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Applicable Analysis
An International Journal
Volume 95, 2016 - Issue 10: Mathematical & Numerical Analysis of Flow and Transport in Porous Media
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Original Articles

Generalized multiscale finite element methods for problems in perforated heterogeneous domains

Eric T. ChungDepartment of Mathematics, The Chinese University of Hong Kong (CUHK), Hong Kong SAR, China.View further author information
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Yalchin EfendievDepartment of Mathematics & Institute for Scientific Computation (ISC), Texas A&M University, College Station, TX, USA.;Center for Numerical Porous Media (NumPor), King Abdullah University of Science and Technology (KAUST), Thuwal, 23955-6900Kingdom of Saudi Arabia.Correspondence[email protected]
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,
Guanglian LiDepartment of Mathematics, Texas A&M University, College Station, TX, 77843-3368USA.View further author information
&
Maria VasilyevaDepartment of Computational Technologies, Institute of Mathematics and Informatics, North-Eastern Federal University, Yakutsk, Republic of Sakha (Yakutia), 677980Russia.;Institute for Scientific Computation, Texas A&M University, College Station, TX, 77843-3368USA.View further author information
Pages 2254-2279 | Received 05 Jan 2015, Accepted 11 Apr 2015, Published online: 08 Jun 2015

Citations (35)

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Eric T. Chung, Yalchin Efendiev, Wing Tat Leung, Maria Vasilyeva & Yating Wang. (2017) Online adaptive local multiscale model reduction for heterogeneous problems in perforated domains. Applicable Analysis 96:12, pages 2002-2031.
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Articles from other publishers (34)

Miranda Boutilier, Konstantin Brenner & Victorita Dolean. (2024) Robust methods for multiscale coarse approximations of diffusion models in perforated domains. Applied Numerical Mathematics 201, pages 561-578.
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Maria VasilyevaS. M. Mallikarjunaiah. (2024) Generalized Multiscale Finite Element Treatment of a Heterogeneous Nonlinear Strain-limiting Elastic Model. Multiscale Modeling & Simulation 22:1, pages 334-368.
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Dmitry Ammosov, Andrey Nasedkin & Galina Muratova. (2024) A computational macroscopic model of piezomagnetoelectric materials using Generalized Multiscale Finite Element Method. Journal of Computational and Applied Mathematics 437, pages 115420.
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Maria Vasilyeva, Nana Adjoah Mbroh & Mehrube Mehrubeoglu. (2023) Lower-Dimensional Model of the Flow and Transport Processes in Thin Domains by Numerical Averaging Technique. Fluids 9:1, pages 4.
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Maria Vasilyeva, Alexey Sadovski & D. Palaniappan. (2023) Multiscale solver for multi-component reaction–diffusion systems in heterogeneous media. Journal of Computational and Applied Mathematics 427, pages 115150.
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Martin Drieschner, Robert Gruhlke, Yuri Petryna, Martin Eigel & Dietmar Hömberg. (2023) Local surrogate responses in the Schwarz alternating method for elastic problems on random voided domains. Computer Methods in Applied Mechanics and Engineering 405, pages 115858.
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Xin Su & Sai-Mang Pun. (2022) A multiscale method for the heterogeneous Signorini problem. Journal of Computational and Applied Mathematics 409, pages 114160.
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Dmitry Ammosov, Yalchin Efendiev, Elena Grekova & Maria Vasilyeva. (2022) Generalized macroscale model for Cosserat elasticity using Generalized Multiscale Finite Element Method. Journal of Computational Physics 461, pages 111011.
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Eric T. Chung, Uygulaana Kalachikova, Maria Vasilyeva & Valentin Alekseev. (2022) Generalized multiscale discontinuous Galerkin method for convection–diffusion equation in perforated media. Mathematics and Computers in Simulation 193, pages 666-688.
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Dmitry Ammosov, Maria Vasilyeva, Andrey Nasedkin & Yalchin Efendiev. (2022) Generalized Multiscale Finite Element Method for piezoelectric problem in heterogeneous media. Engineering Analysis with Boundary Elements 135, pages 12-25.
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V. I. Vasil’ev, M. V. Vasil’eva, D. Ya. Nikiforov, N. I. Sidnyaev, S. P. Stepanov & A. N. Tseeva. (2022) Computational Implementation of a Mixed-Dimensional Model of Heat Transfer in the Soil–Pipe System in Cryolithic Zone. Computational Mathematics and Mathematical Physics 61:12, pages 2054-2067.
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Jun Sur Richard Park, Siu Wun Cheung & Tina Mai. (2021) Multiscale simulations for multi-continuum Richards equations. Journal of Computational and Applied Mathematics 397, pages 113648.
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Maria Vasilyeva, Valentin Alekseev, Eric T. Chung & Yalchin Efendiev. (2021) Multiscale dimension reduction for flow and transport problems in thin domain with reactive boundaries. Journal of Computational Physics 442, pages 110512.
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Eric Chung, Wing Tat Leung, Sai-Mang Pun & Zecheng Zhang. (2021) A multi-stage deep learning based algorithm for multiscale model reduction. Journal of Computational and Applied Mathematics 394, pages 113506.
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Valentin Alekseev, Maria Vasilyeva, Uygulaana Kalachikova & Eric T. Chung. (2021) DG-GMsFEM for Problems in Perforated Domains with Non-Homogeneous Boundary Conditions. Computation 9:7, pages 75.
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Robert Altmann, Patrick Henning & Daniel Peterseim. (2021) Numerical homogenization beyond scale separation. Acta Numerica 30, pages 1-86.
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Aleksei Tyrylgin, Yaoyao Chen, Maria Vasilyeva & Eric T. Chung. (2021) Multiscale model reduction for the Allen–Cahn problem in perforated domains. Journal of Computational and Applied Mathematics 381, pages 113010.
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Valentin Alekseev, Qili Tang, Maria Vasilyeva, Eric T. Chung & Yalchin Efendiev. (2020) Mixed Generalized Multiscale Finite Element Method for a Simplified Magnetohydrodynamics Problem in Perforated Domains. Computation 8:2, pages 58.
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Zecheng Zhang, Eric T. Chung, Yalchin Efendiev & Wing Tat Leung. (2020) Learning Algorithms for Coarsening Uncertainty Space and Applications to Multiscale Simulations. Mathematics 8:5, pages 720.
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Denis Spiridonov, Maria Vasilyeva & Eric T. Chung. (2020) Generalized Multiscale Finite Element method for multicontinua unsaturated flow problems in fractured porous media. Journal of Computational and Applied Mathematics 370, pages 112594.
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Kanghun Cho & Minam Moon. (2020) Multiscale hybridizable discontinuous Galerkin method for elliptic problems in perforated domains. Journal of Computational and Applied Mathematics 365, pages 112346.
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Valentin Alekseev, Maria Vasilyeva & Vasily Vasiliev. (2019) Multiscale simulation of the heat and mass transfer with Brinkman model. Journal of Physics: Conference Series 1392:1, pages 012063.
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Denis Spiridonov, Maria Vasilyeva & Wing Tat Leung. (2019) A Generalized Multiscale Finite Element Method (GMsFEM) for perforated domain flows with Robin boundary conditions. Journal of Computational and Applied Mathematics 357, pages 319-328.
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Maria Vasilyeva, Eric T. Chung, Wing Tat Leung, Yating Wang & Denis Spiridonov. (2019) Upscaling method for problems in perforated domains with non-homogeneous boundary conditions on perforations using Non-Local Multi-Continuum method (NLMC). Journal of Computational and Applied Mathematics 357, pages 215-227.
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Siu Wun Cheung & Nilabja Guha. (2019) Dynamic data-driven Bayesian GMsFEM. Journal of Computational and Applied Mathematics 353, pages 72-85.
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M.I. Epov, E.P. Shurina, N.B. Itkina, A.Y. Kutishcheva & S.I. Markov. (2019) Finite element modeling of a multi-physics poro-elastic problem in multiscale media. Journal of Computational and Applied Mathematics 352, pages 1-22.
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M Vasilyeva, J D De Basabe, Y Efendiev & R L GibsonJrJr. (2019) Multiscale model reduction of the wave propagation problem in viscoelastic fractured media. Geophysical Journal International 217:1, pages 558-571.
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Samy Wu Fung & Lars Ruthotto. (2019) A multiscale method for model order reduction in PDE parameter estimation. Journal of Computational and Applied Mathematics 350, pages 19-34.
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Eric T. Chung & Chak Shing Lee. (2019) A mixed generalized multiscale finite element method for planar linear elasticity. Journal of Computational and Applied Mathematics 348, pages 298-313.
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M Vasilyeva & A Tyrylgin. (2019) Convolutional neural network for fast prediction of the effective properties of domains with random inclusions. Journal of Physics: Conference Series 1158, pages 042034.
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Maria Vasilyeva, Eric T. Chung, Yalchin Efendiev, Wing Tat Leung & Yating Wang. 2019. Finite Difference Methods. Theory and Applications. Finite Difference Methods. Theory and Applications 604 611 .
D. Spiridonov & M. Vasilyeva. 2019. Finite Difference Methods. Theory and Applications. Finite Difference Methods. Theory and Applications 517 524 .
V. Alekseev, U. Gavrileva, D. Spiridonov, A. Tyrylgin & M. Vasilyeva. Numerical simulation of the transport and flow problems in perforated domains using generalized multiscale finite element method. Numerical simulation of the transport and flow problems in perforated domains using generalized multiscale finite element method.
Eric Chung, Yalchin Efendiev, Wing Leung & Jun Ren. (2015) Multiscale Simulations for Coupled Flow and Transport Using the Generalized Multiscale Finite Element Method. Computation 3:4, pages 670-686.
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