Download or read book Finite Element Methods in Linear Ideal Magnetohydrodynamics written by Ralf Gruber and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than ten years we have been working with the ideal linear MHD equations used to study the stability of thermonuc1ear plasmas. Even though the equations are simple and the problem is mathematically well formulated, the numerical problems were much harder to solve than anticipated. Already in the one-dimensional cylindrical case, what we called "spectral pollution" appeared. We were able to eliminate it by our "ecological solution". This solution was applied to the two-dimensional axisymmetric toroidal geometry. Even though the spectrum was unpolluted the precision was not good enough. Too many mesh points were necessary to obtain the demanded precision. Our solution was what we called the "finite hybrid elements". These elements are efficient and cheap. They have also proved their power when applied to calculating equilibrium solutions and will certainly penetrate into other domains in physics and engineering. During all these years, many colleagues have contributed to the construc tion, testing and using of our stability code ERATO. We would like to thank them here. Some ofthem gave partial contributions to the book. Among them we mention Dr. Kurt Appert, Marie-Christine Festeau-Barrioz, Roberto Iacono, Marie-Alix Secretan, Sandro Semenzato, Dr. Jan Vac1avik, Laurent Villard and Peter Merkel who kindly agreed to write Chap. 6. Special thanks go to Hans Saurenmann who drew most of the figures, to Dr
Download or read book Finite Element Methods in Linear Ideal Magnetohydrodynamics written by Ralf Gruber and published by . This book was released on 1985-07-01 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 The Finite Element Method written by Darrell W. Pepper and published by CRC Press. This book was released on 2017-04-11 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-explanatory guide introduces the basic fundamentals of the Finite Element Method in a clear manner using comprehensive examples. Beginning with the concept of one-dimensional heat transfer, the first chapters include one-dimensional problems that can be solved by inspection. The book progresses through more detailed two-dimensional elements to three-dimensional elements, including discussions on various applications, and ending with introductory chapters on the boundary element and meshless methods, where more input data must be provided to solve problems. Emphasis is placed on the development of the discrete set of algebraic equations. The example problems and exercises in each chapter explain the procedure for defining and organizing the required initial and boundary condition data for a specific problem, and computer code listings in MATLAB and MAPLE are included for setting up the examples within the text, including COMSOL files. Widely used as an introductory Finite Element Method text since 1992 and used in past ASME short courses and AIAA home study courses, this text is intended for undergraduate and graduate students taking Finite Element Methodology courses, engineers working in the industry that need to become familiar with the FEM, and engineers working in the field of heat transfer. It can also be used for distance education courses that can be conducted on the web. Highlights of the new edition include: - Inclusion of MATLAB, MAPLE code listings, along with several COMSOL files, for the example problems within the text. Power point presentations per chapter and a solution manual are also available from the web. - Additional introductory chapters on the boundary element method and the meshless method. - Revised and updated content. -Simple and easy to follow guidelines for understanding and applying the Finite Element Method.
Download or read book Finite Element Method written by Sinan Muftu and published by Academic Press. This book was released on 2022-07-14 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Element Method: Physics and Solution Methods aims to provide the reader a sound understanding of the physical systems and solution methods to enable effective use of the finite element method. This book focuses on one- and two-dimensional elasticity and heat transfer problems with detailed derivations of the governing equations. The connections between the classical variational techniques and the finite element method are carefully explained. Following the chapter addressing the classical variational methods, the finite element method is developed as a natural outcome of these methods where the governing partial differential equation is defined over a subsegment (element) of the solution domain. As well as being a guide to thorough and effective use of the finite element method, this book also functions as a reference on theory of elasticity, heat transfer, and mechanics of beams. Covers the detailed physics governing the physical systems and the computational methods that provide engineering solutions in one place, encouraging the reader to conduct fully informed finite element analysis Addresses the methodology for modeling heat transfer, elasticity, and structural mechanics problems Extensive worked examples are provided to help the reader to understand how to apply these methods in practice
Download or read book Introduction to Finite and Spectral Element Methods using MATLAB written by Constantine Pozrikidis and published by CRC Press. This book was released on 2005-06-17 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why another book on the finite element method? There are currently more than 200 books in print with "Finite Element Method" in their titles. Many are devoted to special topics or emphasize error analysis and numerical accuracy. Others stick to the fundamentals and do little to describe the development and implementation of algorithms for solving real-world problems. Introduction to Finite and Spectral Element Methods Using MATLAB provides a means of quickly understanding both the theoretical foundation and practical implementation of the finite element method and its companion spectral element method. Written in the form of a self-contained course, it introduces the fundamentals on a need-to-know basis and emphasizes algorithm development and computer implementation of the essential procedures. Firmly asserting the importance of simultaneous practical experience when learning any numerical method, the author provides FSELIB: a software library of user-defined MATLAB functions and complete finite and spectral element codes. FSELIB is freely available for download from http://dehesa.freeshell.org, which is also a host for the book, providing further information, links to resources, and FSELIB updates. The presentation is suitable for both self-study and formal course work, and its state-of-the-art review of the field make it equally valuable as a professional reference. With this book as a guide, you immediately will be able to run the codes as given and graphically display solutions to a wide variety of problems in heat transfer and solid, fluid, and structural mechanics.
Download or read book Finite Elements and Fast Iterative Solvers written by Howard C. Elman and published by Oxford University Press. This book was released on 2014 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical graduate text on Scientific Computing with a focus on numerical solution of partial differential equations and numerical linear algebra. This book, and its associated freely downloadable MATLAB software, is relevant to engineers, applied mathematicians, numerical analysts, and people working in interdisciplinary Scientific Computing.
Download or read book The Finite Element Method written by Patrick Ciarlet and published by John Wiley & Sons. This book was released on 2023-08-29 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite element method, which emerged in the 1950s to deal with structural mechanics problems, has since undergone continuous development. Using partial differential equation models, it is now present in such fields of application as mechanics, physics, chemistry, economics, finance and biology. It is also used in most scientific computing software, and many engineers become adept at using it in their modeling and numerical simulation activities. This book presents all the essential elements of the finite element method in a progressive and didactic way: the theoretical foundations, practical considerations of implementation, algorithms, as well as numerical illustrations created in MATLAB. Original exercises with detailed answers are provided at the end of each chapter.
Download or read book Finite Elements written by J. Bonet and published by Bloomsbury Publishing. This book was released on 1996-11-11 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite element method is popular among engineers and scientists as a numerical technique for solving practical problems. At the same time, the links with classical variational methods make the technique of interest to mathematicians. This book introduces the main concepts of the finite element method in a simple and carefully paced manner, using numerical examples wherever possible. Both the theoretical and practical aspects are described and explained. A basic knowledge of engineering mathematics is all that is required, and the style is not formal. The approach and treatment are intended to appeal to the advanced undergraduate or postgraduate, or to the practising engineer who wishes to acquire a deeper understanding of the finite element software that he is using.
Download or read book Finite Element Methods in CAD written by Jean Claude Sabonnadiere and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite element method (FEM) has been understood, at least in principle, for more than 50 years. The integral formulation on which it is based has been known for a longer time (thanks to the work of Galerkin, Ritz, Courant and Hilbert,1.4 to mention the most important). However, the method could not be applied in a practical way since it involved the solution of a large number of linear or non-linear algebraic equations. Today it is quite common, with the aid of computers, to solve non-linear algebraic problems of several thousand equations. The necessary numerical methods and programming techniques are now an integral part of the teaching curriculum in most engineering schools. Mechanical engineers, confronted with very complicated structural problems, were the first to take advantage of advanced computational methods and high level languages (FORTRAN) to transform the mechanical models into algebraic equations (1956). In recent times (1960), the FEM has been studied by applied mathematicians and, having received rigorous treatment, has become a part of the more general study of partial differential equations, gradually replacing the finite difference method which had been considered the universal tool to solve these types of problems.
Download or read book Finite Element Methods for Maxwell s Equations written by Peter Monk and published by Clarendon Press. This book was released on 2003-04-17 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the middle of the last century, computing power has increased sufficiently that the direct numerical approximation of Maxwell's equations is now an increasingly important tool in science and engineering. Parallel to the increasing use of numerical methods in computational electromagnetism there has also been considerable progress in the mathematical understanding of the properties of Maxwell's equations relevant to numerical analysis. The aim of this book is to provide an up to date and sound theoretical foundation for finite element methods in computational electromagnetism. The emphasis is on finite element methods for scattering problems that involve the solution of Maxwell's equations on infinite domains. Suitable variational formulations are developed and justified mathematically. An error analysis of edge finite element methods that are particularly well suited to Maxwell's equations is the main focus of the book. The methods are justified for Lipschitz polyhedral domains that can cause strong singularities in the solution. The book finishes with a short introduction to inverse problems in electromagnetism.
Download or read book Introduction to the Finite Element Method in Electromagnetics written by Anastasis C. Polycarpou and published by Morgan & Claypool Publishers. This book was released on 2006 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is an introduction to the finite element method with applications in electromagnetics. Author Anastasis Polycarpou begins with the basics of the method, including formulating a boundary-value problem using a weighted-residual method and the Galerkin approach, followed by the imposition of all three types of boundary conditions, including absorbing boundary conditions. Another important topic of emphasis is the development of shape functions including those of higher order. This book provides the reader with all information necessary to apply the finite element method to one- and two-dimensional boundary-value problems in electromagnetics."--BOOK JACKET.
Download or read book Finite Element Method written by Gouri Dhatt and published by John Wiley & Sons. This book was released on 2012-12-27 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an in-depth presentation of the finite element method, aimed at engineers, students and researchers in applied sciences. The description of the method is presented in such a way as to be usable in any domain of application. The level of mathematical expertise required is limited to differential and matrix calculus. The various stages necessary for the implementation of the method are clearly identified, with a chapter given over to each one: approximation, construction of the integral forms, matrix organization, solution of the algebraic systems and architecture of programs. The final chapter lays the foundations for a general program, written in Matlab, which can be used to solve problems that are linear or otherwise, stationary or transient, presented in relation to applications stemming from the domains of structural mechanics, fluid mechanics and heat transfer.
Download or read book The Finite Element Method written by Zhu and published by John Wiley & Sons. This book was released on 2018-03-20 with total page 872 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive review of the Finite Element Method (FEM), this book provides the fundamentals together with a wide range of applications in civil, mechanical and aeronautical engineering. It addresses both the theoretical and numerical implementation aspects of the FEM, providing examples in several important topics such as solid mechanics, fluid mechanics and heat transfer, appealing to a wide range of engineering disciplines. Written by a renowned author and academician with the Chinese Academy of Engineering, The Finite Element Method would appeal to researchers looking to understand how the fundamentals of the FEM can be applied in other disciplines. Researchers and graduate students studying hydraulic, mechanical and civil engineering will find it a practical reference text.
Download or read book Finite Element Methods written by Jonathan Whiteley and published by Springer. This book was released on 2017-01-26 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.
Download or read book The Finite Element Method written by Douglas H. Norrie and published by Academic Press. This book was released on 2014-05-10 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Finite Element Method: Fundamentals and Applications demonstrates the generality of the finite element method by providing a unified treatment of fundamentals and a broad coverage of applications. Topics covered include field problems and their approximate solutions; the variational method based on the Hilbert space; and the Ritz finite element method. Finite element applications in solid and structural mechanics are also discussed. Comprised of 16 chapters, this book begins with an introduction to the formulation and classification of physical problems, followed by a review of field or continuum problems and their approximate solutions by the method of trial functions. It is shown that the finite element method is a subclass of the method of trial functions and that a finite element formulation can, in principle, be developed for most trial function procedures. Variational and residual trial function methods are considered in some detail and their convergence is examined. After discussing the calculus of variations, both in classical and Hilbert space form, the fundamentals of the finite element method are analyzed. The variational approach is illustrated by outlining the Ritz finite element method. The application of the finite element method to solid and structural mechanics is also considered. This monograph will appeal to undergraduate and graduate students, engineers, scientists, and applied mathematicians.
Download or read book The Finite Element Method written by Patrick Ciarlet and published by John Wiley & Sons. This book was released on 2023-07-26 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite element method, which emerged in the 1950s to deal with structural mechanics problems, has since undergone continuous development. Using partial differential equation models, it is now present in such fields of application as mechanics, physics, chemistry, economics, finance and biology. It is also used in most scientific computing software, and many engineers become adept at using it in their modeling and numerical simulation activities. This book presents all the essential elements of the finite element method in a progressive and didactic way: the theoretical foundations, practical considerations of implementation, algorithms, as well as numerical illustrations created in MATLAB. Original exercises with detailed answers are provided at the end of each chapter.
