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Multigrid Methods For Finite Elements


Multigrid Methods For Finite Elements
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Multigrid Methods For Finite Elements


Multigrid Methods For Finite Elements
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Author : V.V. Shaidurov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Multigrid Methods For Finite Elements written by V.V. Shaidurov 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 2013-03-09 with Mathematics categories.


Multigrid Methods for Finite Elements combines two rapidly developing fields: finite element methods, and multigrid algorithms. At the theoretical level, Shaidurov justifies the rate of convergence of various multigrid algorithms for self-adjoint and non-self-adjoint problems, positive definite and indefinite problems, and singular and spectral problems. At the practical level these statements are carried over to detailed, concrete problems, including economical constructions of triangulations and effective work with curvilinear boundaries, quasilinear equations and systems. Great attention is given to mixed formulations of finite element methods, which allow the simplification of the approximation of the biharmonic equation, the steady-state Stokes, and Navier--Stokes problems.



Multigrid Methods


Multigrid Methods
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Author : Ulrich Trottenberg
language : en
Publisher: Academic Press
Release Date : 2001

Multigrid Methods written by Ulrich Trottenberg and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.


Mathematics of Computing -- Numerical Analysis.



A Multigrid Tutorial


A Multigrid Tutorial
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Author : William L. Briggs
language : en
Publisher: SIAM
Release Date : 2000-07-01

A Multigrid Tutorial written by William L. Briggs and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-01 with Mathematics categories.


Mathematics of Computing -- Numerical Analysis.



Practical Fourier Analysis For Multigrid Methods


Practical Fourier Analysis For Multigrid Methods
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Author : Roman Wienands
language : en
Publisher: CRC Press
Release Date : 2004-10-28

Practical Fourier Analysis For Multigrid Methods written by Roman Wienands and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-28 with Mathematics categories.


Before applying multigrid methods to a project, mathematicians, scientists, and engineers need to answer questions related to the quality of convergence, whether a development will pay out, whether multigrid will work for a particular application, and what the numerical properties are. Practical Fourier Analysis for Multigrid Methods uses a detaile



The Mathematical Theory Of Finite Element Methods


The Mathematical Theory Of Finite Element Methods
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Author : Susanne Brenner
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-04-12

The Mathematical Theory Of Finite Element Methods written by Susanne Brenner 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 2002-04-12 with Mathematics categories.


A rigorous and thorough mathematical introduction to the subject; A clear and concise treatment of modern fast solution techniques such as multigrid and domain decomposition algorithms; Second edition contains two new chapters, as well as many new exercises; Previous edition sold over 3000 copies worldwide



Multigrid Finite Element Methods For Electromagnetic Field Modeling


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.



Multigrid Methods


Multigrid Methods
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Author : Stephen F. Mccormick
language : en
Publisher: CRC Press
Release Date : 2020-08-12

Multigrid Methods written by Stephen F. Mccormick and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-12 with Mathematics categories.


This book is a collection of research papers on a wide variety of multigrid topics, including applications, computation and theory. It represents proceedings of the Third Copper Mountain Conference on Multigrid Methods, which was held at Copper Mountain, Colorado.



Multi Grid Methods And Applications


Multi Grid Methods And Applications
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Author : Wolfgang Hackbusch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Multi Grid Methods And Applications written by Wolfgang Hackbusch 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 2013-03-09 with Mathematics categories.


Multi-grid methods are the most efficient tools for solving elliptic boundary value problems. The reader finds here an elementary introduction to multi-grid algorithms as well as a comprehensive convergence analysis. One section describes special applications (convection-diffusion equations, singular perturbation problems, eigenvalue problems, etc.). The book also contains a complete presentation of the multi-grid method of the second kind, which has important applications to integral equations (e.g. the "panel method") and to numerous other problems. Readers with a practical interest in multi-grid methods will benefit from this book as well as readers with a more theoretical interest.



Multigrid Methods


Multigrid Methods
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Author : James H Bramble
language : en
Publisher: Routledge
Release Date : 2019-01-22

Multigrid Methods written by James H Bramble and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-22 with Mathematics categories.


Multigrid methods are among the most efficient iterative methods for the solution of linear systems which arise in many large scale scientific calculations. Every researcher working with the numerical solution of partial differential equations should at least be familiar with this powerful technique. This invaluable book presents results concerning the rates of convergence of multigrid iterations.



Introduction To Numerical Geodynamic Modelling


Introduction To Numerical Geodynamic Modelling
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Author : Taras Gerya
language : en
Publisher: Cambridge University Press
Release Date : 2009-12-17

Introduction To Numerical Geodynamic Modelling written by Taras Gerya and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-17 with Science categories.


Numerical modelling of geodynamic processes was predominantly the domain of high-level mathematicians experienced in numerical and computational techniques. Now, for the first time, students and new researchers in the Earth Sciences can learn the basic theory and applications from a single, accessible reference text. Assuming only minimal prerequisite mathematical training (simple linear algebra and derivatives) the author provides a solid grounding in basic mathematical theory and techniques, including continuum mechanics and partial differential equations, before introducing key numerical and modelling methods. 8 well-documented, state-of–the-art visco-elasto-plastic, 2-D models are then presented, which allow robust modelling of key dynamic processes such as subduction, lithospheric extension, collision, slab break-off, intrusion emplacement, mantle convection and planetary core formation. Incorporating 47 practical exercises and 67 MATLAB examples (for which codes are available online at www.cambridge.org/gerya), this textbook provides a user-friendly introduction for graduate courses or self-study, encouraging readers to experiment with geodynamic models.