Book Description
This second edition of the popular A Multigrid Tutorial preserves the introductory spirit of the first edition while roughly doubling the amount of material covered. The topics of the first edition have been enhanced with additional discussion, new numerical experiments, and improved figures. New topics in the second edition include nonlinear equations, Neumann boundary conditions, variable mesh and variable coefficient problems, anisotropic problems, algebraic multigrid (AMG), adaptive methods, and finite elements. This introductory book is ideally suited as a companion textbook for graduate numerical analysis courses. It is written for computational mathematicians, engineers, and other scientists interested in learning about multigrid.
Customer Reviews:
An Accessible Multigrid Introduction...No, Really, I Mean It.......2005-04-28
Mathematicians who write well are a rare commodity. Briggs is one of them. He has the ability to break down complex numerics with understandable prose making concepts accessible to non-specialists. He operates under the rare assumption that his readers weren't born knowing this stuff. This multigrid primer written with Henson and McCormick is no exception. Expository discussions are lucid, compact and informative; examples and plots are helpful and well selected; and pseudo code is well documented with corresponding outputs to verify understanding. If you are embarking on Multigrid from scratch this short (if somewhat pricy) primer is worth the time and money.
Good introduction to Multigrid.......2002-04-05
Anyone with some background in applied mathmatics should find this book accessible. It is well laid-out and focuses on algorithms as opposed to mathematical proofs. It is ideal for someone interested in multigrid methods but who doesn't want to get lost in lots of mathematical theory. It doesn't cover cell centered methods, which is somewhat limiting, but other than that it was useful and informative.
Excellent basic multigrid theory.......1996-12-02
This is a great book. Clearly written, well
organized.
Average customer rating:
- multigrid explained
- for actual programmers/scientists
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Multigrid
Ulrich Trottenberg ,
Cornelius W. Oosterlee , and
Anton Schuller
Manufacturer: Academic Press
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A Multigrid Tutorial
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An Introduction to Multigrid Methods
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Iterative Krylov Methods for Large Linear Systems (Cambridge Monographs on Applied and Computational Mathematics)
ASIN: 012701070X |
Book Description
Multigrid presents both an elementary introduction to multigrid methods for solving partial differential equations and a contemporary survey of advanced multigrid techniques and real-life applications.
Multigrid methods are invaluable to researchers in scientific disciplines including physics, chemistry, meteorology, fluid and continuum mechanics, geology, biology, and all engineering disciplines. They are also becoming increasingly important in economics and financial mathematics.
Readers are presented with an invaluable summary covering 25 years of practical experience acquired by the multigrid research group at the Germany National Research Center for Information Technology. The book presents both practical and theoretical points of view.
* Covers the whole field of multigrid methods from its elements up to the most advanced applications
* Style is essentially elementary but mathematically rigorous
* No other book is so comprehensive and written for both practitioners and students
Customer Reviews:
multigrid explained.......2006-12-02
as opposed to what another reviewer states, this book has nothing to do with grid computing. instead, it presents a mathematical technique for solving linear systems of equations (with the focus on large, sparse systems arising from the discretization of PDEs). lots of math inside, there's nothing whatsoever for the layman here. the introduction to the basic concepts is quite thorough, and they cover some advanced topics like adaptive multigrid, algebraic multigrid (an extension of MG to general linear systems) and application of MG in computational fluid dynamics. overall, a good book, but I strongly recommend Briggs' and Van Emden Henson's "Multigrid Tutorial" text as a 1st read before tackling this book. the reader is assumed to be familiar with linear algebra (with a focus on matrix calculus and classical iterative methods). to fully understand the later chapters, more advanced exposure to let's say CFD is needed.
for actual programmers/scientists.......2005-01-13
IBM and other companies have been promoting a vision of grid computing. Books have been written, including "Grid Computing" by Joseph and Fellenstein, that describe this approach at a high level. Suitable for system administrators and managers.
By contrast, this book by Trottenberg et al is aimed directly at the scientists and engineers who might be actually writing software for their problems. The mathematical treatment is looser than that in a pure maths book. It's at the typical level for a physic or engineering text. The intent here is not in proving theorems, but in applying them to real world problems.
Specifically, for solving PDEs and linear systems.
Book Description
Inspired by a series of lectures given in Delft, Bristol, Lyons, Zurich, and Beijing, this book is a corrected reprint of the 1992 classic. Provides a complete introduction to multigrid methods for partial differential equations, without requiring an advanced knowledge of mathematics. Topics such as the basic multigrid principle, smoothing methods and their Fourier analysis, course grid approximation, multigrid cycles and results of multigrid theory are treated. Applications in computational fluid dynamics are discussed extensively.
Customer Reviews:
A Reprint of a Classic.......2004-09-05
This is a corrected version of one of the real classics in the multigrid field. Its first publisher allowed the price to skyrocket to the point that it still stands today as the most expensive multigrid book I own. The reprint is over $100 USD less than what I paid for my copy.
The book is completely self contained. It has one of nicest descriptions of finite volume methods in it that I know of. It covers all of the basic multigrid concepts in detail, both algorithmically and theoretically. It covers a lot more than basics as well.
While it was between regular publishers the author gratiously allowed a scanned copy to be downloaded from the multigrid community web site http://www.mgnet.org. It was one of the most downloaded items while it was there. (As an aside, it is no longer available on the web.)
While not the most recent multigrid book, it still is one of the best. The price, considering it is a hardback, is also very competitive.
I highly recommend this book, particularly for students who have not studied in depth numerical methods for solving partial differential equation.
Free on (...).......2001-12-11
It's a very good book to begin in MG, with analysis made in an accessible way to someone acquainted with von Neuman method and common matrix analysis. (...)
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Practical Fourier Analysis for Multigrid Methods (Numerical Insights)
Roman Wienands , and
Wolfgang Joppich
Manufacturer: Chapman & Hall/CRC
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ASIN: 1584884924 |
Book Description
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 detailed and systematic description of local Fourier k-grid (k=1,2,3) analysis for general systems of partial differential equations to provide a framework that answers these questions. This volume contains software that confirms written statements about convergence and efficiency of algorithms and is easily adapted to new applications. Providing theoretical background and the linkage between theory and practice, the text and software quickly combine learning by reading and learning by doing. The book enables understanding of basic principles of multigrid and local Fourier analysis, and also describes the theory important to those who need to delve deeper into the details of the subject. The first chapter delivers an explanation of concepts, including Fourier components and multigrid principles. Chapter 2 highlights the basic elements of local Fourier analysis and the limits to this approach. Chapter 3 examines multigrid methods and components, supported by a user-friendly GUI. Chapter 4 provides case studies for two- and three-dimensional problems. Chapters 5 and 6 detail the mathematics embedded within the software system. Chapter 7 presents recent developments and further applications of local Fourier analysis for multigrid methods.
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Multigrid Methods (Frontiers in Applied Mathematics)
Manufacturer: Society for Industrial Mathematics
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ASIN: 0898712149 |
Book Description
A thoughtful consideration of the current level of development of multigrid methods, this volume is a carefully edited collection of papers that addresses its topic on several levels. The first three chapters orient the reader who is familiar with standard numerical techniques to multigrid methods, first by discussing multigrid in the context of standard techniques, second by detailing the mechanics of use of the method, and third by applying the basic method to some current problems in fluid dynamics. The fourth chapter provides a unified development, complete with theory, of algebraic multigrid (AMG), which is a linear equation solver based on multigrid principles. The last chapter is an ambitious development of a very general theory of multigrid methods for variationally posed problems. Included as an appendix is the latest edition of the Multigrid Bibliography, an attempted compilation of all existing research publications on multigrid.
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Computational Grids: Generations, Adaptation & Solution Strategies (Series in Computational and Physical Processes in Mechanics and Thermal Sciences)
Graham F. Carey
Manufacturer: CRC
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The Finite Element Method: Its Basis and Fundamentals, Sixth Edition
ASIN: 1560326352 |
Book Description
In this comprehensive volume a treatment of grid generation, adaptive refinement, and redistribution techniques is developed together with supporting mathematical, algorithmic, and software concepts. Efficient solution strategies that exploit grid hierarchies are also described and analyzed. Emphasis is on the fundamental ideas, but the presentation includes practical guidelines for designing and implementing grid strategies.
Customer Reviews:
Grids and Solutions.......2000-04-27
The title is a bit misleading. It is a book about solutions(finite-element method) and adaptations. You can learn how to generate and modify(adaptation) the computational grid (mainly triangular)for solutions by finite-element method. It is a bit too mathematical, but not too much for engineers to read. Many algorithms are described such as Delaunay triangulation, and also data structures for adaptation. A useful book to those who wants to learn about solution adaptation procedure.
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Multigrid Methods V: Proceedings of the Fifth European Multigrid Conference held in Stuttgart, Germany, October 1-4, 1996 (Lecture Notes in Computational Science and Engineering)
Manufacturer: Springer
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ASIN: 354063133X |
Book Description
This book is the proceedings of a top-quality meeting on multigrid methods and will become a standard reference for researchers in computational science and engineering as well as numerical analysis.
Book Description
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.
Download Description
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.
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Numerical Solution of Partial Differential Equations on Parallel Computers (Lecture Notes in Computational Science and Engineering)
Manufacturer: Springer
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The Sourcebook of Parallel Computing (The Morgan Kaufmann Series in Computer Architecture and Design)
ASIN: 3540290761 |
Book Description
This book surveys the major topics that are essential to high-performance simulation on parallel computers or computational clusters. These topics, including programming models, load balancing, mesh generation, efficient numerical solvers, and scientific software, are vital ingredients in the research fields of computer science, numerical analysis, and scientific computing. In addition to presenting the technological basis, this volume addresses selected applications that combine different techniques in order to meet demanding computational challenges. Through contributions from a wide range of internationally acknowledged experts, this book gives a to-the-point and self-containing overview of efficient ways to deal with large-scale simulation problems.
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Adaptive Methods of Calculus Mathematics and Mechanics: Stochastic Variant
D. G. Arsenev ,
V. M. Ivanov , and
O. Iu Kulchitskii
Manufacturer: World Scientific Publishing Company
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Multigrid
A First Course in the Numerical Analysis of Differential Equations (Cambridge Texts in Applied Mathematics)
