An Introduction To Multigrid Methods
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Author | : Wolfgang Hackbusch |
Publisher | : Springer Science & Business Media |
Total Pages | : 391 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 3662024276 |
Download Multi-Grid Methods and Applications Book in PDF, Epub and Kindle
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.
Author | : William L. Briggs |
Publisher | : SIAM |
Total Pages | : 318 |
Release | : 2000-07-01 |
Genre | : Mathematics |
ISBN | : 9780898714623 |
Download A Multigrid Tutorial Book in PDF, Epub and Kindle
Mathematics of Computing -- Numerical Analysis.
Author | : Pieter Wesseling |
Publisher | : R.T. Edwards, Inc. |
Total Pages | : 300 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : |
Download An Introduction to Multigrid Methods Book in PDF, Epub and Kindle
Introduces the principles, techniques, applications and literature of multigrid methods. Aimed at an audience with non-mathematical but computing-intensive disciplines and basic knowledge of analysis, partial differential equations and numerical mathematics, it is packed with helpful exercises, examples and illustrations.
Author | : Ulrich Trottenberg |
Publisher | : Academic Press |
Total Pages | : 652 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 9780127010700 |
Download Multigrid Methods Book in PDF, Epub and Kindle
Mathematics of Computing -- Numerical Analysis.
Author | : Pieter Wesseling (Dr. Ir.) |
Publisher | : |
Total Pages | : 284 |
Release | : 1992 |
Genre | : Multigrid methods (Numerical analysis) |
ISBN | : |
Download An Introduction to Multigrid Methods Book in PDF, Epub and Kindle
Author | : James Lottes |
Publisher | : Springer |
Total Pages | : 138 |
Release | : 2017-03-24 |
Genre | : Mathematics |
ISBN | : 3319563068 |
Download Towards Robust Algebraic Multigrid Methods for Nonsymmetric Problems Book in PDF, Epub and Kindle
This thesis presents a rigorous, abstract analysis of multigrid methods for positive nonsymmetric problems, particularly suited to algebraic multigrid, with a completely new approach to nonsymmetry which is based on a new concept of absolute value for nonsymmetric operators. Multigrid, and in particular algebraic multigrid, has become an indispensable tool for the solution of discretizations of partial differential equations. While used in both the symmetric and nonsymmetric cases, the theory for the nonsymmetric case has lagged substantially behind that for the symmetric case. This thesis closes some of this gap, presenting a major and highly original contribution to an important problem of computational science. The new approach to nonsymmetry will be of interest to anyone working on the analysis of discretizations of nonsymmetric operators, even outside the context of multigrid. The presentation of the convergence theory may interest even those only concerned with the symmetric case, as it sheds some new light on and extends existing results.
Author | : Taras Gerya |
Publisher | : Cambridge University Press |
Total Pages | : 359 |
Release | : 2010 |
Genre | : Mathematics |
ISBN | : 0521887542 |
Download Introduction to Numerical Geodynamic Modelling Book in PDF, Epub and Kindle
This user-friendly reference for students and researchers presents the basic mathematical theory, before introducing modelling of key geodynamic processes.
Author | : Yu Zhu |
Publisher | : John Wiley & Sons |
Total Pages | : 438 |
Release | : 2006-03-10 |
Genre | : Science |
ISBN | : 0471786373 |
Download Multigrid Finite Element Methods for Electromagnetic Field Modeling Book in PDF, Epub and Kindle
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.
Author | : Roman Wienands |
Publisher | : CRC Press |
Total Pages | : 235 |
Release | : 2004-10-28 |
Genre | : Mathematics |
ISBN | : 1420034995 |
Download Practical Fourier Analysis for Multigrid Methods Book in PDF, Epub and Kindle
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
Author | : Sergey I. Martynenko |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 264 |
Release | : 2017-09-25 |
Genre | : Mathematics |
ISBN | : 3110537621 |
Download The Robust Multigrid Technique Book in PDF, Epub and Kindle
This book presents a detailed description of a robust pseudomultigrid algorithm for solving (initial-)boundary value problems on structured grids in a black-box manner. To overcome the problem of robustness, the presented Robust Multigrid Technique (RMT) is based on the application of the essential multigrid principle in a single grid algorithm. It results in an extremely simple, very robust and highly parallel solver with close-to-optimal algorithmic complexity and the least number of problem-dependent components. Topics covered include an introduction to the mathematical principles of multigrid methods, a detailed description of RMT, results of convergence analysis and complexity, possible expansion on unstructured grids, numerical experiments and a brief description of multigrid software, parallel RMT and estimations of speed-up and efficiency of the parallel multigrid algorithms, and finally applications of RMT for the numerical solution of the incompressible Navier Stokes equations. Potential readers are graduate students and researchers working in applied and numerical mathematics as well as multigrid practitioners and software programmers. Contents Introduction to multigrid Robust multigrid technique Parallel multigrid methods Applications of multigrid methods in computational fluid dynamics