The Finite Element Method For Electromagnetic Modeling

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The Finite Element Method for Electromagnetic Modeling

Author : Gérard Meunier
Publisher : John Wiley & Sons
ISBN 13 : 0470393807
Total Pages : 618 pages
Book Rating : 4.4/5 (73 download)

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Book Synopsis The Finite Element Method for Electromagnetic Modeling by : Gérard Meunier

Download or read book The Finite Element Method for Electromagnetic Modeling written by Gérard Meunier and published by John Wiley & Sons. This book was released on 2010-01-05 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by specialists of modeling in electromagnetism, this book provides a comprehensive review of the finite element method for low frequency applications. Fundamentals of the method as well as new advances in the field are described in detail. Chapters 1 to 4 present general 2D and 3D static and dynamic formulations by the use of scalar and vector unknowns and adapted interpolations for the fields (nodal, edge, face or volume). Chapter 5 is dedicated to the presentation of different macroscopic behavior laws of materials and their implementation in a finite element context: anisotropy and hysteretic properties for magnetic sheets, iron losses, non-linear permanent magnets and superconductors. More specific formulations are then proposed: the modeling of thin regions when finite elements become misfit (Chapter 6), infinite domains by using geometrical transformations (Chapter 7), the coupling of 2D and 3D formulations with circuit equations (Chapter 8), taking into account the movement, particularly in the presence of Eddy currents (Chapter 9) and an original approach for the treatment of geometrical symmetries when the sources are not symmetric (Chapter 10). Chapters 11 to 13 are devoted to coupled problems: magneto-thermal coupling for induction heating, magneto-mechanical coupling by introducing the notion of strong and weak coupling and magneto-hydrodynamical coupling focusing on electromagnetic instabilities in fluid conductors. Chapter 14 presents different meshing methods in the context of electromagnetism (presence of air) and introduces self-adaptive mesh refinement procedures. Optimization techniques are then covered in Chapter 15, with the adaptation of deterministic and probabilistic methods to the numerical finite element environment. Chapter 16 presents a variational approach of electromagnetism, showing how Maxwell equations are derived from thermodynamic principles.

Electromagnetic Modeling by Finite Element Methods

Author : João Pedro A. Bastos
Publisher : CRC Press
ISBN 13 : 9780203911174
Total Pages : 512 pages
Book Rating : 4.9/5 (111 download)

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Book Synopsis Electromagnetic Modeling by Finite Element Methods by : João Pedro A. Bastos

Download or read book Electromagnetic Modeling by Finite Element Methods written by João Pedro A. Bastos and published by CRC Press. This book was released on 2003-04-01 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike any other source in the field, this valuable reference clearly examines key aspects of the finite element method (FEM) for electromagnetic analysis of low-frequency electrical devices. The authors examine phenomena such as nonlinearity, mechanical force, electrical circuit coupling, vibration, heat, and movement for applications in the elect

The Finite Element Method in Electromagnetics

Author : Jian-Ming Jin
Publisher : John Wiley & Sons
ISBN 13 : 1118842022
Total Pages : 728 pages
Book Rating : 4.1/5 (188 download)

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Book Synopsis The Finite Element Method in Electromagnetics by : Jian-Ming Jin

Download or read book The Finite Element Method in Electromagnetics written by Jian-Ming Jin and published by John Wiley & Sons. This book was released on 2015-02-18 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetics The finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration. The Finite Element Method in Electromagnetics, Third Edition explains the method’s processes and techniques in careful, meticulous prose and covers not only essential finite element method theory, but also its latest developments and applications—giving engineers a methodical way to quickly master this very powerful numerical technique for solving practical, often complicated, electromagnetic problems. Featuring over thirty percent new material, the third edition of this essential and comprehensive text now includes: A wider range of applications, including antennas, phased arrays, electric machines, high-frequency circuits, and crystal photonics The finite element analysis of wave propagation, scattering, and radiation in periodic structures The time-domain finite element method for analysis of wideband antennas and transient electromagnetic phenomena Novel domain decomposition techniques for parallel computation and efficient simulation of large-scale problems, such as phased-array antennas and photonic crystals Along with a great many examples, The Finite Element Method in Electromagnetics is an ideal book for engineering students as well as for professionals in the field.

MATLAB-based Finite Element Programming in Electromagnetic Modeling

Author : Özlem Özgün
Publisher : CRC Press
ISBN 13 : 0429854609
Total Pages : 428 pages
Book Rating : 4.4/5 (298 download)

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Book Synopsis MATLAB-based Finite Element Programming in Electromagnetic Modeling by : Özlem Özgün

Download or read book MATLAB-based Finite Element Programming in Electromagnetic Modeling written by Özlem Özgün and published by CRC Press. This book was released on 2018-09-03 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a self-contained, programming-oriented and learner-centered book on finite element method (FEM), with special emphasis given to developing MATLAB® programs for numerical modeling of electromagnetic boundary value problems. It provides a deep understanding and intuition of FEM programming by means of step-by-step MATLAB® programs with detailed descriptions, and eventually enabling the readers to modify, adapt and apply the provided programs and formulations to develop FEM codes for similar problems through various exercises. It starts with simple one-dimensional static and time-harmonic problems and extends the developed theory to more complex two- or three-dimensional problems. It supplies sufficient theoretical background on the topic, and it thoroughly covers all phases (pre-processing, main body and post-processing) in FEM. FEM formulations are obtained for boundary value problems governed by a partial differential equation that is expressed in terms of a generic unknown function, and then, these formulations are specialized to various electromagnetic applications together with a post-processing phase. Since the method is mostly described in a general context, readers from other disciplines can also use this book and easily adapt the provided codes to their engineering problems. After forming a solid background on the fundamentals of FEM by means of canonical problems, readers are guided to more advanced applications of FEM in electromagnetics through a survey chapter at the end of the book. Offers a self-contained and easy-to-understand introduction to the theory and programming of finite element method. Covers various applications in the field of static and time-harmonic electromagnetics. Includes one-, two- and three-dimensional finite element codes in MATLAB®. Enables readers to develop finite element programming skills through various MATLAB® codes and exercises. Promotes self-directed learning skills and provides an effective instruction tool.

Iterative and Self-adaptive Finite-elements in Electromagnetic Modeling

Author : Magdalena Salazar-Palma
Publisher : Artech House Publishers
ISBN 13 :
Total Pages : 824 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Iterative and Self-adaptive Finite-elements in Electromagnetic Modeling by : Magdalena Salazar-Palma

Download or read book Iterative and Self-adaptive Finite-elements in Electromagnetic Modeling written by Magdalena Salazar-Palma and published by Artech House Publishers. This book was released on 1998 with total page 824 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ensure the accuracy of your results when applying the Finite Element Method (FEM) to electromagnetic and antenna problems with this self-contained reference. It provides you with a solid understanding of the method, describes its key elements and numerical techniques, and identifies various approaches to using the FEM in solving real-world microwave field problems.

Electromagnetic Modeling by Finite Element Methods

Author : João Pedro A. Bastos
Publisher : CRC Press
ISBN 13 : 0203911172
Total Pages : 510 pages
Book Rating : 4.2/5 (39 download)

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Book Synopsis Electromagnetic Modeling by Finite Element Methods by : João Pedro A. Bastos

Download or read book Electromagnetic Modeling by Finite Element Methods written by João Pedro A. Bastos and published by CRC Press. This book was released on 2003-04-01 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike any other source in the field, this valuable reference clearly examines key aspects of the finite element method (FEM) for electromagnetic analysis of low-frequency electrical devices. The authors examine phenomena such as nonlinearity, mechanical force, electrical circuit coupling, vibration, heat, and movement for applications in the elect

Magnetic Materials and 3D Finite Element Modeling

Author : João Pedro A. Bastos
Publisher : CRC Press
ISBN 13 : 1351831518
Total Pages : 398 pages
Book Rating : 4.3/5 (518 download)

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Book Synopsis Magnetic Materials and 3D Finite Element Modeling by : João Pedro A. Bastos

Download or read book Magnetic Materials and 3D Finite Element Modeling written by João Pedro A. Bastos and published by CRC Press. This book was released on 2017-04-28 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: Magnetic Materials and 3D Finite Element Modeling explores material characterization and finite element modeling (FEM) applications. This book relates to electromagnetic analysis based on Maxwell’s equations and application of the finite element (FE) method to low frequency devices. A great source for senior undergraduate and graduate students in electromagnetics, it also supports industry professionals working in magnetics, electromagnetics, ferromagnetic materials science and electrical engineering. The authors present current concepts on ferromagnetic material characterizations and losses. They provide introductory material; highlight basic electromagnetics, present experimental and numerical modeling related to losses and focus on FEM applied to 3D applications. They also explain various formulations, and discuss numerical codes. • Furnishes algorithms in computational language • Summarizes concepts related to the FE method • Uses classical algebra to present the method, making it easily accessible to engineers Written in an easy-to-understand tutorial format, the text begins with a short presentation of Maxwell’s equations, discusses the generation mechanism of iron losses, and introduces their static and dynamic components. It then demonstrates simplified models for the hysteresis phenomena under alternating magnetic fields. The book also focuses on the Preisach and Jiles–Atherton models, discusses vector hysterisis modeling, introduces the FE technique, and presents nodal and edge elements applied to 3D FE formulation connected to the hysteretic phenomena. The book discusses the concept of source-field for magnetostatic cases, magnetodynamic fields, eddy currents, and anisotropy. It also explores the need for more sophisticated coding, and presents techniques for solving linear systems generated by the FE cases while considering advantages and drawbacks.

Finite Element Method Electromagnetics

Author : John L. Volakis
Publisher : John Wiley & Sons
ISBN 13 : 9780780334250
Total Pages : 364 pages
Book Rating : 4.3/5 (342 download)

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Book Synopsis Finite Element Method Electromagnetics by : John L. Volakis

Download or read book Finite Element Method Electromagnetics written by John L. Volakis and published by John Wiley & Sons. This book was released on 1998-06-15 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Employed in a large number of commercial electromagnetic simulation packages, the finite element method is one of the most popular and well-established numerical techniques in engineering. This book covers the theory, development, implementation, and application of the finite element method and its hybrid versions to electromagnetics. FINITE ELEMENT METHOD FOR ELECTROMAGNETICS begins with a step-by-step textbook presentation of the finite method and its variations then goes on to provide up-to-date coverage of three dimensional formulations and modern applications to open and closed domain problems. Worked out examples are included to aid the reader with the fine features of the method and the implementation of its hybridization with other techniques for a robust simulation of large scale radiation and scattering. The crucial treatment of local boundary conditions is carefully worked out in several stages in the book. Sponsored by: IEEE Antennas and Propagation Society.

Finite Element Analysis of Antennas and Arrays

Author : Jian-Ming Jin
Publisher : John Wiley & Sons
ISBN 13 : 9780470409725
Total Pages : 472 pages
Book Rating : 4.4/5 (97 download)

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Book Synopsis Finite Element Analysis of Antennas and Arrays by : Jian-Ming Jin

Download or read book Finite Element Analysis of Antennas and Arrays written by Jian-Ming Jin and published by John Wiley & Sons. This book was released on 2009-02-23 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Most Complete, Up-to-Date Coverage of the Finite Element Analysis and Modeling of Antennas and Arrays Aimed at researchers as well as practical engineers—and packed with over 200 illustrations including twenty-two color plates—Finite Element Analysis of Antennas and Arrays presents: Time- and frequency-domain formulations and mesh truncation techniques Antenna source modeling and parameter calculation Modeling of complex materials and fine geometrical details Analysis and modeling of narrowband and broadband antennas Analysis and modeling of infinite and finite phased-array antennas Analysis and modeling of antenna and platform interactions Recognizing the strengths of other numerical methods, this book goes beyond the finite element method and covers hybrid techniques that combine the finite element method with the finite difference time-domain method, the method of moments, and the high-frequency asymptotic methods to efficiently deal with a variety of complex antenna problems. Complemented with numerous examples, this cutting-edge resource fully demonstrates the power and capabilities of the finite element analysis and its many practical applications.

Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials

Author : Jichun Li
Publisher : Springer Science & Business Media
ISBN 13 : 3642337899
Total Pages : 309 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials by : Jichun Li

Download or read book Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials written by Jichun Li and published by Springer Science & Business Media. This book was released on 2012-12-15 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to provide an up-to-date introduction to the time-domain finite element methods for Maxwell’s equations involving metamaterials. Since the first successful construction of a metamaterial with both negative permittivity and permeability in 2000, the study of metamaterials has attracted significant attention from researchers across many disciplines. Thanks to enormous efforts on the part of engineers and physicists, metamaterials present great potential applications in antenna and radar design, sub-wavelength imaging, and invisibility cloak design. Hence the efficient simulation of electromagnetic phenomena in metamaterials has become a very important issue and is the subject of this book, in which various metamaterial modeling equations are introduced and justified mathematically. The development and practical implementation of edge finite element methods for metamaterial Maxwell’s equations are the main focus of the book. The book finishes with some interesting simulations such as backward wave propagation and time-domain cloaking with metamaterials.

Modeling and Computations in Electromagnetics

Author : Habib Ammari
Publisher : Springer Science & Business Media
ISBN 13 : 3540737782
Total Pages : 239 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Modeling and Computations in Electromagnetics by : Habib Ammari

Download or read book Modeling and Computations in Electromagnetics written by Habib Ammari and published by Springer Science & Business Media. This book was released on 2008-01-12 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is nothing less than an essential text in what is a new and growing discipline. Electromagnetic modeling and computations is expanding as a result of the steadily increasing demand for designing electrical devices, modeling electromagnetic materials, and simulating electromagnetic fields in nanoscale structures. The aim of this volume is to bring together prominent worldwide experts to review state-of-the-art developments and future trends of modeling and computations in electromagnetics.

Electromagnetic Modeling and Simulation

Author : Levent Sevgi
Publisher : John Wiley & Sons
ISBN 13 : 111887711X
Total Pages : 665 pages
Book Rating : 4.1/5 (188 download)

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Book Synopsis Electromagnetic Modeling and Simulation by : Levent Sevgi

Download or read book Electromagnetic Modeling and Simulation written by Levent Sevgi and published by John Wiley & Sons. This book was released on 2014-03-13 with total page 665 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book presents simple, easy-to-use, but effective short codes as well as virtual tools that can be used by electrical, electronic, communication, and computer engineers in a broad range of electrical engineering problems Electromagnetic modeling is essential to the design and modeling of antenna, radar, satellite, medical imaging, and other applications. In this book, author Levent Sevgi explains techniques for solving real-time complex physical problems using MATLAB-based short scripts and comprehensive virtual tools. Unique in coverage and tutorial approach, Electromagnetic Modeling and Simulation covers fundamental analytical and numerical models that are widely used in teaching, research, and engineering designs—including mode and ray summation approaches with the canonical 2D nonpenetrable parallel plate waveguide as well as FDTD, MoM, and SSPE scripts. The book also establishes an intelligent balance among the essentials of EM MODSIM: The Problem (the physics), The Theory and Models (mathematical background and analytical solutions), and The Simulations (code developing plus validation, verification, and calibration). Classroom tested in graduate-level and short courses, Electromagnetic Modeling and Simulation: Clarifies concepts through numerous worked problems and quizzes provided throughout the book Features valuable MATLAB-based, user-friendly, effective engineering and research virtual design tools Includes sample scenarios and video clips recorded during characteristic simulations that visually impact learning—available on wiley.com Provides readers with their first steps in EM MODSIM as well as tools for medium and high-level code developers and users Electromagnetic Modeling and Simulation thoroughly covers the physics, mathematical background, analytical solutions, and code development of electromagnetic modeling, making it an ideal resource for electrical engineers and researchers.

Matlab-Based Finite Element Programming in Electromagnetic Modeling

Author : Ozlem Ozgun
Publisher : CRC Press
ISBN 13 : 9781138746923
Total Pages : 434 pages
Book Rating : 4.7/5 (469 download)

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Book Synopsis Matlab-Based Finite Element Programming in Electromagnetic Modeling by : Ozlem Ozgun

Download or read book Matlab-Based Finite Element Programming in Electromagnetic Modeling written by Ozlem Ozgun and published by CRC Press. This book was released on with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on finite element methods with emphasis on MATLAB for numerical modeling of electromagnetic problems. Providing readers with knowledge and skills thorough which they can develop their own finite element codes for practical applications, this book also gives beginning researchers an understanding of finite element programming in the context of certain canonical electromagnetic problems. Through the inclusion of step-by-step MATLAB programs with detailed descriptions, readers will be able to modify, adapt, and apply the provided programs and formulations as to other similar programs through various open-ended questions and exercises.

Numerical Electromagnetics

Author : Umran S. Inan
Publisher : Cambridge University Press
ISBN 13 : 1139497987
Total Pages : 405 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Numerical Electromagnetics by : Umran S. Inan

Download or read book Numerical Electromagnetics written by Umran S. Inan and published by Cambridge University Press. This book was released on 2011-04-07 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Beginning with the development of finite difference equations, and leading to the complete FDTD algorithm, this is a coherent introduction to the FDTD method (the method of choice for modeling Maxwell's equations). It provides students and professional engineers with everything they need to know to begin writing FDTD simulations from scratch and to develop a thorough understanding of the inner workings of commercial FDTD software. Stability, numerical dispersion, sources and boundary conditions are all discussed in detail, as are dispersive and anisotropic materials. A comparative introduction of the finite volume and finite element methods is also provided. All concepts are introduced from first principles, so no prior modeling experience is required, and they are made easier to understand through numerous illustrative examples and the inclusion of both intuitive explanations and mathematical derivations.

Multigrid Finite Element Methods for Electromagnetic Field Modeling

Author : Yu Zhu
Publisher : John Wiley & Sons
ISBN 13 : 0471786373
Total Pages : 438 pages
Book Rating : 4.4/5 (717 download)

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Book Synopsis Multigrid Finite Element Methods for Electromagnetic Field Modeling by : Yu Zhu

Download or read book Multigrid Finite Element Methods for Electromagnetic Field Modeling written by Yu Zhu and published by John Wiley & Sons. This book was released on 2006-03-10 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first comprehensive monograph that features state-of-the-art multigrid methods for enhancing the modeling versatility, numerical robustness, and computational efficiency of one of the most popular classes of numerical electromagnetic field modeling methods: the method of finite elements. The focus of the publication is the development of robust preconditioners for the iterative solution of electromagnetic field boundary value problems (BVPs) discretized by means of finite methods. Specifically, the authors set forth their own successful attempts to utilize concepts from multigrid and multilevel methods for the effective preconditioning of matrices resulting from the approximation of electromagnetic BVPs using finite methods. Following the authors' careful explanations and step-by-step instruction, readers can duplicate the authors' results and take advantage of today's state-of-the-art multigrid/multilevel preconditioners for finite element-based iterative electromagnetic field solvers. Among the highlights of coverage are: * Application of multigrid, multilevel, and hybrid multigrid/multilevel preconditioners to electromagnetic scattering and radiation problems * Broadband, robust numerical modeling of passive microwave components and circuits * Robust, finite element-based modal analysis of electromagnetic waveguides and cavities * Application of Krylov subspace-based methodologies for reduced-order macromodeling of electromagnetic devices and systems * Finite element modeling of electromagnetic waves in periodic structures The authors provide more than thirty detailed algorithms alongside pseudo-codes to assist readers with practical computer implementation. In addition, each chapter includes an applications section with helpful numerical examples that validate the authors' methodologies and demonstrate their computational efficiency and robustness. This groundbreaking book, with its coverage of an exciting new enabling computer-aided design technology, is an essential reference for computer programmers, designers, and engineers, as well as graduate students in engineering and applied physics.

Finite Element Methods for Maxwell's Equations

Author : Peter Monk
Publisher : Clarendon Press
ISBN 13 : 0191545228
Total Pages : 468 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Finite Element Methods for Maxwell's Equations by : Peter Monk

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.

Magnetic Materials and 3D Finite Element Modeling

Author : João Pedro A. Bastos
Publisher : CRC Press
ISBN 13 : 1466592524
Total Pages : 396 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Magnetic Materials and 3D Finite Element Modeling by : João Pedro A. Bastos

Download or read book Magnetic Materials and 3D Finite Element Modeling written by João Pedro A. Bastos and published by CRC Press. This book was released on 2017-04-28 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Magnetic Materials and 3D Finite Element Modeling explores material characterization and finite element modeling (FEM) applications. This book relates to electromagnetic analysis based on Maxwell’s equations and application of the finite element (FE) method to low frequency devices. A great source for senior undergraduate and graduate students in electromagnetics, it also supports industry professionals working in magnetics, electromagnetics, ferromagnetic materials science and electrical engineering. The authors present current concepts on ferromagnetic material characterizations and losses. They provide introductory material; highlight basic electromagnetics, present experimental and numerical modeling related to losses and focus on FEM applied to 3D applications. They also explain various formulations, and discuss numerical codes. • Furnishes algorithms in computational language • Summarizes concepts related to the FE method • Uses classical algebra to present the method, making it easily accessible to engineers Written in an easy-to-understand tutorial format, the text begins with a short presentation of Maxwell’s equations, discusses the generation mechanism of iron losses, and introduces their static and dynamic components. It then demonstrates simplified models for the hysteresis phenomena under alternating magnetic fields. The book also focuses on the Preisach and Jiles–Atherton models, discusses vector hysterisis modeling, introduces the FE technique, and presents nodal and edge elements applied to 3D FE formulation connected to the hysteretic phenomena. The book discusses the concept of source-field for magnetostatic cases, magnetodynamic fields, eddy currents, and anisotropy. It also explores the need for more sophisticated coding, and presents techniques for solving linear systems generated by the FE cases while considering advantages and drawbacks.