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Author : Eren Atilla Ozgul
Publisher :
ISBN 13 :
Total Pages : 40 pages
Book Rating : 4.:/5 (532 download)
Download or read book On Multiscale Finite Element Methods for Elliptic Problems in Porous Media written by Eren Atilla Ozgul and published by . This book was released on 2003 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yalchin Efendiev
Publisher : Springer Science & Business Media
ISBN 13 : 0387094962
Total Pages : 242 pages
Book Rating : 4.3/5 (87 download)
Download or read book Multiscale Finite Element Methods written by Yalchin Efendiev and published by Springer Science & Business Media. This book was released on 2009-01-10 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this monograph is to describe the main concepts and recent - vances in multiscale ?nite element methods. This monograph is intended for thebroaderaudienceincludingengineers,appliedscientists,andforthosewho are interested in multiscale simulations. The book is intended for graduate students in applied mathematics and those interested in multiscale compu- tions. It combines a practical introduction, numerical results, and analysis of multiscale ?nite element methods. Due to the page limitation, the material has been condensed. Each chapter of the book starts with an introduction and description of the proposed methods and motivating examples. Some new techniques are introduced using formal arguments that are justi?ed later in the last chapter. Numerical examples demonstrating the signi?cance of the proposed methods are presented in each chapter following the description of the methods. In the last chapter, we analyze a few representative cases with the objective of demonstrating the main error sources and the convergence of the proposed methods. A brief outline of the book is as follows. The ?rst chapter gives a general introductiontomultiscalemethodsandanoutlineofeachchapter.Thesecond chapter discusses the main idea of the multiscale ?nite element method and its extensions. This chapter also gives an overview of multiscale ?nite element methods and other related methods. The third chapter discusses the ext- sion of multiscale ?nite element methods to nonlinear problems. The fourth chapter focuses on multiscale methods that use limited global information.
Author : Minam Moon
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (956 download)
Download or read book Generalized Discontinuous Multiscale Methods for Flows in Highly Heterogeneous Porous Media written by Minam Moon and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation is devoted to the development, study and testing of numerical methods for elliptic and parabolic equations with heterogeneous coefficients. The motivation for this study is to meet the need for fast and robust methods for numerical upscaling and simulation of single and multi-phase fluid flow in highly heterogeneous porous media. We consider the multiscale model reduction technique in the framework of the discontinuous Galerkin (DG) and the hybridizable discontinuous Galerkin (HDG) finite element methods. First, we design multiscale finite element methods for second order elliptic equations by applying the symmetric interior penalty discontinuous Galekin finite element method. We propose two different types of finite element spaces on the coarse mesh within DG framework. The first type of spaces is based on a local spectral problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the mass matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. Second, we develop multiscale model reduction methods within the HDG framework. We provide construction of several multiscale finite element spaces (related to the coarse-mesh edges) that guarantee a reasonable approximation on a reduced dimensional space of the numerical traces. In these approaches, we use local snapshot spaces and local spectral decomposition following the concept of Generalized Multiscale Finite Element Methods. We also provide a general framework for systematic construction of multiscale spaces. By using local snapshots we were able to add local features to the solution space and to avoid high dimensional representation of trace spaces. Further, we extend multiscale finite element methods within HDG method to nonlinear and/or time-dependent problems. These extensions demonstrate the potential of the proposed constructions for some advanced and more practical applications. For most of the proposed methods, we investigate their stability and derive error estimates for the approximate solutions. Furthermore we study the performance of all proposed methods on a representative number of numerical examples. In the numerical tests, we use various permeability data of highly heterogeneous porous media and contrasts ranging from 103 to 106. Since the exact solution is in general unknown, we first generate solutions on a very fine mesh and use them as reference solutions in our tests. The numerical results confirm the theoretical study of the accuracy of the proposed methods and their robustness with respect to the media contrast. Our numerical experiments also show that the proposed methods could be implemented in a practical and efficient way. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/155430
Author : John Zhangxin Chen
Publisher : World Scientific Publishing Company
ISBN 13 : 9813100656
Total Pages : 349 pages
Book Rating : 4.8/5 (131 download)
Download or read book Finite Element Method, The: Its Fundamentals And Applications In Engineering written by John Zhangxin Chen and published by World Scientific Publishing Company. This book was released on 2011-10-06 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Finite Element Method offers a fundamental and practical introduction to the finite element method, its variants, and their applications in engineering. Every concept is introduced in the simplest possible setting, while maintaining a level of treatment that is as rigorous as possible without being unnecessarily abstract. Various finite elements in one, two, and three space dimensions are introduced, and their applications to elliptic, parabolic, hyperbolic, and nonlinear equations and to solid mechanics, fluid mechanics, and porous media flow problems are addressed. The variants include the control volume, multipoint flux approximation, nonconforming, mixed, discontinuous, characteristic, adaptive, and multiscale finite element methods. Illustrative computer programs in Fortran and C++ are described. An extensive set of exercises are provided in each chapter. This book serves as a text a for one-semester course for upper-level undergraduates and beginning graduate students and as a professional reference for engineers, mathematicians, and scientists.
Author : Md Selim Akhtar
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783843374170
Total Pages : 80 pages
Book Rating : 4.3/5 (741 download)
Download or read book Multiscale Finite Element Methods For Second Order Elliptic BVPs written by Md Selim Akhtar and published by LAP Lambert Academic Publishing. This book was released on 2010 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the convergence of the multiscale finite element method (MsFEM) for second order elliptic equations with oscillating coefficient in two space dimension is studied. Such equations often arise in composite materials and flows in porous media. The main purpose is to understand the theoretical background of this method and its convergence analysis. The oscillating coefficient is assumed to be of two scales and is periodic in the large scale. The MsFEM is capable of correctly capturing the large scale components of the solution on a coarse grid without accurately resolving all the small scale features in the solution. This is accomplished by incorporating the local microstructure of the differential operator into the finite element base functions. As a consequence, the base functions are adapted to the local properties of the differential operator.
Author : Roland W. Lewis
Publisher : John Wiley & Sons
ISBN 13 : 0471928097
Total Pages : 517 pages
Book Rating : 4.4/5 (719 download)
Download or read book The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media written by Roland W. Lewis and published by John Wiley & Sons. This book was released on 1999-01-07 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: Seit der Veröffentlichung der Erstauflage 1987 haben Forschungaktivitäten und professionelle Anwendungen auf dem Gebiet poröser Medien rapide zugenommen. Deshalb wurde die 2. Auflage komplett überarbeitet und aktualisiert. Führende Experten stellen die mechanischen und numerischen Aspekte des Fließens im porösen Medium sehr detailliert dar. (09/98)
Author : Ivan G. Graham
Publisher : Springer Science & Business Media
ISBN 13 : 3642220614
Total Pages : 376 pages
Book Rating : 4.6/5 (422 download)
Download or read book Numerical Analysis of Multiscale Problems written by Ivan G. Graham and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 91st London Mathematical Society Durham Symposium took place from July 5th to 15th 2010, with more than 100 international participants attending. The Symposium focused on Numerical Analysis of Multiscale Problems and this book contains 10 invited articles from some of the meeting's key speakers, covering a range of topics of contemporary interest in this area. Articles cover the analysis of forward and inverse PDE problems in heterogeneous media, high-frequency wave propagation, atomistic-continuum modeling and high-dimensional problems arising in modeling uncertainty. Novel upscaling and preconditioning techniques, as well as applications to turbulent multi-phase flow, and to problems of current interest in materials science are all addressed. As such this book presents the current state-of-the-art in the numerical analysis of multiscale problems and will be of interest to both practitioners and mathematicians working in those fields.
Author : P.G. Ciarlet
Publisher : Elsevier
ISBN 13 : 0080875254
Total Pages : 551 pages
Book Rating : 4.0/5 (88 download)
Download or read book The Finite Element Method for Elliptic Problems written by P.G. Ciarlet and published by Elsevier. This book was released on 1978-01-01 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this book is to analyze within reasonable limits (it is not a treatise) the basic mathematical aspects of the finite element method. The book should also serve as an introduction to current research on this subject. On the one hand, it is also intended to be a working textbook for advanced courses in Numerical Analysis, as typically taught in graduate courses in American and French universities. For example, it is the author's experience that a one-semester course (on a three-hour per week basis) can be taught from Chapters 1, 2 and 3 (with the exception of Section 3.3), while another one-semester course can be taught from Chapters 4 and 6. On the other hand, it is hoped that this book will prove to be useful for researchers interested in advanced aspects of the numerical analysis of the finite element method. In this respect, Section 3.3, Chapters 5, 7 and 8, and the sections on "Additional Bibliography and Comments should provide many suggestions for conducting seminars.
Author : Björn Engquist
Publisher : Springer Science & Business Media
ISBN 13 : 3540888578
Total Pages : 332 pages
Book Rating : 4.5/5 (48 download)
Download or read book Multiscale Modeling and Simulation in Science written by Björn Engquist and published by Springer Science & Business Media. This book was released on 2009-02-11 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most problems in science involve many scales in time and space. An example is turbulent ?ow where the important large scale quantities of lift and drag of a wing depend on the behavior of the small vortices in the boundarylayer. Another example is chemical reactions with concentrations of the species varying over seconds and hours while the time scale of the oscillations of the chemical bonds is of the order of femtoseconds. A third example from structural mechanics is the stress and strain in a solid beam which is well described by macroscopic equations but at the tip of a crack modeling details on a microscale are needed. A common dif?culty with the simulation of these problems and many others in physics, chemistry and biology is that an attempt to represent all scales will lead to an enormous computational problem with unacceptably long computation times and large memory requirements. On the other hand, if the discretization at a coarse level ignoresthe?nescale informationthenthesolutionwillnotbephysicallymeaningful. The in?uence of the ?ne scales must be incorporated into the model. This volume is the result of a Summer School on Multiscale Modeling and S- ulation in Science held at Boso ¤n, Lidingo ¤ outside Stockholm, Sweden, in June 2007. Sixty PhD students from applied mathematics, the sciences and engineering parti- pated in the summer school.
Author : Roland Wynne Lewis
Publisher : John Wiley & Sons
ISBN 13 :
Total Pages : 368 pages
Book Rating : 4.3/5 (91 download)
Download or read book The Finite Element Method in the Deformation and Consolidation of Porous Media written by Roland Wynne Lewis and published by John Wiley & Sons. This book was released on 1987 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 5 pages
Book Rating : 4.:/5 (727 download)
Download or read book Multiscale Finite Element Methods for Miscible and Immiscible Flow in Porous Media written by and published by . This book was released on 2002 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Vahid Nassehi
Publisher : World Scientific
ISBN 13 : 1848164297
Total Pages : 265 pages
Book Rating : 4.8/5 (481 download)
Download or read book Finite Element Modeling of Multiscale Transport Phenomena written by Vahid Nassehi and published by World Scientific. This book was released on 2011 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex multiscale systems such as combined free or porous flow regimes and transport processes governed by combined diffusion, convection and reaction mechanisms, which cannot be readily modeled using traditional methods, can be solved by multiscale or stabilized finite element schemes. Due to the importance of the described multiscale processes in applications such as separation processes, reaction engineering and environmental systems analysis, a sound knowledge of such methods is essential for many researchers and design engineers who wish to develop reliable solutions for industrially relevant problems. The main scope of this book is to provide an authoritative description of recent developments in the field of finite element analysis, with a particular emphasis on the multiscale finite element modeling of transport phenomena and flow problem.
Author : Jielong Wang
Publisher : Springer Nature
ISBN 13 : 9811984417
Total Pages : 367 pages
Book Rating : 4.8/5 (119 download)
Download or read book Multiscale Multibody Dynamics written by Jielong Wang and published by Springer Nature. This book was released on 2023-03-24 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a novel theory of multibody dynamics with distinct features, including unified continuum theory, multiscale modeling technology of multibody system, and motion formalism implementation. All these features together with the introductions of fundamental concepts of vector, dual vector, tensor, dual tensor, recursive descriptions of joints, and the higher-order implicit solvers formulate the scope of the book’s content. In this book, a multibody system is defined as a set consisted of flexible and rigid bodies which are connected by any kinds of joints or constraints to achieve the desired motion. Generally, the motion of multibody system includes the translation and rotation; it is more efficient to describe the motion by using the dual vector or dual tensor directly instead of defining two types of variables, the translation and rotation separately. Furthermore, this book addresses the detail of motion formalism and its finite element implementation of the solid, shell-like, and beam-like structures. It also introduces the fundamental concepts of mechanics, such as the definition of vector, dual vector, tensor, and dual tensor, briefly. Without following the Einstein summation convention, the first- and second-order tensor operations in this book are depicted by linear algebraic operation symbols of row array, column array, and two-dimensional matrix, making these operations easier to understand. In addition, for the integral of governing equations of motion, a set of ordinary differential equations for the finite element-based discrete system, the book discussed the implementation of implicit solvers in detail and introduced the well-developed RADAU IIA algorithms based on post-error estimation to make the contents of the book complete. The intended readers of this book are senior engineers and graduate students in related engineering fields.
Author : Gavriel Salvendy
Publisher : CRC Press
ISBN 13 : 0429621019
Total Pages : 8218 pages
Book Rating : 4.4/5 (296 download)
Download or read book Advances in Human Factors and Ergonomics 2012- 14 Volume Set written by Gavriel Salvendy and published by CRC Press. This book was released on 2012-08-06 with total page 8218 pages. Available in PDF, EPUB and Kindle. Book excerpt: With contributions from an international group of authors with diverse backgrounds, this set comprises all fourteen volumes of the proceedings of the 4th AHFE Conference 21-25 July 2012. The set presents the latest research on current issues in Human Factors and Ergonomics. It draws from an international panel that examines cross-cultural differences, design issues, usability, road and rail transportation, aviation, modeling and simulation, and healthcare.
Author : Zhangxin Chen
Publisher : World Scientific
ISBN 13 : 9814350567
Total Pages : 349 pages
Book Rating : 4.8/5 (143 download)
Download or read book The Finite Element Method written by Zhangxin Chen and published by World Scientific. This book was released on 2011 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fundamental and practical introduction to the finite element method, its variants, and their applications in engineering.
Author : Daniele Mortari
Publisher : MDPI
ISBN 13 : 3039435914
Total Pages : 172 pages
Book Rating : 4.0/5 (394 download)
Download or read book Computational Mathematics, Algorithms, and Data Processing written by Daniele Mortari and published by MDPI. This book was released on 2020-12-07 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Computational Mathematics, Algorithms, and Data Processing” of MDPI consists of articles on new mathematical tools and numerical methods for computational problems. Topics covered include: numerical stability, interpolation, approximation, complexity, numerical linear algebra, differential equations (ordinary, partial), optimization, integral equations, systems of nonlinear equations, compression or distillation, and active learning.
Author : Ivo Babuska
Publisher : Springer Science & Business Media
ISBN 13 : 3642562884
Total Pages : 300 pages
Book Rating : 4.6/5 (425 download)
Download or read book Mathematical Modeling and Numerical Simulation in Continuum Mechanics written by Ivo Babuska and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first international symposium on mathematical foundations of the finite element method was held at the University of Maryland in 1973. During the last three decades there has been great progress in the theory and practice of solving partial differential equations, and research has extended in various directions. Full-scale nonlinear problems have come within the range of nu merical simulation. The importance of mathematical modeling and analysis in science and engineering is steadily increasing. In addition, new possibili ties of analysing the reliability of computations have appeared. Many other developments have occurred: these are only the most noteworthy. This book is the record of the proceedings of the International Sympo sium on Mathematical Modeling and Numerical Simulation in Continuum Mechanics, held in Yamaguchi, Japan from 29 September to 3 October 2000. The topics covered by the symposium ranged from solids to fluids, and in cluded both mathematical and computational analysis of phenomena and algorithms. Twenty-one invited talks were delivered at the symposium. This volume includes almost all of them, and expresses aspects of the progress mentioned above. All the papers were individually refereed. We hope that this volume will be a stepping-stone for further developments in this field.
