Higher-Order Finite Element Methods PDF Download
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Author: Pavel Solin
Publisher: CRC Press
ISBN: 0203488040
Category : Mathematics
Languages : en
Pages : 404
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Book Description
The finite element method has always been a mainstay for solving engineering problems numerically. The most recent developments in the field clearly indicate that its future lies in higher-order methods, particularly in higher-order hp-adaptive schemes. These techniques respond well to the increasing complexity of engineering simulations and
Author: Pavel Solin
Publisher: CRC Press
ISBN: 0203488040
Category : Mathematics
Languages : en
Pages : 404
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Book Description
The finite element method has always been a mainstay for solving engineering problems numerically. The most recent developments in the field clearly indicate that its future lies in higher-order methods, particularly in higher-order hp-adaptive schemes. These techniques respond well to the increasing complexity of engineering simulations and
Author:
Publisher: Springer Nature
ISBN: 3031743709
Category :
Languages : en
Pages : 444
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Book Description
Author: Michal Kleiber
Publisher: CRC Press
ISBN: 1315645068
Category : Computers
Languages : en
Pages : 650
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Book Description
Advances in Mechanics: Theoretical, Computational and Interdisciplinary Issues covers the domain of theoretical, experimental and computational mechanics as well as interdisciplinary issues, such as industrial applications. Special attention is paid to the theoretical background and practical applications of computational mechanics.This volume
Author: Josef Malek
Publisher: SIAM
ISBN: 1611973848
Category : Mathematics
Languages : en
Pages : 106
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Book Description
Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs is about the interplay between modeling, analysis, discretization, matrix computation, and model reduction. The authors link PDE analysis, functional analysis, and calculus of variations with matrix iterative computation using Krylov subspace methods and address the challenges that arise during formulation of the mathematical model through to efficient numerical solution of the algebraic problem. The book?s central concept, preconditioning of the conjugate gradient method, is traditionally developed algebraically using the preconditioned finite-dimensional algebraic system. In this text, however, preconditioning is connected to the PDE analysis, and the infinite-dimensional formulation of the conjugate gradient method and its discretization and preconditioning are linked together. This text challenges commonly held views, addresses widespread misunderstandings, and formulates thought-provoking open questions for further research.
Author: David B. Davidson
Publisher: Cambridge University Press
ISBN: 1139471643
Category : Technology & Engineering
Languages : en
Pages : 413
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Book Description
The numerical approximation of Maxwell's equations, Computational Electromagnetics (CEM), has emerged as a crucial enabling technology for radio-frequency, microwave and wireless engineering. The three most popular 'full-wave' methods - the Finite Difference Time Domain Method, the Method of Moments and the Finite Element Method - are introduced in this book by way of one or two-dimensional problems. Commercial or public domain codes implementing these methods are then applied to complex, real-world engineering problems, and a careful analysis of the reliability of the results obtained is performed, along with a discussion of the many pitfalls which can result in inaccurate and misleading solutions. The book will empower readers to become discerning users of CEM software, with an understanding of the underlying methods, and confidence in the results obtained. It also introduces readers to the art of code development. Aimed at senior undergraduate/graduate students taking CEM courses and practising engineers in the industry.
Author: HACKBUSCH
Publisher: Birkhäuser
ISBN: 3034857128
Category : Science
Languages : en
Pages : 394
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Book Description
These proceedings contain a selection of papers presented at the Third European Conference on Multigrid Methods which was held in Bonn on October 1-4, 1990. Following conferences in 1981 and 1985, a platform for the presentation of new Multigrid results was provided for a third time. Multigrid methods no longer have problems being accepted by numerical analysts and users of numerical methods; on the contrary, they have been further developed in such a successful way that they have penetrated a variety of new fields of application. The high number of 154 participants from 18 countries and 76 presented papers show the need to continue the series of the European Multigrid Conferences. The papers of this volume give a survey on the current Multigrid situation; in particular, they correspond to those fields where new developments can be observed. For example, se veral papers study the appropriate treatment of time dependent problems. Improvements can also be noticed in the Multigrid approach for semiconductor equations. The field of parallel Multigrid variants, having been started at the second European Multigrid Conference, is now at the centre of interest.
Author: Owe Axelsson
Publisher: Bentham Science Publishers
ISBN: 1608052915
Category : Mathematics
Languages : en
Pages : 153
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Book Description
This e-book presents several research areas of elliptical problems solved by differential equations. The mathematical models explained in this e-book have been contributed by experts in the field and can be applied to a wide range of real life examples. M
Author: Mats G. Larson
Publisher: Springer Science & Business Media
ISBN: 3642332870
Category : Computers
Languages : en
Pages : 403
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Book Description
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: Panayot S. Vassilevski
Publisher: Springer Science & Business Media
ISBN: 0387715649
Category : Mathematics
Languages : en
Pages : 527
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Book Description
This monograph is the first to provide a comprehensive, self-contained and rigorous presentation of some of the most powerful preconditioning methods for solving finite element equations in a common block-matrix factorization framework. The book covers both algorithms and analysis using a common block-matrix factorization approach which emphasizes its unique feature. Topics covered include the classical incomplete block-factorization preconditioners, the most efficient methods such as the multigrid, algebraic multigrid, and domain decomposition. This text can serve as an indispensable reference for researchers, graduate students, and practitioners. It can also be used as a supplementary text for a topics course in preconditioning and/or multigrid methods at the graduate level.
Author: Dietrich Braess
Publisher: Cambridge University Press
ISBN: 9780521011952
Category : Mathematics
Languages : en
Pages : 374
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Book Description
"This definitive introduction to finite element methods has been updated thoroughly for this third edition, which features important new material for both research and application of the finite element method. The discussion of saddle point problems is a highlight of the book and has been elaborated to include many more non-standard applications. The chapter on applications in elasticity now contains a complete discussion of locking phenomena." "Graduate students who do not necessarily have any particular background in differential equations, but require an introduction to finite element methods, will find the text invaluable. Specifically, the chapter on finite elements in solid mechanics provides a bridge between mathematics and engineering."--BOOK JACKET.
