The Robust Multigrid Technique

DOWNLOAD

Download The Robust Multigrid Technique PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get The Robust Multigrid Technique book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Towards Robust Algebraic Multigrid Methods For Nonsymmetric Problems

DOWNLOAD
Author : James Lottes
language : en
Publisher: Springer
Release Date : 2017-03-24

Towards Robust Algebraic Multigrid Methods For Nonsymmetric Problems written by James Lottes and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-24 with Mathematics categories.

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.

Multi Grid Methods And Applications

DOWNLOAD
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.

The Robust Multigrid Technique

DOWNLOAD
Author : Sergey I. Martynenko
language : en
Publisher:
Release Date : 2017

The Robust Multigrid Technique written by Sergey I. Martynenko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Boundary value problems categories.

Robust Multi Grid Methods

DOWNLOAD
Author : W. Hackbusch
language : en
Publisher: Vieweg+teubner Verlag
Release Date : 1989

Robust Multi Grid Methods written by W. Hackbusch and has been published by Vieweg+teubner Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Science categories.

In full multigrid methods for elliptic difference equations one works on a sequence of meshes where a number of pre- and/or postsmoothing steps are performed on each level. As is well known these methods can converge very fast on problems with a smooth solution and a regular mesh, but the rate of convergence can be severely degraded for problems with unisotropy or discontinuous coefficients unless some form of robust smoother is used. Also problems can arise with the increasingly coarser meshes because for some types of discretization methods, coercivity may be lost on coarse meshes and on massively parallel computers the computation cost of transporting information between computer processors devoted to work on various levels of the mesh can dominate the whole computing time. For discussions about some of these problems, see (11). Here we propose a method that uses only two levels of meshes, the fine and the coarse level, respec­ tively, and where the corrector on the coarse level is equal to a new type of preconditioner which uses an algebraic substructuring of the stiffness matrix. It is based on the block matrix tridiagonal structure one gets when the domain is subdivided into strips. This block-tridiagonal form is used to compute an approximate factorization whereby the Schur complements which arise in the recursive factorization are approximated in an indirect way, i. e.

Multigrid Methods Iv

DOWNLOAD
Author : P.W. Hemker
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Multigrid Methods Iv written by P.W. Hemker and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This volume contains a selection from the papers presented at the Fourth European Multigrid Conference, held in Amsterdam, July 6-9,1993. There were 78 registered participants from 14 different countries, and 56 presentations were given. The preceding conferences in this series were held in Cologne (1981, 1985) and in Bonn (1990). Also at the other side of the Atlantic special multigrid conferences are held regularly, at intervals of two years, always in Copper Mountain, Colorado, US. The Sixth Copper Mountain Conference on Multigrid Methods took place in April, 1993. Circumstances prevented us from putting a larger time interval between the Copper and Amsterdam meetings. The next European meeting is planned in 1996, a year later than the next Copper Meeting. When the first multigrid conference was held in 1981 there was no doubt about the usefulness of a conference dedicated specially to multigrid, because multigrid was a new and relatively unexplored subject, still in a pioneering stage, and pursued by specialists. The past twenty years have shown a rapid growth in theoretical understanding, useful applications and widespread acceptance of multi grid in the applied disciplines. Hence, one might ask whether there is still a need today for conferences specially dedicated to multigrid. The general consensus is that the answer is affirmative. New issues have arisen that are best addressed or need also be addressed from a special multigrid point of view.

Multigrid Methods

DOWNLOAD
Author : Stephen F. McCormick
language : en
Publisher: SIAM
Release Date : 1987-12-01

Multigrid Methods written by Stephen F. McCormick and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-12-01 with Mathematics categories.

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.

Multigrid Methods

DOWNLOAD
Author : W. Hackbusch
language : en
Publisher: Springer
Release Date : 2006-11-15

Multigrid Methods written by W. Hackbusch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

Multigrid Techniques

DOWNLOAD
Author : Achi Brandt
language : en
Publisher: SIAM
Release Date : 2011-01-01

Multigrid Techniques written by Achi Brandt and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-01 with Mathematics categories.

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.

Introduction To Numerical Geodynamic Modelling

DOWNLOAD
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.

A Multigrid Tutorial

DOWNLOAD
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.