous Media 107 (1), 235–260, 2015 ), where we derived an upscaled Model in the form of generalized nonlinear diffusion Model to describe the effects of kerogen. To Model the interaction between the matrix and the fractures, we use Generalized Multiscale Finite Element Method (Efendiev et al. J. Comput. Phys. 251 , 116–135, 2013 , 2015 ). In this approach, the matrix and the fracture interaction is Modeled via local Multiscale basis functions. In Efendiev et al. ( 2015 ), we developed the GMsFEM and applied for linear flows with horizontal or vertical fracture orientations aligned with a Cartesian fine grid. The approach in Efendiev et al. ( 2015 ) does not allow handling arbitrary fracture distributions. In this paper, we (1) consider arbitrary fracture distributions on an unstructured grid; (2) develop GMsFEM for nonlinear flows; and (3) develop online basis function strategies to adaptively improve the convergence. The number of Multiscale basis functions in each coarse region represents the degrees of freedom needed to achieve a certain error threshold. Our approach is adaptive in a sense that the Multiscale basis functions can be added in the regions of interest. Numerical results for two-dimensional problem are presented to demonstrate the efficiency of proposed approach.
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adaptive Multiscale Model reduction with generalized Multiscale finite element methods
Journal of Computational Physics, 2016Co-Authors: Eric T Chung, Yalchin Efendiev, Thomas Y HouAbstract:In this paper, we discuss a general Multiscale Model reduction framework based on Multiscale finite element methods. We give a brief overview of related Multiscale methods. Due to page limitations, the overview focuses on a few related methods and is not intended to be comprehensive. We present a general adaptive Multiscale Model reduction framework, the Generalized Multiscale Finite Element Method. Besides the method's basic outline, we discuss some important ingredients needed for the method's success. We also discuss several applications. The proposed method allows performing local Model reduction in the presence of high contrast and no scale separation.
Min Wang - One of the best experts on this subject based on the ideXlab platform.
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deep Multiscale Model learning
Journal of Computational Physics, 2020Co-Authors: Yalchin Efendiev, Eric T Chung, Yating Wang, Siu Wun Cheung, Min WangAbstract:Abstract The objective of this paper is to design novel multi-layer neural networks for Multiscale simulations of flows taking into account the observed fine data and physical Modeling concepts. Our approaches use deep learning techniques combined with local Multiscale Model reduction methodologies to predict flow dynamics. Using reduced-order Model concepts is important for constructing robust deep learning architectures since the reduced-order Models provide fewer degrees of freedom. We consider flow dynamics in porous media as multi-layer networks in this work. More precisely, the solution (e.g., pressures and saturation) at the time instant n + 1 depends on the solution at the time instant n and input parameters, such as permeability fields, forcing terms, and initial conditions. One can regard the solution as a multi-layer network, where each layer, in general, is a nonlinear forward map and the number of layers relates to the internal time steps. We will rely on rigorous Model reduction concepts to define unknowns and connections between layers. It is critical to use reduced-order Models for this purpose, which will identify the regions of influence and the appropriate number of variables. Furthermore, due to the lack of available observed fine data, the reduced-order Model can provide us sufficient inexpensive data as needed. The designed deep neural network will be trained using both coarse simulation data which is obtained from the reduced-order Model and observed fine data. We will present the main ingredients of our approach and numerical examples. Numerical results show that using deep learning with data generated from Multiscale Models as well as available observed fine data, we can obtain an improved forward map which can better approximate the fine scale Model.
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deep Multiscale Model learning
arXiv: Numerical Analysis, 2018Co-Authors: Yalchin Efendiev, Eric T Chung, Yating Wang, Siu Wun Cheung, Min WangAbstract:The objective of this paper is to design novel multi-layer neural network architectures for Multiscale simulations of flows taking into account the observed data and physical Modeling concepts. Our approaches use deep learning concepts combined with local Multiscale Model reduction methodologies to predict flow dynamics. Using reduced-order Model concepts is important for constructing robust deep learning architectures since the reduced-order Models provide fewer degrees of freedom. Flow dynamics can be thought of as multi-layer networks. More precisely, the solution (e.g., pressures and saturations) at the time instant $n+1$ depends on the solution at the time instant $n$ and input parameters, such as permeability fields, forcing terms, and initial conditions. One can regard the solution as a multi-layer network, where each layer, in general, is a nonlinear forward map and the number of layers relates to the internal time steps. We will rely on rigorous Model reduction concepts to define unknowns and connections for each layer. In each layer, our reduced-order Models will provide a forward map, which will be modified ("trained") using available data. It is critical to use reduced-order Models for this purpose, which will identify the regions of influence and the appropriate number of variables. Because of the lack of available data, the training will be supplemented with computational data as needed and the interpolation between data-rich and data-deficient Models. We will also use deep learning algorithms to train the elements of the reduced Model discrete system. We will present main ingredients of our approach and numerical results. Numerical results show that using deep learning and Multiscale Models, we can improve the forward Models, which are conditioned to the available data.
Yating Wang - One of the best experts on this subject based on the ideXlab platform.
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deep Multiscale Model learning
Journal of Computational Physics, 2020Co-Authors: Yalchin Efendiev, Eric T Chung, Yating Wang, Siu Wun Cheung, Min WangAbstract:Abstract The objective of this paper is to design novel multi-layer neural networks for Multiscale simulations of flows taking into account the observed fine data and physical Modeling concepts. Our approaches use deep learning techniques combined with local Multiscale Model reduction methodologies to predict flow dynamics. Using reduced-order Model concepts is important for constructing robust deep learning architectures since the reduced-order Models provide fewer degrees of freedom. We consider flow dynamics in porous media as multi-layer networks in this work. More precisely, the solution (e.g., pressures and saturation) at the time instant n + 1 depends on the solution at the time instant n and input parameters, such as permeability fields, forcing terms, and initial conditions. One can regard the solution as a multi-layer network, where each layer, in general, is a nonlinear forward map and the number of layers relates to the internal time steps. We will rely on rigorous Model reduction concepts to define unknowns and connections between layers. It is critical to use reduced-order Models for this purpose, which will identify the regions of influence and the appropriate number of variables. Furthermore, due to the lack of available observed fine data, the reduced-order Model can provide us sufficient inexpensive data as needed. The designed deep neural network will be trained using both coarse simulation data which is obtained from the reduced-order Model and observed fine data. We will present the main ingredients of our approach and numerical examples. Numerical results show that using deep learning with data generated from Multiscale Models as well as available observed fine data, we can obtain an improved forward map which can better approximate the fine scale Model.
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deep Multiscale Model learning
arXiv: Numerical Analysis, 2018Co-Authors: Yalchin Efendiev, Eric T Chung, Yating Wang, Siu Wun Cheung, Min WangAbstract:The objective of this paper is to design novel multi-layer neural network architectures for Multiscale simulations of flows taking into account the observed data and physical Modeling concepts. Our approaches use deep learning concepts combined with local Multiscale Model reduction methodologies to predict flow dynamics. Using reduced-order Model concepts is important for constructing robust deep learning architectures since the reduced-order Models provide fewer degrees of freedom. Flow dynamics can be thought of as multi-layer networks. More precisely, the solution (e.g., pressures and saturations) at the time instant $n+1$ depends on the solution at the time instant $n$ and input parameters, such as permeability fields, forcing terms, and initial conditions. One can regard the solution as a multi-layer network, where each layer, in general, is a nonlinear forward map and the number of layers relates to the internal time steps. We will rely on rigorous Model reduction concepts to define unknowns and connections for each layer. In each layer, our reduced-order Models will provide a forward map, which will be modified ("trained") using available data. It is critical to use reduced-order Models for this purpose, which will identify the regions of influence and the appropriate number of variables. Because of the lack of available data, the training will be supplemented with computational data as needed and the interpolation between data-rich and data-deficient Models. We will also use deep learning algorithms to train the elements of the reduced Model discrete system. We will present main ingredients of our approach and numerical results. Numerical results show that using deep learning and Multiscale Models, we can improve the forward Models, which are conditioned to the available data.
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a conservative local Multiscale Model reduction technique for stokes flows in heterogeneous perforated domains
Journal of Computational and Applied Mathematics, 2017Co-Authors: Eric T Chung, Maria Vasilyeva, Yating WangAbstract:Abstract In this paper, we present a new Multiscale Model reduction technique for the Stokes flows in heterogeneous perforated domains. The challenge in the numerical simulations of this problem lies in the fact that the solution contains many Multiscale features and requires a very fine mesh to resolve all details. In order to efficiently compute the solutions, some Model reductions are necessary. To obtain a reduced Model, we apply the generalized Multiscale finite element approach, which is a framework allowing systematic construction of reduced Models. Based on this general framework, we will first construct a local snapshot space, which contains many possible Multiscale features of the solution. Using the snapshot space and a local spectral problem, we identify dominant modes in the snapshot space and use them as the Multiscale basis functions. Our basis functions are constructed locally with non-overlapping supports, which enhances the sparsity of the resulting linear system. In order to enforce the mass conservation, we propose a hybridized technique, and uses a Lagrange multiplier to achieve mass conservation. We will mathematically analyze the stability and the convergence of the proposed method. In addition, we will present some numerical examples to show the performance of the scheme. We show that, with a few basis functions per coarse region, one can obtain a solution with excellent accuracy.
Noels Ludovic - One of the best experts on this subject based on the ideXlab platform.
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Bayesian inference of non-linear Multiscale Model parameters accelerated by a Deep Neural Network
2020Co-Authors: Wu Ling, Zulueta Uriondo Kepa, Major Zoltan, Arriaga Aitor, Noels LudovicAbstract:We develop a Bayesian Inference (BI) of a non-linear Multiscale Model and material parameters using experimental composite coupons tests as observation data. In particular we consider non-aligned Short Fibers Reinforced Polymer (SFRP) as a composite material system and Mean-Field Homogenization (MFH) as a Multiscale Model. Although MFH is computationally efficient, when considering non-aligned inclusions, the evaluation cost of a non-linear response for a given set of Model and material parameters remains too prohibitive to be coupled with the sampling process required by the BI. Therefore, a Neural-Network-type (NNW) is first trained using the MFH Model, and is then used as a surrogate Model during the BI process, making the identification process affordable.Peer reviewe
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Bayesian inference of non-linear Multiscale Model parameters accelerated by a Deep Neural Network
'Elsevier BV', 2020Co-Authors: Wu Ling, Zulueta Uriondo Kepa, Major Zoltan, Arriaga Aitor, Noels LudovicAbstract:peer reviewedaudience: researcher, professional, studentWe develop a Bayesian Inference (BI) of a non-linear Multiscale Model and material parameters using experimental composite coupons tests as observation data. In particular we consider non-aligned Short Fibers Reinforced Polymer (SFRP) as a composite material system and Mean-Field Homogenization (MFH) as a Multiscale Model. Although MFH is computationally efficient, when considering non-aligned inclusions, the evaluation cost of a non-linear response for a given set of Model and material parameters remains too prohibitive to be coupled with the sampling process required by the BI. Therefore, a Neural-Network-type (NNW) is first trained using the MFH Model, and is then used as a surrogate Model during the BI process, making the identification process affordable.The research has been funded by the Walloon Region under the agreement no 1410246-STOMMMAC (CT-INT 2013-03-28), by the Gaitek 2015 programm of the Basque Government, and by the Austrian Research Promotion Agency (ffg) under the agreement no 850392 (STOMMMAC) in the context of the M-ERA.NET Joint Call 2014
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Stochastic Multiscale Model of MEMS stiction accounting for high order statistical moments of non-Gaussian contacting surfaces
2018Co-Authors: Hoang Truong Vinh, Wu Ling, Golinval Jean-claude, Arnst Maarten, Noels LudovicAbstract:Stiction is a failure mode of microelectromechanical systems (MEMS) involving permanent adhesion of moving surfaces. Models of stiction typically describe the adhesion as a multiple asperity adhesive contact between random rough surfaces, and they thus require a sufficiently accurate statistical representation of the surface, which may be non-Gaussian. If the stiction is caused primarily by multiple asperity adhesive contact in only a small portion of the apparent area of the contacting surfaces, the number of adhesive contacts between asperities may not be sufficiently statistically significant for a homogenized Model to be representative. In [Hoang et al., A computational stochastic Multiscale methodology for MEMS structures involving adhesive contact, Tribology International, 110:401-425, 2017], the authors have proposed a probabilistic Multiscale Model of multiple asperity adhesive contact that can capture the uncertainty in stiction behavior. Whereas the previous paper considered Gaussian random rough surfaces, the aim of the present paper is to extend this probabilistic Multiscale Model to non-Gaussian random rough surfaces whose probabilistic representation accounts for the high order statistical moments of the surface height. The probabilistic Multiscale Model thus obtained is validated by means of a comparison with experimental data of stiction tests of cantilever beams reported in the literature.Peer reviewe
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Stochastic Multiscale Model of MEMS stiction accounting for high order statistical moments of non-Gaussian contacting surfaces
'Institute of Electrical and Electronics Engineers (IEEE)', 2018Co-Authors: Hoang Truong Vinh, Wu Ling, Golinval Jean-claude, Arnst Maarten, Noels LudovicAbstract:peer reviewedaudience: researcher, professionalStiction is a failure mode of microelectromechanical systems (MEMS) involving permanent adhesion of moving surfaces. Models of stiction typically describe the adhesion as a multiple asperity adhesive contact between random rough surfaces, and they thus require a sufficiently accurate statistical representation of the surface, which may be non-Gaussian. If the stiction is caused primarily by multiple asperity adhesive contact in only a small portion of the apparent area of the contacting surfaces, the number of adhesive contacts between asperities may not be sufficiently statistically significant for a homogenized Model to be representative. In [Hoang et al., A computational stochastic Multiscale methodology for MEMS structures involving adhesive contact, Tribology International, 110:401-425, 2017], the authors have proposed a probabilistic Multiscale Model of multiple asperity adhesive contact that can capture the uncertainty in stiction behavior. Whereas the previous paper considered Gaussian random rough surfaces, the aim of the present paper is to extend this probabilistic Multiscale Model to non-Gaussian random rough surfaces whose probabilistic representation accounts for the high order statistical moments of the surface height. The probabilistic Multiscale Model thus obtained is validated by means of a comparison with experimental data of stiction tests of cantilever beams reported in the literature
Eric T Chung - One of the best experts on this subject based on the ideXlab platform.
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deep Multiscale Model learning
Journal of Computational Physics, 2020Co-Authors: Yalchin Efendiev, Eric T Chung, Yating Wang, Siu Wun Cheung, Min WangAbstract:Abstract The objective of this paper is to design novel multi-layer neural networks for Multiscale simulations of flows taking into account the observed fine data and physical Modeling concepts. Our approaches use deep learning techniques combined with local Multiscale Model reduction methodologies to predict flow dynamics. Using reduced-order Model concepts is important for constructing robust deep learning architectures since the reduced-order Models provide fewer degrees of freedom. We consider flow dynamics in porous media as multi-layer networks in this work. More precisely, the solution (e.g., pressures and saturation) at the time instant n + 1 depends on the solution at the time instant n and input parameters, such as permeability fields, forcing terms, and initial conditions. One can regard the solution as a multi-layer network, where each layer, in general, is a nonlinear forward map and the number of layers relates to the internal time steps. We will rely on rigorous Model reduction concepts to define unknowns and connections between layers. It is critical to use reduced-order Models for this purpose, which will identify the regions of influence and the appropriate number of variables. Furthermore, due to the lack of available observed fine data, the reduced-order Model can provide us sufficient inexpensive data as needed. The designed deep neural network will be trained using both coarse simulation data which is obtained from the reduced-order Model and observed fine data. We will present the main ingredients of our approach and numerical examples. Numerical results show that using deep learning with data generated from Multiscale Models as well as available observed fine data, we can obtain an improved forward map which can better approximate the fine scale Model.
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deep Multiscale Model learning
arXiv: Numerical Analysis, 2018Co-Authors: Yalchin Efendiev, Eric T Chung, Yating Wang, Siu Wun Cheung, Min WangAbstract:The objective of this paper is to design novel multi-layer neural network architectures for Multiscale simulations of flows taking into account the observed data and physical Modeling concepts. Our approaches use deep learning concepts combined with local Multiscale Model reduction methodologies to predict flow dynamics. Using reduced-order Model concepts is important for constructing robust deep learning architectures since the reduced-order Models provide fewer degrees of freedom. Flow dynamics can be thought of as multi-layer networks. More precisely, the solution (e.g., pressures and saturations) at the time instant $n+1$ depends on the solution at the time instant $n$ and input parameters, such as permeability fields, forcing terms, and initial conditions. One can regard the solution as a multi-layer network, where each layer, in general, is a nonlinear forward map and the number of layers relates to the internal time steps. We will rely on rigorous Model reduction concepts to define unknowns and connections for each layer. In each layer, our reduced-order Models will provide a forward map, which will be modified ("trained") using available data. It is critical to use reduced-order Models for this purpose, which will identify the regions of influence and the appropriate number of variables. Because of the lack of available data, the training will be supplemented with computational data as needed and the interpolation between data-rich and data-deficient Models. We will also use deep learning algorithms to train the elements of the reduced Model discrete system. We will present main ingredients of our approach and numerical results. Numerical results show that using deep learning and Multiscale Models, we can improve the forward Models, which are conditioned to the available data.
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a conservative local Multiscale Model reduction technique for stokes flows in heterogeneous perforated domains
Journal of Computational and Applied Mathematics, 2017Co-Authors: Eric T Chung, Maria Vasilyeva, Yating WangAbstract:Abstract In this paper, we present a new Multiscale Model reduction technique for the Stokes flows in heterogeneous perforated domains. The challenge in the numerical simulations of this problem lies in the fact that the solution contains many Multiscale features and requires a very fine mesh to resolve all details. In order to efficiently compute the solutions, some Model reductions are necessary. To obtain a reduced Model, we apply the generalized Multiscale finite element approach, which is a framework allowing systematic construction of reduced Models. Based on this general framework, we will first construct a local snapshot space, which contains many possible Multiscale features of the solution. Using the snapshot space and a local spectral problem, we identify dominant modes in the snapshot space and use them as the Multiscale basis functions. Our basis functions are constructed locally with non-overlapping supports, which enhances the sparsity of the resulting linear system. In order to enforce the mass conservation, we propose a hybridized technique, and uses a Lagrange multiplier to achieve mass conservation. We will mathematically analyze the stability and the convergence of the proposed method. In addition, we will present some numerical examples to show the performance of the scheme. We show that, with a few basis functions per coarse region, one can obtain a solution with excellent accuracy.
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adaptive Multiscale Model reduction with generalized Multiscale finite element methods
Journal of Computational Physics, 2016Co-Authors: Eric T Chung, Yalchin Efendiev, Thomas Y HouAbstract:In this paper, we discuss a general Multiscale Model reduction framework based on Multiscale finite element methods. We give a brief overview of related Multiscale methods. Due to page limitations, the overview focuses on a few related methods and is not intended to be comprehensive. We present a general adaptive Multiscale Model reduction framework, the Generalized Multiscale Finite Element Method. Besides the method's basic outline, we discuss some important ingredients needed for the method's success. We also discuss several applications. The proposed method allows performing local Model reduction in the presence of high contrast and no scale separation.
