Finite Element Methods For Eigenvalue Problems
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Finite Element Methods For Eigenvalue Problems
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Author : Jiguang Sun
language : en
Publisher: CRC Press
Release Date : 2016-08-19
Finite Element Methods For Eigenvalue Problems written by Jiguang Sun and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-19 with Mathematics categories.
This book covers finite element methods for several typical eigenvalues that arise from science and engineering. Both theory and implementation are covered in depth at the graduate level. The background for typical eigenvalue problems is included along with functional analysis tools, finite element discretization methods, convergence analysis, techniques for matrix evaluation problems, and computer implementation. The book also presents new methods, such as the discontinuous Galerkin method, and new problems, such as the transmission eigenvalue problem.
Finite Element Method For Eigenvalue Problems In Electromagnetics
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Author : C. J. Reddy
language : en
Publisher:
Release Date : 1994
Finite Element Method For Eigenvalue Problems In Electromagnetics written by C. J. Reddy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Computer programs categories.
Mixed Finite Element Methods And Applications
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Author : Daniele Boffi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-02
Mixed Finite Element Methods And Applications written by Daniele Boffi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-02 with Mathematics categories.
Non-standard finite element methods, in particular mixed methods, are central to many applications. In this text the authors, Boffi, Brezzi and Fortin present a general framework, starting with a finite dimensional presentation, then moving on to formulation in Hilbert spaces and finally considering approximations, including stabilized methods and eigenvalue problems. This book also provides an introduction to standard finite element approximations, followed by the construction of elements for the approximation of mixed formulations in H(div) and H(curl). The general theory is applied to some classical examples: Dirichlet's problem, Stokes' problem, plate problems, elasticity and electromagnetism.
The Finite Element Method In Engineering
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Author : Singiresu S. Rao
language : en
Publisher: Butterworth-Heinemann
Release Date : 2005
The Finite Element Method In Engineering written by Singiresu S. Rao and has been published by Butterworth-Heinemann this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
With the revolution in readily available computing power, the finite element method has become one of the most important tools for the modern engineer. This book offers a comprehensive introduction to the principles involved.
The Finite Element Method In Electromagnetics
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Author : Jian-Ming Jin
language : en
Publisher: John Wiley & Sons
Release Date : 2015-02-18
The Finite Element Method In Electromagnetics written by Jian-Ming Jin and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-18 with Science categories.
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.
Numerical Methods For Large Eigenvalue Problems
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Author : Yousef Saad
language : en
Publisher: SIAM
Release Date : 2011-05-26
Numerical Methods For Large Eigenvalue Problems written by Yousef Saad and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-26 with Mathematics categories.
This revised edition discusses numerical methods for computing the eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method and automatic multilevel substructuring.
The Finite Element Method Theory Implementation And Applications
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Author : Mats G. Larson
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-13
The Finite Element Method Theory Implementation And Applications written by Mats G. Larson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-13 with Computers categories.
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.
Finite Element Solution Of Boundary Value Problems
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Author : O. Axelsson
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Finite Element Solution Of Boundary Value Problems written by O. Axelsson and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Finite Element Solution of Boundary Value Problems: Theory and Computation provides an introduction to both the theoretical and computational aspects of the finite element method for solving boundary value problems for partial differential equations. This book is composed of seven chapters and begins with surveys of the two kinds of preconditioning techniques, one based on the symmetric successive overrelaxation iterative method for solving a system of equations and a form of incomplete factorization. The subsequent chapters deal with the concepts from functional analysis of boundary value problems. These topics are followed by discussions of the Ritz method, which minimizes the quadratic functional associated with a given boundary value problem over some finite-dimensional subspace of the original space of functions. Other chapters are devoted to direct methods, including Gaussian elimination and related methods, for solving a system of linear algebraic equations. The final chapter continues the analysis of preconditioned conjugate gradient methods, concentrating on applications to finite element problems. This chapter also looks into the techniques for reducing rounding errors in the iterative solution of finite element equations. This book will be of value to advanced undergraduates and graduates in the areas of numerical analysis, mathematics, and computer science, as well as for theoretically inclined workers in engineering and the physical sciences.
Finite Element Methods
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Author : 林群
language : en
Publisher: Elsevier
Release Date : 2007-11-28
Finite Element Methods written by 林群 and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-28 with Business & Economics categories.
Distributed by Elsevier Science on behalf of Science Press. This book discusses the accuracy of various finite element approximations and how to improve them, with the help of extrapolations and super convergence's post-processing technique. The discussion is based on asymptotic expansions for finite elements and finally reduces to the technique of integration by parts, embedding theorems and norm equivalence lemmas. The book is also devoted to explaining the origin of theorems. Masterly exposition of the accuracy and improvement of finite element methods, highlighting the postprocessing Emphasis on understanding of higher knowledge Accessible to students, engaging for experts and professionals Written by leading Chinese mathematicians, available internationally for the first time
Multigrid Finite Element Methods For Electromagnetic Field Modeling
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Author : Yu Zhu
language : en
Publisher: John Wiley & Sons
Release Date : 2006-03-10
Multigrid Finite Element Methods For Electromagnetic Field Modeling written by Yu Zhu and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-10 with Science categories.
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.