On generalized multiscale methods for flow in complex porous media and their applications

ilustraciones, diagramas

Autores:: Contreras Hernandez, Luis Fernando
Fernando, Luis

Tipo de recurso:: Doctoral thesis

Fecha de publicación:: 2023

Institución:: Universidad Nacional de Colombia

Repositorio:: Universidad Nacional de Colombia

Idioma:

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dc.title.eng.fl_str_mv	On generalized multiscale methods for flow in complex porous media and their applications
dc.title.translated.spa.fl_str_mv	Sobre métodos multiescala generalizados para flujo en medios porosos complejos y sus aplicaciones
title	On generalized multiscale methods for flow in complex porous media and their applications
spellingShingle	On generalized multiscale methods for flow in complex porous media and their applications 510 - Matemáticas::518 - Análisis numérico Método de elementos finitos Análisis numéricos Análisis espectral Finite element method Numerical analysis Spectrum analysis Multiesca Alto contraste FEM Métodos numéricos
title_short	On generalized multiscale methods for flow in complex porous media and their applications
title_full	On generalized multiscale methods for flow in complex porous media and their applications
title_fullStr	On generalized multiscale methods for flow in complex porous media and their applications
title_full_unstemmed	On generalized multiscale methods for flow in complex porous media and their applications
title_sort	On generalized multiscale methods for flow in complex porous media and their applications
dc.creator.fl_str_mv	Contreras Hernandez, Luis Fernando Fernando, Luis
dc.contributor.advisor.none.fl_str_mv	Galvis Arrieta, Juan Carlos
dc.contributor.author.none.fl_str_mv	Contreras Hernandez, Luis Fernando Fernando, Luis
dc.subject.ddc.spa.fl_str_mv	510 - Matemáticas::518 - Análisis numérico
topic	510 - Matemáticas::518 - Análisis numérico Método de elementos finitos Análisis numéricos Análisis espectral Finite element method Numerical analysis Spectrum analysis Multiesca Alto contraste FEM Métodos numéricos
dc.subject.lemb.spa.fl_str_mv	Método de elementos finitos Análisis numéricos Análisis espectral
dc.subject.lemb.eng.fl_str_mv	Finite element method Numerical analysis Spectrum analysis
dc.subject.proposal.spa.fl_str_mv	Multiesca Alto contraste FEM Métodos numéricos
description	ilustraciones, diagramas
publishDate	2023
dc.date.accessioned.none.fl_str_mv	2023-08-04T14:36:18Z
dc.date.available.none.fl_str_mv	2023-08-04T14:36:18Z
dc.date.issued.none.fl_str_mv	2023-06-27
dc.type.spa.fl_str_mv	Trabajo de grado - Doctorado
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dc.identifier.uri.none.fl_str_mv	https://repositorio.unal.edu.co/handle/unal/84452
dc.identifier.instname.spa.fl_str_mv	Universidad Nacional de Colombia
dc.identifier.reponame.spa.fl_str_mv	Repositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourl.spa.fl_str_mv	https://repositorio.unal.edu.co/
url	https://repositorio.unal.edu.co/handle/unal/84452 https://repositorio.unal.edu.co/
identifier_str_mv	Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia
dc.relation.references.spa.fl_str_mv	E.Abreu, C.Diaz, and J.Galvis. A convergence analysis of generalized multiscale finite element methods. Journal of Computational Physics, 396:303--324, 2019. E. Abreu, C. Diaz, J. Galvis, and J. Perez. On the conservation properties in multiple scale coupling and simulation for darcy flow with hyperbolic-transport in complex flows. Multiscale Modeling \& Simulation , 18(4):1375--1408, 2020. Awad H. Al-Mohy and Nicholas J. Higham. Computing the action of the matrix exponential, with an application to exponential integrators. SIAM Journal on Scientific Computing , 33(2):488--511, 2011. Todd Arbogast and Mary F. Wheeler. A nonlinear mixed finite element method for a degenerate parabolic equation arising in flow in porous media. SIAM Journal on Numerical Analysis , 33(4):1669--1687, 1996. I. Arregui, J.J. Cend\'an, C. Par\'es, and C. V{\'a zquez. Numerical solution of a 1-d elastohydrodynamic problem in magnetic storage devices. ESAIM: Math. Model. Num. Anali. , 42:645--665, 2008. G. Bayada, S. Martin, and C. V{\'a zquez. Homogenization of a nonlocal elastohydrodynamic lubrication problem: a new free boundary model. Math. Mod. Meth. Appl. Sci. , 15(12):1923--1956, 2005. G. Bayada, S. Martin, and C. V{\'a zquez. Homogéneisation du modéle d'{E lrod-{A dams hydrodynamique. J. Asymp. Anali. , 44(1-2):75--110, 2005. Havard Berland, Bard Skaflestad, and Will M. Wright. Expint---a matlab package for exponential integrators. ACM Trans. Math. Softw. , 33(1):4–es, mar 2007. A. Bermúdez and J Durany. Numerical solution of steady-state flow through a porous dam. Comput. Methods Appl. Mech. Engrg. , 68(1):55--65, 1988. A. Bermúdez and C. Moreno. Duality methods for solving variational inequalities. Comput. Math. Appl. , 7(1):43--58, 1981. D. Braess. FINITE ELEMENTS Theory, Fast Solvers, and Applications in Elasticity Theory . Cambridge University press, Cambridge, 2007. H. Brezis. Functional analysis, Sovolev Space and Partial Differential Equations . Springer, Rutgers University, 2011. F. Contreras C. Vazquez, J. Galvis. Numerical upscaling of the free boundary dam problem in multiscale high-contrast media. Journal of Computational and Applied Mathematics , 367, 2020. V. M. Calo, Y. Efendiev, and J. Galvis. Asymptotic expansions for high-contrast elliptic equations. Math. Models Methods Appl. Sci. , 24(3):465--494, 2014. V. M. Calo, Y. Efendiev, J. Galvis, and G. Li. Randomized oversampling for generalized multiscale finite element methods. Multiscale Model. Simul. , 14(1):482--501, 2016. Victor M Calo, Yalchin Efendiev, Juan Galvis, and Guanglian Li. Randomized oversampling for generalized multiscale finite element methods. Multiscale Modeling \& Simulation , 14(1):482--501, 2016. M. A. Christie and M. J. Blunt. {Tenth SPE Comparative Solution Project: A Comparison of Upscaling Techniques . SPE Reservoir Evaluation & Engineering , 4(04):308--317, 08 2001. Eric Chung, Yalchin Efendiev, and Thomas Y. Hou. Adaptive multiscale model reduction with generalized multiscale finite element methods. Journal of Computational Physics , 320:69--95, 2016. Eric Chung, Yalchin Efendiev, Sai-Mang Pun, and Zecheng Zhang. Computational multiscale method for parabolic wave approximations in heterogeneous media. Applied Mathematics and Computation , 425:127044, 2022. Eric T. Chung, Yalchin Efendiev, Wing Tat Leung, and Petr N. Vabishchevich. Contrast-independent partially explicit time discretizations for multiscale flow problems. Journal of Computational Physics , 445:110578, 2021. Zeidler E. Nonlinear functional analysis and its applications I Variational methods and optimization . Springer science+business media, Springer verlag New York, 1985. Zeidler E. Nonlinear functional analysis and its applications II Variational methods and optimization . Springer science+business media, Springer verlag New York, 1985. Zeidler E. Nonlinear functional analysis and its applications III Variational methods and optimization . Springer science+business media, Springer verlag New York, 1985. L. Macul E. Abreu1, P. Ferraz. A multiscale recursive numerical method for semilinear parabolic problems. CILAMCE, PANACM , 2021. Y. Efendiev and J. Galvis. Domain decomposition preconditioner for multiscale high-contrast problems. In Proceedings of DD19 , 2009. Y. Efendiev and J. Galvis. A domain decomposition preconditioner for multiscale high-contrast problems. In Y. Huang, R. Kornhuber, O. Widlund, and J. Xu, editors, Domain Decomposition Methods in Science and Engineering XIX , volume 78 of Lect. Notes in Comput. Science and Eng. , pages 189--196. Springer-Verlag, 2011. Y. Efendiev and J. Galvis. Domain decomposition preconditioner for multiscale high-contrast problems. In Y. Huang, R. Kornhuber, O. Widlund, and J. Xu, editors, {\em Domain Decomposition Methods in Science and Engineering XIX , volume 78 of {\em Lecture Notes in Computational Science and Engineering , pages 189--196, Berlin, 2011. Springer-Verlag. Y. Efendiev, J. Galvis, and T. Hou. Generalized multiscale finite element methods. Journal of Computational Physics , 251:116--135, 2013. Y. Efendiev, J. Galvis, S. Ki Kang, and R.D. Lazarov. Robust multiscale iterative solvers for nonlinear flows in highly heterogeneous media. Numer. Math. Theory Methods Appl. , 5(3):359--383, 2012. Y. Efendiev, J. Galvis, R. Lazarov, and J. Willems. Robust domain decomposition preconditioners for abstract symmetric positive definite bilinear forms. ESAIM Math. Model. Numer. Anali. , 46(5):1175--1199, 2012. Y. Efendiev, J. Galvis, G. Li, and M. Presho. Generalized multiscale finite element methods: Oversampling strategies. International Journal for Multiscale Computational Engineering , 12(6), 2014. Y. Efendiev, J. Galvis, and P.S. Vassilevski. Spectral element agglomerate algebraic multigrid methods for elliptic problems with high-contrast coefficients. In Domain decomposition methods in science and engineering {XIX , volume 78 of Lect. Notes Comput. Sci. Eng. , pages 407--414. Springer, Heidelberg, 2011. Y. Efendiev and T. Hou. {Multiscale Finite Element Methods: Theory and Applications , volume 4 of {\em Surveys and Tutorials in the Applied Mathematical Sciences . Springer, New York, 2009. Yalchin Efendiev, Sai-Mang Pun, and Petr N. Vabishchevich. Temporal splitting algorithms for non-stationary multiscale problems. Journal of Computational Physics , 439:110375, 2021. L.C. Evans. Partial Differential Equations . Graduate studies in mathematics. American Mathematical Society, 2010. J. Galvis and Y. Efendiev. Domain decomposition preconditioners for multiscale flows in high contrast media. SIAM J. Multiscale Modeling and Simulation , 8:1461--1483, 2010. J. Galvis and Y. Efendiev. Domain decomposition preconditioners for multiscale flows in high contrast media. reduced dimension coarse spaces. SIAM J. Multiscale Modeling and Simulation , 8:1621--1644, 2010. R. Glowinski. Numerical Methods for Nonlinear Variational Problems . Computational Physics Series. Springer-Verlag, 1984. N. Higham. Functions of matrix theory and computation . SIAM, University of Manchester, United Kingdom, 2008. Marlis Hochbruck, Christian Lubich, and Hubert Selhofer. Exponential integrators for large systems of differential equations. SIAM Journal on Scientific Computing , 19(5):1552--1574, 1998. Marlis Hochbruck and Alexander Ostermann. Exponential integrators. Acta Numerica , 19:209--286, 2010. T. Hou and X.H. Wu. A multiscale finite element method for elliptic problems in composite materials and porous media. J. Comput. Phys. , 134:169--189, 1997. B. Wu J. Huang, L. Ju. A fast compact exponential time differencing method for semilinear parabolic equations with neumann boundary conditions. Applied Mathematics Letters , (94):257--265, 2019. D. Pardo J. Muñoz and L. Demkowicz. Equivalence between the dpg method and the exponential integrator for linear parabolic problems. Journal of Computational Physics , 2020. J. Galvis J. Olmos and F. Martinez. A geometric mean algorithm of symmetric positive definite matrices. unpublished . Lijian Jiang, Yalchin Efendiev, and Victor Ginting. Multiscale methods for parabolic equations with continuum spatial scales. Discrete and Continuous Dynamical Systems - B , 8(4):833--859, 2007. Claes Johnson. Numerical solution of partial differential equations by the finite element method. Acta Applicandae Mathematica , 18:184--186, 1988. E. Abreu C. Diaz J. Muñoz-Matute J. Galvis L. F. Contreras, D. Pardo. An exponential integration generalized multiscale finite element method for parabolic problems. Submitted . S. Martin and C. V\'azquez. Homogenization of the layer-structured dam problem with isotropic permeability. Nonlinear Anali. Real World Appl. , 14(6):2133--2151, 2013. Axel Målqvist and Anna Persson. Multiscale techniques for parabolic equations. Numerische Mathematik , 138, 01 2018. M Park and Michael V Tretyakov. Stochastic resin transfer molding process. SIAM/ASA Journal on Uncertainty Quantification , 5(1):1110--1135, 2017. Michael Presho and Juan Galvis. A mass conservative generalized multiscale finite element method applied to two-phase flow in heterogeneous porous media. Journal of Computational and Applied Mathematics , 296:376--388, 2016. R. Tyrrell Rockafellar. On the maximal monotonicity of subdifferential mappings. Pacific Journal of Mathematics , 33:209--216, 1970. Zheng Sun, José A. Carrillo, and Chi-Wang Shu. A discontinuous galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials. Journal of Computational Physics , 352:76--104, 2018. R. Toja. Contributions of the numerical simulation of coupled models in glaciology. PhD thesis, Universidade da Coruña, 2010. H. Thomas Y. Efendiev, J. Galvis. Generalized multiscale finite element methods (gmsfem). Journal of Computational Physics , 251:116--135, 2013. J. Galvis Y. Efendiev and X. Wu. Multiscale finite element methods for high-contrast problems using local spectral basis functions. Journal of Computational Physics , 230:937--955, 2011. Miguel Zambrano, Sintya Serrano, Boyan S Lazarov, and Juan Galvis. Fast multiscale contrast independent preconditioners for linear elastic topology optimization problems. Journal of Computational and Applied Mathematics , 389:113366, 2021.
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dc.format.extent.spa.fl_str_mv	xiii, 104 páginas
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dc.publisher.program.spa.fl_str_mv	Bogotá - Ciencias - Doctorado en Ciencias - Matemáticas
dc.publisher.faculty.spa.fl_str_mv	Facultad de Ciencias
dc.publisher.place.spa.fl_str_mv	Bogotá,Colombia
dc.publisher.branch.spa.fl_str_mv	Universidad Nacional de Colombia - Sede Bogotá
institution	Universidad Nacional de Colombia
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spelling	Atribución-NoComercial 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Galvis Arrieta, Juan Carlos083500f8dbd93663cffc3776002b7be1Contreras Hernandez, Luis Fernando450ce71e41a4a5bb605557499a56cdbeFernando, Luised9da7e171ef23bddcb056d1db6e867a2023-08-04T14:36:18Z2023-08-04T14:36:18Z2023-06-27https://repositorio.unal.edu.co/handle/unal/84452Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, diagramasIn this document, the Generalized Multiscale Finite Element Method (GMsFEM) is studied, which deals with constructing multiscale spectral basis functions designed for high-contrast multiscale problems. The multiscale basis functions are built from the product of the eigenvectors, computed from a local spectral problem and a partition of unity over the study domain. The eigenvalues detect essential features of the solutions that are not captured by the initial multiscale basis functions. This document reviews the general convergence study where the error estimates are written in terms of the eigenvalues associated with the eigenvectors not used in the construction. Error analysis involves local and global norms that measure the convergence speed of the expansion of the solution in terms of local eigenvectors; this is achieved with a careful choice of the initial multiscale basis functions and the configuration of the eigenvalue problems. Two novel important numerical applications are presented: the first is the free-boundary dam problem posed on a heterogeneous high-contrast medium, where we introduce a fictitious time variable that motivates an adequate time discretization that can be understood as a fixed-point iteration. For the steady-state solution, we use the duality method to deal with the multivalued nonlinear terms involved; then, efficient approximations of pressure and saturation are calculated using the GMsFEM method. The second application is the solution of a parabolic equation. Here implementing time discretizations, such as finite differences or exponential integrators in the presence of a high contrast coefficient, it may not be practical in because each time iteration one needs the computation of matrix operators involving very large and extremely ill-conditioned sparse matrices. The GMsFEM is essential since it allows obtaining the solution of the problem more simply, allowing to combine the GMsFEM with the method of exponential integrators in time to get a good approximation of the final temporary solution. (Texto tomado de la fuente)En este documento se estudia el M´etodo de Elementos Finitos Multiescala Generalizados (GMsFEM), el cual trata de la construcci´on de funciones base espectrales multiescala que est´an dise˜nadas para problemas de alto contraste. Las funciones base multiescala se construyen a partir del producto entre los vectores propios, construidos a partir de un problema espectral local y una partici´on de la unidad sobre el dominio de estudio. Los valores propios detectan caracter´ısticas importantes de las soluciones que no son capturadas por las funciones base multiescala iniciales. En este trabajo, se presenta un estudio de convergencia donde las estimaciones de error son generales, y est´an escritas en t´erminos de los valores propios asociados a los vectores propios no utilizados en la construcci´on. El an´alisis de errores implica normas locales y globales que miden la descomposici´on de la expansi´on de la soluci´on en t´erminos de vectores propios locales, esto se logra con una elecci´on cuidadosa de las funciones de base multiescala iniciales y la configuraci´on de los problemas de valores propios. Se presentan dos aplicaciones num´ericas importantes: la primera, es el problema de represa con frontera libre planteado sobre un medio heterog´eneo de alto contraste, donde introducimos una variable de tiempo ficticia que motiva una discretizaci´on de tiempo adecuada que puede entenderse como una iteraci´on de punto fijo a la soluci´on de estado estacionario, y usamos el m´etodo de dualidad para tratar con los t´erminos no lineales multivaluados involucrados; luego, se calculan aproximaciones eficientes de la presi´on y la saturaci´on usando el m´etodo GMsFEM. La segunda aplicaci´on es la soluci´on de una ecuaci´on parab´olica donde al implementar discretizaciones de tiempo como diferencias finitas o integradores exponenciales sobre un coeficiente de alto contraste, puede no ser pr´actico porque cada iteraci´on de tiempo necesita el c´alculo de operadores matriciales que involucran matrices dispersas, muy grandes y mal condicionadas; es por esto que el GMsFEM es importante ya que permite la obtenci´on de la soluci´on del problema de una forma m´as sencilla, permitiendo combinar GMsFEM con el m´etodo de integradores exponenciales en el tiempo para obtener una buena aproximaci´on de la soluci´on temporal finalDoctoradoNumerical analysis, Partial differential equations.xiii, 104 páginasapplication/pdf510 - Matemáticas::518 - Análisis numéricoMétodo de elementos finitosAnálisis numéricosAnálisis espectralFinite element methodNumerical analysisSpectrum analysisMultiescaAlto contrasteFEMMétodos numéricosOn generalized multiscale methods for flow in complex porous media and their applicationsSobre métodos multiescala generalizados para flujo en medios porosos complejos y sus aplicacionesTrabajo de grado - Doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_db06Texthttp://purl.org/redcol/resource_type/TDBogotá - Ciencias - Doctorado en Ciencias - MatemáticasFacultad de CienciasBogotá,ColombiaUniversidad Nacional de Colombia - Sede BogotáE.Abreu, C.Diaz, and J.Galvis. A convergence analysis of generalized multiscale finite element methods. Journal of Computational Physics, 396:303--324, 2019.E. Abreu, C. Diaz, J. Galvis, and J. Perez. On the conservation properties in multiple scale coupling and simulation for darcy flow with hyperbolic-transport in complex flows. Multiscale Modeling \& Simulation , 18(4):1375--1408, 2020.Awad H. Al-Mohy and Nicholas J. Higham. Computing the action of the matrix exponential, with an application to exponential integrators. SIAM Journal on Scientific Computing , 33(2):488--511, 2011.Todd Arbogast and Mary F. Wheeler. A nonlinear mixed finite element method for a degenerate parabolic equation arising in flow in porous media. SIAM Journal on Numerical Analysis , 33(4):1669--1687, 1996.I. Arregui, J.J. Cend\'an, C. Par\'es, and C. V{\'a zquez. Numerical solution of a 1-d elastohydrodynamic problem in magnetic storage devices. ESAIM: Math. Model. Num. Anali. , 42:645--665, 2008.G. Bayada, S. Martin, and C. V{\'a zquez. Homogenization of a nonlocal elastohydrodynamic lubrication problem: a new free boundary model. Math. Mod. Meth. Appl. Sci. , 15(12):1923--1956, 2005.G. Bayada, S. Martin, and C. V{\'a zquez. Homogéneisation du modéle d'{E lrod-{A dams hydrodynamique. J. Asymp. Anali. , 44(1-2):75--110, 2005.Havard Berland, Bard Skaflestad, and Will M. Wright. Expint---a matlab package for exponential integrators. ACM Trans. Math. Softw. , 33(1):4–es, mar 2007.A. Bermúdez and J Durany. Numerical solution of steady-state flow through a porous dam. Comput. Methods Appl. Mech. Engrg. , 68(1):55--65, 1988.A. Bermúdez and C. Moreno. Duality methods for solving variational inequalities. Comput. Math. Appl. , 7(1):43--58, 1981.D. Braess. FINITE ELEMENTS Theory, Fast Solvers, and Applications in Elasticity Theory . Cambridge University press, Cambridge, 2007.H. Brezis. Functional analysis, Sovolev Space and Partial Differential Equations . Springer, Rutgers University, 2011.F. Contreras C. Vazquez, J. Galvis. Numerical upscaling of the free boundary dam problem in multiscale high-contrast media. Journal of Computational and Applied Mathematics , 367, 2020.V. M. Calo, Y. Efendiev, and J. Galvis. Asymptotic expansions for high-contrast elliptic equations. Math. Models Methods Appl. Sci. , 24(3):465--494, 2014.V. M. Calo, Y. Efendiev, J. Galvis, and G. Li. Randomized oversampling for generalized multiscale finite element methods. Multiscale Model. Simul. , 14(1):482--501, 2016.Victor M Calo, Yalchin Efendiev, Juan Galvis, and Guanglian Li. Randomized oversampling for generalized multiscale finite element methods. Multiscale Modeling \& Simulation , 14(1):482--501, 2016.M. A. Christie and M. J. Blunt. {Tenth SPE Comparative Solution Project: A Comparison of Upscaling Techniques . SPE Reservoir Evaluation & Engineering , 4(04):308--317, 08 2001.Eric Chung, Yalchin Efendiev, and Thomas Y. Hou. Adaptive multiscale model reduction with generalized multiscale finite element methods. Journal of Computational Physics , 320:69--95, 2016.Eric Chung, Yalchin Efendiev, Sai-Mang Pun, and Zecheng Zhang. Computational multiscale method for parabolic wave approximations in heterogeneous media. Applied Mathematics and Computation , 425:127044, 2022.Eric T. Chung, Yalchin Efendiev, Wing Tat Leung, and Petr N. Vabishchevich. Contrast-independent partially explicit time discretizations for multiscale flow problems. Journal of Computational Physics , 445:110578, 2021.Zeidler E. Nonlinear functional analysis and its applications I Variational methods and optimization . Springer science+business media, Springer verlag New York, 1985.Zeidler E. Nonlinear functional analysis and its applications II Variational methods and optimization . Springer science+business media, Springer verlag New York, 1985.Zeidler E. Nonlinear functional analysis and its applications III Variational methods and optimization . Springer science+business media, Springer verlag New York, 1985.L. Macul E. Abreu1, P. Ferraz. A multiscale recursive numerical method for semilinear parabolic problems. CILAMCE, PANACM , 2021.Y. Efendiev and J. Galvis. Domain decomposition preconditioner for multiscale high-contrast problems. In Proceedings of DD19 , 2009.Y. Efendiev and J. Galvis. A domain decomposition preconditioner for multiscale high-contrast problems. In Y. Huang, R. Kornhuber, O. Widlund, and J. Xu, editors, Domain Decomposition Methods in Science and Engineering XIX , volume 78 of Lect. Notes in Comput. Science and Eng. , pages 189--196. Springer-Verlag, 2011.Y. Efendiev and J. Galvis. Domain decomposition preconditioner for multiscale high-contrast problems. In Y. Huang, R. Kornhuber, O. Widlund, and J. Xu, editors, {\em Domain Decomposition Methods in Science and Engineering XIX , volume 78 of {\em Lecture Notes in Computational Science and Engineering , pages 189--196, Berlin, 2011. Springer-Verlag.Y. Efendiev, J. Galvis, and T. Hou. Generalized multiscale finite element methods. Journal of Computational Physics , 251:116--135, 2013.Y. Efendiev, J. Galvis, S. Ki Kang, and R.D. Lazarov. Robust multiscale iterative solvers for nonlinear flows in highly heterogeneous media. Numer. Math. Theory Methods Appl. , 5(3):359--383, 2012.Y. Efendiev, J. Galvis, R. Lazarov, and J. Willems. Robust domain decomposition preconditioners for abstract symmetric positive definite bilinear forms. ESAIM Math. Model. Numer. Anali. , 46(5):1175--1199, 2012.Y. Efendiev, J. Galvis, G. Li, and M. Presho. Generalized multiscale finite element methods: Oversampling strategies. International Journal for Multiscale Computational Engineering , 12(6), 2014.Y. Efendiev, J. Galvis, and P.S. Vassilevski. Spectral element agglomerate algebraic multigrid methods for elliptic problems with high-contrast coefficients. In Domain decomposition methods in science and engineering {XIX , volume 78 of Lect. Notes Comput. Sci. Eng. , pages 407--414. Springer, Heidelberg, 2011.Y. Efendiev and T. Hou. {Multiscale Finite Element Methods: Theory and Applications , volume 4 of {\em Surveys and Tutorials in the Applied Mathematical Sciences . Springer, New York, 2009.Yalchin Efendiev, Sai-Mang Pun, and Petr N. Vabishchevich. Temporal splitting algorithms for non-stationary multiscale problems. Journal of Computational Physics , 439:110375, 2021.L.C. Evans. Partial Differential Equations . Graduate studies in mathematics. American Mathematical Society, 2010.J. Galvis and Y. Efendiev. Domain decomposition preconditioners for multiscale flows in high contrast media. SIAM J. Multiscale Modeling and Simulation , 8:1461--1483, 2010.J. Galvis and Y. Efendiev. Domain decomposition preconditioners for multiscale flows in high contrast media. reduced dimension coarse spaces. SIAM J. Multiscale Modeling and Simulation , 8:1621--1644, 2010.R. Glowinski. Numerical Methods for Nonlinear Variational Problems . Computational Physics Series. Springer-Verlag, 1984.N. Higham. 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Journal of Computational and Applied Mathematics , 389:113366, 2021.ORIGINAL1030535037_2023.pdf1030535037_2023.pdfTesis de Doctorado en Ciencias - Matemáticasapplication/pdf2836028https://repositorio.unal.edu.co/bitstream/unal/84452/2/1030535037_2023.pdfb97b40291a1317abba642cab567ec3a3MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-85879https://repositorio.unal.edu.co/bitstream/unal/84452/1/license.txteb34b1cf90b7e1103fc9dfd26be24b4aMD51THUMBNAIL1030535037_2023.pdf.jpg1030535037_2023.pdf.jpgGenerated Thumbnailimage/jpeg4423https://repositorio.unal.edu.co/bitstream/unal/84452/3/1030535037_2023.pdf.jpgaaafc9e74be0606659fbe57b397dcd6aMD53unal/84452oai:repositorio.unal.edu.co:unal/844522023-08-15 23:03:55.729Repositorio Institucional Universidad Nacional de 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