Author : William L. Briggs
Publisher : SIAM
Page : 318 pages
File Size : 35,26 MB
Release : 2000-07-01
Category : Mathematics
ISBN : 9780898714623
Mathematics of Computing -- Numerical Analysis.
Author : Wolfgang Hackbusch
Publisher : Springer Science & Business Media
Page : 391 pages
File Size : 24,84 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 3662024276
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 : Pieter Wesseling
Publisher : R.T. Edwards, Inc.
Page : 300 pages
File Size : 36,77 MB
Release : 2004
Category : Mathematics
ISBN :
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
Page : 652 pages
File Size : 11,76 MB
Release : 2001
Category : Mathematics
ISBN : 9780127010700
Mathematics of Computing -- Numerical Analysis.
Author : Achi Brandt
Publisher : SIAM
Page : 239 pages
File Size : 46,24 MB
Release : 2011-01-01
Category : Mathematics
ISBN : 9781611970753
This classic text presents the best practices of developing multigrid solvers for large-scale computational problems in science and engineering. By representing a problem at multiple scales and employing suitable interscale interactions, multigrid avoids slowdown due to stiffness and reduces the computational cost of classical algorithms by orders of magnitude. Starting from simple examples, this book guides the reader through practical stages for developing reliable multigrid solvers, methodically supported by accurate performance predictors. The revised edition presents discretization and fast solution of linear and nonlinear partial differential systems; treatment of boundary conditions, global constraints and singularities; grid adaptation, high-order approximations, and system design optimization; applications to fluid dynamics, from simple models to advanced systems; new quantitative performance predictors, a MATLAB sample code, and more. Readers will also gain access to the Multigrid Guide 2.0 Web site, where updates and new developments will be continually posted, including a chapter on Algebraic Multigrid.
Author : James Lottes
Publisher : Springer
Page : 138 pages
File Size : 40,50 MB
Release : 2017-03-24
Category : Mathematics
ISBN : 3319563068
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
Page : 359 pages
File Size : 22,52 MB
Release : 2010
Category : Mathematics
ISBN : 0521887542
This user-friendly reference for students and researchers presents the basic mathematical theory, before introducing modelling of key geodynamic processes.
Author : Roman Wienands
Publisher : CRC Press
Page : 235 pages
File Size : 27,84 MB
Release : 2004-10-28
Category : Mathematics
ISBN : 1420034995
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
Page : 264 pages
File Size : 29,25 MB
Release : 2017-09-25
Category : Mathematics
ISBN : 3110537621
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
Author : Stephen F. McCormick
Publisher : SIAM
Page : 292 pages
File Size : 37,50 MB
Release : 1987-12-01
Category : Mathematics
ISBN : 1611971888
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.
