Finite Elements

Theory, Fast Solvers, and Applications in Solid Mechanics

Author: Dietrich Braess

Publisher: Cambridge University Press

ISBN: 9780521011952

Category: Mathematics

Page: 352

View: 5418

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Revised version of first edition: ideal graduate level introduction to finite element methods.
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Finite Elements

Theory, Fast Solvers, and Applications in Solid Mechanics

Author: Dietrich Braess

Publisher: Cambridge University Press

ISBN: 113946146X

Category: Mathematics

Page: N.A

View: 9308

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This definitive introduction to finite element methods was thoroughly updated for this 2007 third edition, which features important 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 nonstandard applications. The chapter on applications in elasticity now contains a complete discussion of locking phenomena. The numerical solution of elliptic partial differential equations is an important application of finite elements and the author discusses this subject comprehensively. These equations are treated as variational problems for which the Sobolev spaces are the right framework. Graduate students who do not necessarily have any particular background in differential equations, but require an introduction to finite element methods will find this text invaluable. Specifically, the chapter on finite elements in solid mechanics provides a bridge between mathematics and engineering.
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Finite Elements

Theory, Fast Solvers, and Applications in Solid Mechanics

Author: Dietrich Braess

Publisher: Cambridge University Press

ISBN: 9780521581875

Category: Mathematics

Page: 339

View: 8724

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The most important application of the finite element method is the numerical solution of elliptical partial differential equations. This is covered in depth in this book. It is a textbook for graduate students who do not necessarily have any particular background in differential equations, but require an introduction to finite elements for engineering or mathematics applications.
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Advanced Finite Element Methods and Applications

Author: Thomas Apel,Olaf Steinbach

Publisher: Springer Science & Business Media

ISBN: 3642303161

Category: Technology & Engineering

Page: 376

View: 4395

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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.
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Finite Element and Boundary Element Applications in Quantum Mechanics

Author: Ramdas Ram-Mohan,L. Ramdas Ram-Mohan

Publisher: Oxford University Press on Demand

ISBN: 9780198525226

Category: Mathematics

Page: 605

View: 9224

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This book introduces the finite element and boundary element methods (FEM and BEM) for applications to quantum mechanical systems. A discretization of the action integral with finite elements, followed by application of variational principles, brings a very general approach to the solution ofSchroedinger's equation for physical systems in arbitrary geometries with complex mixed boundary conditions. The variational approach is a common thread through the book and is used for the improvement of solutions to spectroscopic accuracy, to adaptively improve finite element meshs, to develop atime-dependent theory, and also to generate the solution of large sparse matrix eigenvalue problems. A thorough introduction to BEM is given using the modelling of surface plasmons, quantum electron waveguides, and quantum scattering as illustrative examples. The book should be useful to graduatestudents and researchers in basic quantum theory, quantum semiconductor modeling, computational physics, mathematics and chemistry
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Nonlinear Finite Element Methods

Author: Peter Wriggers

Publisher: Springer Science & Business Media

ISBN: 3540710000

Category: Mathematics

Page: 560

View: 2915

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Finite element methods have become ever more important to engineers as tools for design and optimization, now even for solving non-linear technological problems. However, several aspects must be considered for finite-element simulations which are specific for non-linear problems: These problems require the knowledge and the understanding of theoretical foundations and their finite-element discretization as well as algorithms for solving the non-linear equations. This book provides the reader with the required knowledge covering the complete field of finite element analyses in solid mechanics. It is written for advanced students in engineering fields but serves also as an introduction into non-linear simulation for the practising engineer.
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Fast and Accurate Finite-Element Multigrid Solvers for PDE Simulations on GPU Clusters

Author: Dominik Göddeke

Publisher: Logos Verlag Berlin GmbH

ISBN: 3832527680

Category: Computers

Page: 299

View: 1235

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This dissertation demonstrates that graphics processors (GPUs) as representatives of emerging many-core architectures are very well-suited for the fast and accurate solution of large, sparse linear systems of equations, using parallel multigrid methods on heterogeneous compute clusters. Such systems arise for instance in the discretisation of (elliptic) partial differential equations with finite elements. Fine-granular parallelisation techniques and methods to ensure accuracy are developed that enable at least one order of magnitude speedup over highly-tuned conventional CPU implementations, without sacrificing neither accuracy nor functionality.
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Robust Algebraic Multilevel Methods and Algorithms

Author: Johannes Kraus,Svetozar Margenov

Publisher: Walter de Gruyter

ISBN: 3110214830

Category: Mathematics

Page: 256

View: 1288

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This book deals with algorithms for the solution of linear systems of algebraic equations with large-scale sparse matrices, with a focus on problems that are obtained after discretization of partial differential equations using finite element methods. Provides a systematic presentation of the recent advances in robust algebraic multilevel methods. Can be used for advanced courses on the topic.
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Inequalities for the Numerical Radius of Linear Operators in Hilbert Spaces

Author: Silvestru Sever Dragomir

Publisher: Springer Science & Business Media

ISBN: 331901448X

Category: Mathematics

Page: 120

View: 2338

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Aimed toward researchers, postgraduate students, and scientists in linear operator theory and mathematical inequalities, this self-contained monograph focuses on numerical radius inequalities for bounded linear operators on complex Hilbert spaces for the case of one and two operators. Students at the graduate level will learn some essentials that may be useful for reference in courses in functional analysis, operator theory, differential equations, and quantum computation, to name several. Chapter 1 presents fundamental facts about the numerical range and the numerical radius of bounded linear operators in Hilbert spaces. Chapter 2 illustrates recent results obtained concerning numerical radius and norm inequalities for one operator on a complex Hilbert space, as well as some special vector inequalities in inner product spaces due to Buzano, Goldstein, Ryff and Clarke as well as some reverse Schwarz inequalities and Grüss type inequalities obtained by the author. Chapter 3 presents recent results regarding the norms and the numerical radii of two bounded linear operators. The techniques shown in this chapter are elementary but elegant and may be accessible to undergraduate students with a working knowledge of operator theory. A number of vector inequalities in inner product spaces as well as inequalities for means of nonnegative real numbers are also employed in this chapter. All the results presented are completely proved and the original references are mentioned.
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