Finite Elements In ElectroMagnetics and Other Applications.

Book Description from the Back Cover.

A systematic treatment of the finite element method.

The finite element method is one of the preeminent simulation techniques for obtaining solutions to boundary-value problems in mathematical physics. It has applications in a variety of engineering and scientifyc studies. such as antennas, radar, microwaves engineering, high-speed/high-frequency circuits, wireless communication, electro-optical engineering, remotesensing, bioelectromagnetics, and geoelectromagnetics. This second edition of an essential text teaches the finite element method for electromagnetic analysis. It offers engineers a methodical way to quickly master this very powerful technique for solving practical, often complicated, engineering problems.

This book provides the first sustematic treatment of this numerical analysis technique for electromagnetics, including a breif overview of the two classic methods - the Ritz variational method and Galerkin's method - which form the foundation of the finite element function. Employing an example to introduce the concept of the finite element method and describe the essential steps of the technique, the author lays groundwork for a broad-based understanding of the finite element method's usefulness. He completes his coverage by describing the finite element analysis of one-, two-, and three-dimensional problems, developing for each problem a rigorous finite element solution in general form from which solutions to specific problems can be deduced.

Carefully updated to include the most recent developments, the Second Edition now includes new coverage of:

• Absorbing boundary conditions.
• A hydrid technique for pen-region scattering and radiation problems.
• Eigenfunction expansions on elliptical boundaries.
• Time-domain analysis of transient electromagnetic problems.
• The method of moments and its fast solvers.

Jianming Jin, PhD, earned his doctorate in electrical engineering at the University of Michigan and is currently a professor at the University of Illinois. He is the author of the first edition of The Finite Element Method in Electromagnetics, Computation of Special Functions ( with S. Zhang; published by Wiley ), Electromagnetic Analysis and Design in Magnetic Resonance Imaging, and coedited ( with W.C.Chew, E.Michelson, and J.M.Song ) Fast and Efficient Algorithms in Computational Electromagnetics.

Table of Contents.

• 1. Basic Electromagnetic Theory.
• 2. Introduction to Finite Element Method.
• 3. One-Dimensional Finite Element Analysis.
• 4. Two-Dimensional Finite Element Analysis.
• 5. Three-Dimensional Finite Element Analysis.
• 6. Variational Principles for Electromagnetics.
• 7. Eigenvalue Problems: Waveguides and Cavities.
• 8. Vector Finite Elements.
• 9. Absorving Boundary Conditions.
• 10. Finite Element-Boundary Integral Methods.
• 11. Finite Elements and Eigenfunction Expansion.
• 12. Finite Element in the Time Domain.
• 13. Solution of Finite Element Equations.
• 14. The Method of Moments and Fast Solvers.
• Appendix A. Vector Identities and Integral Theorems.
• Appendix B. The Ritz Procedure for Complex-Valued Problems.
• Appendix C. Green's Functions.
• Appendix D. Singular Integral Evaluation References.
• Appendix E. Special Functions.

Unlike any other source in the field, Electromagnetic Modeling by Finite Element Methods examines key aspects of the finite element method (FEM) for electromagnetic analysis of low-frequency electrical devices. This reference examines phenomena such as nonlinearity, mechanical force, electrical circuit coupling, vibration, heat, and movement for applications in the electrical, mechanical, nuclear, aeronautics, and transportation industries. It offers a wide range of examples, including torque, vibration, and iron loss calculation; coupling of the FEM with mechanical equations, circuits, converters, and thermal effects; and proven methods for hysteresis implementation into FEM codes.

Book Info

Text examines key aspects of the finite element method (FEM) for electromagnetic analysis of low-frequency electrical devices. Examines phenomena such as nonlinearity, mechanical force, electrical circuit coupling, and vibration. For advanced undergraduate and graduate students.

Table od Contents.

• Mathematical Preliminaries.
• Maxwell Equations, Electrostatics, Magnetostatics, and Magnetodynamic Fields.
• Brief Presentation of Finite Element Method.
• The Finite Element Method Applied to 2D Electromagnetic Cases.
• Coupling of Field and Electrical Circuit Equations.
• Movement Modeling of Electrical Machines.
• Interaction Between Electromagnetic and Mechanical Forces.
• Iron Losses.

Book Description

From simple to complex analyses, this book leads readers step-by-step through the procedures and illustrates their implementation through examples of both traditional and innovative machines. Although the examples are of specific devices, they demonstrate how the procedures apply to any type of electrical machine, introducing a preliminary theory followed by various considerations for the unique circumstance. The author presents the mathematical background underlying the analysis, but emphasizes application of the techniques, common strategies, and obtained results. He also supplies codes for simple algorithms and reveals analytical methodologies that generalize to any software program.

Book Description- From the Back Cover of third edition.

This is the third edition of the principal text on te finite element method, which has become a major solution technique for problems of engineering electromagnetics. It presents the method in a methematically undemanding style, accessible to undergraduates who may be encountering it for the first time, but the scope is sufficiently broad as to be equally suitable for use by deriving finite elements solutions for the simplest familiar potential fields, then builds on these to formulate elements solutions for a wide range of applied electromagnetics problems. These include wave propagation, diffusion, and static fields; open-boundary problems nd nonlinear materials; axisymmetric, planar and fully three-dimensional geometries; scalar and vector fields.

This new edition is more than half as long again as its predecessor and includes much new material. Exterior problems of wave propagation, edge elements, and many other recent developments are now included. The original material has been extensively revised and in many cases entirely new treatments have been substituted for the old. For example, the authors' development of triangular and tetrahedral elements is greatly simpified yet by far the most comprehensive evailable in print anywhere. A wide selection of fully documented demonstrarion programs accompany the text, allowing the reader to see how the methods are put to work in practice.

This book provides all that is needed for anyone from begining student to experienced engineer to make full use of finite elements in electrical engineering.

NOTE: You can download all programs in this book from: http://publishing.cambridge.org/resources/0521445051/

Table of Contents.

• 1. Finite Elements in One Dimension.
• 2. First-order Triangular Elements for Potential Problems.
• 3. Electromagnetics of Finite Elements.
• 4. Simplex Elements for the Scalar Helmholtz Equation.
• 5. Differential Operations in Ferromagnetic Materials.
• 6. Finite Elements for Integral Operators
• 7. Curvilinear, Vectorial and Unbounded Elements.
• 8. Time and Frequency Domain Problems in Bounded Systems.
• 9. Unbounded Radiation and Scattering.
• 10. Numerical Solution of Finite Element Equations.
• Appendix1. Calculation on Simplex Elements.
• Appendix2. Integration by parts, Green's theorems and Green's Functions.
• Appendix3. Simplex Element Tables.
• Appendix4. Utility Programs and Style Notes.
• Appendix5. Laboratory Problems and Exercices.
• Index.

Book Description

J.N. Reddy's, An Introduction to the Finite Element Method, third edition is an update of one of the most popular FEM textbooks available. The book retains its strong conceptual approach, clearly examining the mathematical underpinnings of FEM, and providing a general approach of engineering application areas.

Known for its detailed, carefully selected example problems and extensive selection of homework problems, the author has comprehensively covered a wide range of engineering areas making the book approriate for all engineering majors, and underscores the wide range of use FEM has in the professional world.

A supplementary text Web site located at http://www.mhhe.com/reddy3e contains password-protected solutions to end-of-chapter problems, general textbook information, supplementary chapters on the FEM1D and FEM2D computer programs, and more!

Book Description. From the Back Cover.

Introduction to Finite Elements in Engineering provides an integrated approach to finite methodologies through the integration of exercices and examples involving engineering applications. The steps used in the development of the theory are implemented in complete, self-contained computer programs, while retaining the strategies and philosophies of previous editions. It serves as a primary textbook for senior undergraduate and first-year students as well as an invaluable learning resource for practicing engineers.

Additional programs and source code on a companion CD. Includes complete self-contained computer programs with source codes in Visual Basic, Excel-based Visual Basic, MATLAB, QUICKBASIC, FORTRAN, and C.

Table of Contents.

• Preface.
• 1. Fundamental Concepts.
• 2. Matrix Algebra and Gaussian Elimination.
• 3. One-Dimensional Problems.
• 4. Trusses.
• 5. Two-Dimensional Problems using Constant Strain Triangles.
• 6. AxiSymmetric Soilds Subjected to AxiSymmetric Loading.
• 7. Two-Dimensional Problems IsoParametric Elements and Numerical Integration.
• 8. Beams and Frames.
• 9. Three-Dimensional Problems in Stress Analysis.
• 10. Scalar Field Problems.
• 11. Dynamic Considerations.
• 12. PreProcessing and PostProcessing.
• Answers to Selected Problems.

Book Description

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.

Back Cover Copy

Following the highly successful previous editions, this Third edition contains programs and subroutine libraries fully updated in Fortran 90, which are also available on the Internet via anonymous ftp. A wide variety of new problem solving analyses are presented, including classical structural analysis, elasticity and plasticity, steady state and transient fluid flow, linear and non-linear solid dynamics and construction processes in geomechanics. The authors provide: a clear outline of programming philosophy programs which illustrate analytic rather than numerical evaluation of element properties exercises for students to solve Unique elements of the text include: practical problems in Fortran 90 instructions to the reader for developing their own computer programs which use the finite element method to solve specific problems guidelines towards vectorisable/parallelisable programs ?Mesh-free or ?element-by-element techniques supplanting traditional ?mesh-dependent or ? global element assembly methods in every chapter.

These improvements all contribute to a more comprehensive book with a wide appeal, but which will be of particular interest to students and practitioners in the application of the finite element method, and problems related to its use; undergraduates and postgraduates in civil engineering (applications in fields of Geomechanics), mechanical engineering (stress and fluid flow problems), applied mathematics and physics (solution of partial differential equations), and engineers in the fields as indicated above. --This text refers to an out of print or unavailable edition of this title.

About the Author

Professor Smith is currently the Head of the Geotechnics Division at the Manchester Centre for Civil and Construction Engineering, UMIST.

Professor Griffiths is Professor of Civil Engineering, Division of Engineering at the Colorado School of Mines.

Table of Contents.

• Preliminaries: Computer Strategies.
• Spatial Discretisation by Finite Elements.
• Programming Finite Element Computations.
• Static Equilibrium of Structures.
• Static Equilibrium of Linear Elastic Solids.
• Material Non-linearity.
• Steady State Flow.
• Transient Problems: First Order.
• Coupled Problems.
• Eigenvalue Problems.
• Forced Vibrations.
• Parallel Processing of Finite Element Analyses.
• A. Equivalent Nodal Loads.
• B. Shape Functions and Element Node Numbering.
• C. Plastic Stress-strain Matrices and Plastic Potential Derivatives.
• D. main Library Subroutines.
• E. geom Library Subroutines.
• F. Parallel Library Subroutine.

Book Description

This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. This expanded second edition contains new chapters on additive Schwarz preconditioners and adaptive meshes. New exercises have also been added throughout. The book will be useful to mathematicians as well as engineers and physical scientists. It can be used for a course that provides an introduction to basic functional analysis, approximation theory, and numerical analysis, while building upon and applying basic techniques of real variable theory. Different course paths can be chosen, allowing the book to be used for courses designed for students with different interests.

Book Info

Develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. Formalizes basic tools that are commonly used by researchers in the field but not previously published.

Table of Contents.

• Basic Concepts.
• Sobolev Spaces.
• Variational Formulation of Elliptic Boundary Value Problems.
• The Construction of a Finite Element Space.
• Polynomial Approximation Theory in Sobolev Spaces.
• n-Dimensional Variational Problems.
• Finite Element Multigrid Methods.
• Additive Schwarz Preconditioners.
• Max-norm Estimates.
• Adaptive Meshes.
• Variational Crimes.
• Applications to Planar Elasticity.
• Mixed Methods.
• Iterative Techniques for Mixed Methods.
• Applications of Operator-Interpolation Theory.

Book Description

This book serves as a text for one- or two-semester courses for upper-level undergraduates and beginning graduate students and as a professional reference for people who want to solve partial differential equations (PDEs) using finite element methods. The author has attempted to introduce every concept in the simplest possible setting and maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. Quite a lot of attention is given to discontinuous finite elements, characteristic finite elements, and to the applications in fluid and solid mechanics including applications to porous media flow, and applications to semiconductor modeling. An extensive set of exercises and references in each chapter are provided.

Table of Contents

• Elementary Finite Elements.
• Nonconforming Finite Elements.
• Mixed Finite Elements.
• Discontinuous Finite Elements.
• Characteristic Finite Elements.
• Adaptive Finite Elements.
• Solid Mechanics.
• Fluid Mechanics.
• Fluid Flow in Porous Media.
• Semiconductor Modeling.