Application And Implementation Of Finite Element Methods
Download Application And Implementation Of Finite Element Methods full books in PDF, epub, and Kindle. Read online free Application And Implementation Of Finite Element Methods ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads.
Author |
: Mats G. Larson |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 403 |
Release |
: 2013-01-13 |
ISBN-10 |
: 9783642332876 |
ISBN-13 |
: 3642332870 |
Rating |
: 4/5 (76 Downloads) |
Synopsis The Finite Element Method: Theory, Implementation, and Applications by : Mats G. Larson
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.
Author |
: F. Thomasset |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 168 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783642870477 |
ISBN-13 |
: 3642870473 |
Rating |
: 4/5 (77 Downloads) |
Synopsis Implementation of Finite Element Methods for Navier-Stokes Equations by : F. Thomasset
In structure mechanics analysis, finite element methods are now well estab lished and well documented techniques; their advantage lies in a higher flexibility, in particular for: (i) The representation of arbitrary complicated boundaries; (ii) Systematic rules for the developments of stable numerical schemes ap proximating mathematically wellposed problems, with various types of boundary conditions. On the other hand, compared to finite difference methods, this flexibility is paid by: an increased programming complexity; additional storage require ment. The application of finite element methods to fluid mechanics has been lagging behind and is relatively recent for several types of reasons: (i) Historical reasons: the early methods were invented by engineers for the analysis of torsion, flexion deformation of bearns, plates, shells, etc ... (see the historics in Strang and Fix (1972) or Zienckiewicz (1977». (ii) Technical reasons: fluid flow problems present specific difficulties: strong gradients,l of the velocity or temperature for instance, may occur which a finite mesh is unable to properly represent; a remedy lies in the various upwind finite element schemes which recently turned up, and which are reviewed in chapter 2 (yet their effect is just as controversial as in finite differences). Next, waves can propagate (e.g. in ocean dynamics with shallowwaters equations) which will be falsely distorted by a finite non regular mesh, as Kreiss (1979) pointed out. We are concerned in this course with the approximation of incompressible, viscous, Newtonian fluids, i.e. governed by N avier Stokes equations.
Author |
: Thomas Apel |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 380 |
Release |
: 2012-07-16 |
ISBN-10 |
: 9783642303166 |
ISBN-13 |
: 3642303161 |
Rating |
: 4/5 (66 Downloads) |
Synopsis Advanced Finite Element Methods and Applications by : Thomas Apel
This volume on some recent aspects of finite element methods and their applications is dedicated to Ulrich Langer and Arnd Meyer on the occasion of their 60th birthdays in 2012. Their work combines the numerical analysis of finite element algorithms, their efficient implementation on state of the art hardware architectures, and the collaboration with engineers and practitioners. In this spirit, this volume contains contributions of former students and collaborators indicating the broad range of their interests in the theory and application of finite element methods. Topics cover the analysis of domain decomposition and multilevel methods, including hp finite elements, hybrid discontinuous Galerkin methods, and the coupling of finite and boundary element methods; the efficient solution of eigenvalue problems related to partial differential equations with applications in electrical engineering and optics; and the solution of direct and inverse field problems in solid mechanics.
Author |
: Gang Li |
Publisher |
: Cambridge University Press |
Total Pages |
: 525 |
Release |
: 2020-07-30 |
ISBN-10 |
: 9781108573863 |
ISBN-13 |
: 110857386X |
Rating |
: 4/5 (63 Downloads) |
Synopsis Introduction to the Finite Element Method and Implementation with MATLAB® by : Gang Li
Connecting theory with numerical techniques using MATLAB®, this practical textbook equips students with the tools required to solve finite element problems. This hands-on guide covers a wide range of engineering problems through nine well-structured chapters including solid mechanics, heat transfer and fluid dynamics; equilibrium, steady state and transient; and 1-D, 2-D and 3-D problems. Engineering problems are discussed using case study examples, which are solved using a systematic approach, both by examining the steps manually and by implementing a complete MATLAB®code. This topical coverage is supplemented by discourse on meshing with a detailed explanation and implementation of 2-D meshing algorithms. Introducing theory and numerical techniques alongside comprehensive examples this text increases engagement and provides students with the confidence needed to implement their own computer codes to solve given problems.
Author |
: Pin Tong |
Publisher |
: Dover Books on Engineering |
Total Pages |
: 0 |
Release |
: 2008 |
ISBN-10 |
: 0486466760 |
ISBN-13 |
: 9780486466767 |
Rating |
: 4/5 (60 Downloads) |
Synopsis Finite Element Method by : Pin Tong
This text introduces mathematical foundations, developing them coherently and rigorously to reveal the method's broad applications. It emphasizes use of the variational approach, providing appendixes on variational calculus and matrix algebra for a self-contained treatment. Detailed examples employ Poisson's equations and the general Sturm-Liouville problem. 1977 edition.
Author |
: Susanne Brenner |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 369 |
Release |
: 2013-03-14 |
ISBN-10 |
: 9781475736588 |
ISBN-13 |
: 1475736584 |
Rating |
: 4/5 (88 Downloads) |
Synopsis The Mathematical Theory of Finite Element Methods by : Susanne Brenner
A rigorous and thorough mathematical introduction to the subject; A clear and concise treatment of modern fast solution techniques such as multigrid and domain decomposition algorithms; Second edition contains two new chapters, as well as many new exercises; Previous edition sold over 3000 copies worldwide
Author |
: Jože Korelc |
Publisher |
: Springer |
Total Pages |
: 367 |
Release |
: 2016-06-08 |
ISBN-10 |
: 9783319390055 |
ISBN-13 |
: 3319390058 |
Rating |
: 4/5 (55 Downloads) |
Synopsis Automation of Finite Element Methods by : Jože Korelc
New finite elements are needed as well in research as in industry environments for thedevelopment of virtual prediction techniques. The design and implementation of novel finiteelements for specific purposes is a tedious and time consuming task, especially for nonlinearformulations. The automation of this process can help to speed up this processconsiderably since the generation of the final computer code can be accelerated by order ofseveral magnitudes.This book provides the reader with the required knowledge needed to employ modernautomatic tools like AceGen within solid mechanics in a successful way. It covers the rangefrom the theoretical background, algorithmic treatments to many different applications. Thebook is written for advanced students in the engineering field and for researchers ineducational and industrial environments.
Author |
: Stéphane P. A. Bordas |
Publisher |
: Springer |
Total Pages |
: 371 |
Release |
: 2018-03-13 |
ISBN-10 |
: 9783319714318 |
ISBN-13 |
: 3319714317 |
Rating |
: 4/5 (18 Downloads) |
Synopsis Geometrically Unfitted Finite Element Methods and Applications by : Stéphane P. A. Bordas
This book provides a snapshot of the state of the art of the rapidly evolving field of integration of geometric data in finite element computations. The contributions to this volume, based on research presented at the UCL workshop on the topic in January 2016, include three review papers on core topics such as fictitious domain methods for elasticity, trace finite element methods for partial differential equations defined on surfaces, and Nitsche’s method for contact problems. Five chapters present original research articles on related theoretical topics, including Lagrange multiplier methods, interface problems, bulk-surface coupling, and approximation of partial differential equations on moving domains. Finally, two chapters discuss advanced applications such as crack propagation or flow in fractured poroelastic media. This is the first volume that provides a comprehensive overview of the field of unfitted finite element methods, including recent techniques such as cutFEM, traceFEM, ghost penalty, and augmented Lagrangian techniques. It is aimed at researchers in applied mathematics, scientific computing or computational engineering.
Author |
: Jonathan Whiteley |
Publisher |
: Springer |
Total Pages |
: 236 |
Release |
: 2017-01-26 |
ISBN-10 |
: 9783319499710 |
ISBN-13 |
: 3319499718 |
Rating |
: 4/5 (10 Downloads) |
Synopsis Finite Element Methods by : Jonathan Whiteley
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.
Author |
: I. M. Smith |
Publisher |
: John Wiley & Sons |
Total Pages |
: 649 |
Release |
: 2005-06-10 |
ISBN-10 |
: 9780470011249 |
ISBN-13 |
: 0470011246 |
Rating |
: 4/5 (49 Downloads) |
Synopsis Programming the Finite Element Method by : I. M. Smith
This title demonstrates how to develop computer programmes which solve specific engineering problems using the finite element method. It enables students, scientists and engineers to assemble their own computer programmes to produce numerical results to solve these problems. The first three editions of Programming the Finite Element Method established themselves as an authority in this area. This fully revised 4th edition includes completely rewritten programmes with a unique description and list of parallel versions of programmes in Fortran 90. The Fortran programmes and subroutines described in the text will be made available on the Internet via anonymous ftp, further adding to the value of this title.