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.
Adaptive Finite Element Method For Eigenvalue Problems
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Author : Corina Spreiter
language : en
Publisher:
Release Date : 2022
Adaptive Finite Element Method For Eigenvalue Problems written by Corina Spreiter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.
Advanced Finite Element Methods And Applications
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Author : Thomas Apel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-07-16
Advanced Finite Element Methods And Applications written by Thomas Apel 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 2012-07-16 with Technology & Engineering categories.
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.
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.
Finite Element Method For Nonlinear Eigenvalue Problems And Its Solution By Multivariate Newton Steps
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Author : Severina Haas
language : en
Publisher:
Release Date : 2022
Finite Element Method For Nonlinear Eigenvalue Problems And Its Solution By Multivariate Newton Steps written by Severina Haas and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.
The Mathematical Foundations Of The Finite Element Method With Applications To Partial Differential Equations
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Author : A. K. Aziz
language : en
Publisher: Academic Press
Release Date : 2014-05-10
The Mathematical Foundations Of The Finite Element Method With Applications To Partial Differential Equations written by A. K. Aziz 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 Technology & Engineering categories.
The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations is a collection of papers presented at the 1972 Symposium by the same title, held at the University of Maryland, Baltimore County Campus. This symposium relates considerable numerical analysis involved in research in both theoretical and practical aspects of the finite element method. This text is organized into three parts encompassing 34 chapters. Part I focuses on the mathematical foundations of the finite element method, including papers on theory of approximation, variational principles, the problems of perturbations, and the eigenvalue problem. Part II covers a large number of important results of both a theoretical and a practical nature. This part discusses the piecewise analytic interpolation and approximation of triangulated polygons; the Patch test for convergence of finite elements; solutions for Dirichlet problems; variational crimes in the field; and superconvergence result for the approximate solution of the heat equation by a collocation method. Part III explores the many practical aspects of finite element method. This book will be of great value to mathematicians, engineers, and physicists.
Advanced Finite Element Methods And Applications
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Author : Thomas Apel
language : en
Publisher: Springer
Release Date : 2012-07-16
Advanced Finite Element Methods And Applications written by Thomas Apel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-16 with Technology & Engineering categories.
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.
Analysis Of A Finite Element Method
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Author : Granville Sewell
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Analysis Of A Finite Element Method written by Granville Sewell 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 2012-12-06 with Mathematics categories.
This text can be used for two quite different purposes. It can be used as a reference book for the PDElPROTRAN user· who wishes to know more about the methods employed by PDE/PROTRAN Edition 1 (or its predecessor, TWODEPEP) in solving two-dimensional partial differential equations. However, because PDE/PROTRAN solves such a wide class of problems, an outline of the algorithms contained in PDElPROTRAN is also quite suitable as a text for an introductory graduate level finite element course. Algorithms which solve elliptic, parabolic, hyperbolic, and eigenvalue partial differential equation problems are pre sented, as are techniques appropriate for treatment of singularities, curved boundaries, nonsymmetric and nonlinear problems, and systems of PDEs. Direct and iterative linear equation solvers are studied. Although the text emphasizes those algorithms which are actually implemented in PDEI PROTRAN, and does not discuss in detail one- and three-dimensional problems, or collocation and least squares finite element methods, for example, many of the most commonly used techniques are studied in detail. Algorithms applicable to general problems are naturally emphasized, and not special purpose algorithms which may be more efficient for specialized problems, such as Laplace's equation. It can be argued, however, that the student will better understand the finite element method after seeing the details of one successful implementation than after seeing a broad overview of the many types of elements, linear equation solvers, and other options in existence.
The Finite Element Method
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Author : Douglas H. Norrie
language : en
Publisher: Academic Press
Release Date : 2014-05-10
The Finite Element Method written by Douglas H. Norrie 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 Technology & Engineering categories.
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.