Download or read book The Multiscale Finite Element Method MsFEM and Its Applications written by Yalchin Rafik Efendiev and published by . This book was released on 1999 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

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.

Download or read book Multiscale Finite Element Methods written by Yalchin Efendiev and published by Springer. This book was released on 2009-02-05 with total page 0 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.

Download or read book Finite Element Methods and Their Applications written by Zhangxin Chen and published by Springer Science & Business Media. This book was released on 2005-10-14 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduce every concept in the simplest setting and to maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. Contains unique recent developments of various finite elements such as nonconforming, mixed, discontinuous, characteristic, and adaptive finite elements, along with their applications. Describes unique recent applications of finite element methods to important fields such as multiphase flows in porous media and semiconductor modelling. Treats the three major types of partial differential equations, i.e., elliptic, parabolic, and hyperbolic equations.

Download or read book Multiscale Model Reduction written by Eric Chung and published by Springer Nature. This book was released on 2023-06-07 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the study of multiscale model reduction methods from the point of view of multiscale finite element methods. Multiscale numerical methods have become popular tools for modeling processes with multiple scales. These methods allow reducing the degrees of freedom based on local offline computations. Moreover, these methods allow deriving rigorous macroscopic equations for multiscale problems without scale separation and high contrast. Multiscale methods are also used to design efficient solvers. This book offers a combination of analytical and numerical methods designed for solving multiscale problems. The book mostly focuses on methods that are based on multiscale finite element methods. Both applications and theoretical developments in this field are presented. The book is suitable for graduate students and researchers, who are interested in this topic.

Download or read book A New Adaptive Multiscale Finite Element Method with Applications to High Contrast Interface Problems written by Raymond Millward and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we show that the finite element error for the high contrast elliptic interface problem is independent of the contrast in the material coefficient under certain assumptions. The error estimate is proved using a particularly technical proof with construction of a specific function from the finite dimensional space of piecewise linear functions. We review the multiscale finite element method of Chu, Graham and Hou to give clearer insight. We present some generalisations to extend their work on a priori contrast independent local boundary conditions, which are then used to find multiscale basis functions by solving a set of local problems. We make use of their regularity result to prove a new relative error estimate for both the standard finte element method and the multiscale finite element method that is completely coefficient independent The analytical results we explore in this thesis require a complicated construction. To avoid this we present an adaptive multiscale finite element method as an enhancement to the adaptive local-global method of Durlofsky, Efendiev and Ginting. We show numerically that this adaptive method converges optimally as if the coefficient were smooth even in the presence of singularities as well as in the case of a realisation of a random field. The novel application of this thesis is where the adaptive multiscale finite element method has been applied to the linear elasticity problem arising from the structural optimisation process in mechanical engineering. We show that a much smoother sensitivity profile is achieved along the edges of a structure with the adaptive method and no additional heuristic smoothing techniques are needed. We finally show that the new adaptive method can be efficiently implemented in parallel and the processing time scales well as the number of processors increases. The biggest advantage of the multiscale method is that the basis functions can be repeatedly used for additional problems with the same high contrast material coefficient.

Download or read book Finite Element Method with Applications in Engineering written by Y. M. Desai and published by Pearson Education India. This book was released on 2011 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book explains the finite element method with various engineering applications to help students, teachers, engineers and researchers. It explains mathematical modeling of engineering problems and approximate methods of analysis and different approaches

Download or read book FINITE ELEMENT METHODS written by CHENNAKESAVA R. ALAVALA and published by PHI Learning Pvt. Ltd.. This book was released on 2008-11-10 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Element Methods form an indispensable part of engineering analysis and design. The strength of FEM is the ease and elegance with which it handles the boundary conditions. This compact and well-organized text presents a comprehensive analysis of Finite Element Methods (FEM). The book gives a clear picture of structural, torsion, free-vibration, heat transfer and fluid flow problems. It also provides detailed description of equations of equilibrium, stress-strain relations, interpolation functions and element design, symmetry and applications of FEM. The text is a synthesis of both the physical and the mathematical characteristics of finite element methods. A question bank at the end of each chapter comprises descriptive and objective type questions to drill the students in self-study. KEY FEATURES Includes step-by-step procedure to solve typical problems using ANSYS® software. Gives numerical problems in SI units. Elaborates shaper functions for higher-order elements. Furnishes a large number of worked-out examples and solved problems. This profusely illustrated, student-friendly text is intended primarily for undergraduate students of Mechanical/Production/Civil and Aeronautical Engineering. By a judicious selection of topics, it can also be profitably used by postgraduate students of these disciplines. In addition, practising engineers and scientists should find it very useful besides students preparing for competitive exams.

Download or read book The Finite Element Method Theory Implementation and Applications written by Mats G. Larson and published by Springer Science & Business Media. This book was released on 2013-01-13 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.​

Download or read book The Finite Element Method written by Darrell W. Pepper and published by Taylor & Francis. This book was released on 2005-10-31 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This much-anticipated second edition introduces the fundamentals of the finite element method featuring clear-cut examples and an applications-oriented approach. Using the transport equation for heat transfer as the foundation for the governing equations, this new edition demonstrates the versatility of the method for a wide range of applications, including structural analysis and fluid flow. Much attention is given to the development of the discrete set of algebraic equations, beginning with simple one-dimensional problems that can be solved by inspection, continuing to two- and three-dimensional elements, and ending with three chapters describing applications. The increased number of example problems per chapter helps build an understanding of the method to define and organize required initial and boundary condition data for specific problems. In addition to exercises that can be worked out manually, this new edition refers to user-friendly computer codes for solving one-, two-, and three-dimensional problems. Among the first FEM textbooks to include finite element software, the book contains a website with access to an even more comprehensive list of finite element software written in FEMLAB, MAPLE, MathCad, MATLAB, FORTRAN, C++, and JAVA - the most popular programming languages. This textbook is valuable for senior level undergraduates in mechanical, aeronautical, electrical, chemical, and civil engineering. Useful for short courses and home-study learning, the book can also serve as an introduction for first-year graduate students new to finite element coursework and as a refresher for industry professionals. The book is a perfect lead-in to Intermediate Finite Element Method: Fluid Flow and Heat and Transfer Applications (Taylor & Francis, 1999, Hb 1560323094).

Download or read book Finite Element Methods and Their Applications written by Mahboub Baccouch and published by BoD – Books on Demand. This book was released on 2021-11-17 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides several applications of the finite element method (FEM) for solving real-world problems. FEM is a widely used technique for numerical simulations in many areas of physics and engineering. It has gained increased popularity over recent years for the solution of complex engineering and science problems. FEM is now a powerful and popular numerical method for solving differential equations, with flexibility in dealing with complex geometric domains and various boundary conditions. The method has a wide range of applications in various branches of engineering such as mechanical engineering, thermal and fluid flows, electromagnetics, business management, and many others. This book describes the development of FEM and discusses and illustrates its specific applications.

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.

Download or read book Finite Element Method for Solids and Structures written by Sung W. Lee and published by Cambridge University Press. This book was released on 2021-06-17 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This innovative approach to teaching the finite element method blends theoretical, textbook-based learning with practical application using online and video resources. This hybrid teaching package features computational software such as MATLAB®, and tutorials presenting software applications such as PTC Creo Parametric, ANSYS APDL, ANSYS Workbench and SolidWorks, complete with detailed annotations and instructions so students can confidently develop hands-on experience. Suitable for senior undergraduate and graduate level classes, students will transition seamlessly between mathematical models and practical commercial software problems, empowering them to advance from basic differential equations to industry-standard modelling and analysis. Complete with over 120 end-of chapter problems and over 200 illustrations, this accessible reference will equip students with the tools they need to succeed in the workplace.

Download or read book A Multiscale stabilized Finite Element Method for Solid Mechanics written by Kaiming Xia and published by . This book was released on 2003 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book Finite Element Method written by Michael R. Gosz and published by CRC Press. This book was released on 2017-03-27 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite element method (FEM) is the dominant tool for numerical analysis in engineering, yet many engineers apply it without fully understanding all the principles. Learning the method can be challenging, but Mike Gosz has condensed the basic mathematics, concepts, and applications into a simple and easy-to-understand reference. Finite Element Method: Applications in Solids, Structures, and Heat Transfer navigates through linear, linear dynamic, and nonlinear finite elements with an emphasis on building confidence and familiarity with the method, not just the procedures. This book demystifies the assumptions made, the boundary conditions chosen, and whether or not proper failure criteria are used. It reviews the basic math underlying FEM, including matrix algebra, the Taylor series expansion and divergence theorem, vectors, tensors, and mechanics of continuous media. The author discusses applications to problems in solid mechanics, the steady-state heat equation, continuum and structural finite elements, linear transient analysis, small-strain plasticity, and geometrically nonlinear problems. He illustrates the material with 10 case studies, which define the problem, consider appropriate solution strategies, and warn against common pitfalls. Additionally, 35 interactive virtual reality modeling language files are available for download from the CRC Web site. For anyone first studying FEM or for those who simply wish to deepen their understanding, Finite Element Method: Applications in Solids, Structures, and Heat Transfer is the perfect resource.