[PDF] Elliptic Marching Methods And Domain Decomposition eBook

Author : Patrick J. Roache
Publisher : CRC Press
Page : 212 pages
File Size : 43,21 MB
Release : 1995-06-29
Category : Mathematics
ISBN : 9780849373787

GET BOOK

One of the first things a student of partial differential equations learns is that it is impossible to solve elliptic equations by spatial marching. This new book describes how to do exactly that, providing a powerful tool for solving problems in fluid dynamics, heat transfer, electrostatics, and other fields characterized by discretized partial differential equations. Elliptic Marching Methods and Domain Decomposition demonstrates how to handle numerical instabilities (i.e., limitations on the size of the problem) that appear when one tries to solve these discretized equations with marching methods. The book also shows how marching methods can be superior to multigrid and pre-conditioned conjugate gradient (PCG) methods, particularly when used in the context of multiprocessor parallel computers. Techniques for using domain decomposition together with marching methods are detailed, clearly illustrating the benefits of these techniques for applications in engineering, applied mathematics, and the physical sciences.

Author : Barry Smith
Publisher : Cambridge University Press
Page : 244 pages
File Size : 15,25 MB
Release : 2004-03-25
Category : Computers
ISBN : 9780521602860

GET BOOK

Presents an easy-to-read discussion of domain decomposition algorithms, their implementation and analysis. Ideal for graduate students about to embark on a career in computational science. It will also be a valuable resource for all those interested in parallel computing and numerical computational methods.

Author : Alfio Quarteroni
Publisher : American Mathematical Soc.
Page : 510 pages
File Size : 48,62 MB
Release : 1994
Category : Mathematics
ISBN : 0821851586

GET BOOK

This book contains the proceedings of the Sixth International Conference on Domain Decomposition, held in June 1992 in Como, Italy. Much of the work in this field focuses on developing numerical methods for large algebraic systems.

Author : Maksymilian Dryja
Publisher : Forgotten Books
Page : 30 pages
File Size : 31,67 MB
Release : 2016-10-20
Category : Mathematics
ISBN : 9781334016790

GET BOOK

Excerpt from Towards an Unified Theory of Domain Decomposition Algorithms for Elliptic Problems The paper is organized as follows. After introducing two elliptic model problems and certain finite element methods in Section 2, we begin Section 3 by reviewing Schwarz's alternating algorithm in its classical setting. Following Sobolev [50] and P. L. Lions we indicate how this algorithm can be expressed in a variational form. Since this formulation is very convenient for the analysis of finite element problems, we work in this Hilbert space setting throughout the paper. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Author : Maksymilian Dryja
Publisher : Palala Press
Page : 24 pages
File Size : 22,62 MB
Release : 2018-02-20
Category : History
ISBN : 9781378206935

GET BOOK

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Author : Xiao-Chuan Cai
Publisher : Forgotten Books
Page : 30 pages
File Size : 31,87 MB
Release : 2015-07-28
Category :
ISBN : 9781332088577

GET BOOK

Excerpt from Domain Decomposition Algorithms for Indefinite Elliptic Problems Iterative methods for the linear systems of algebraic equations arising from elliptic finite element problems are considered. Methods previously known to work well for positive definite, symmetric problems are extended to certain nonsymmetric problems, which also can have some eigenvalues in the left half plane. We first consider an additive Schwarz method applied to linear, second order, symmetric or nonsymmetric, indefinite elliptic boundary value problems in two and three dimensions. An alternative linear system, which has the same solution as the original problem, is derived and this system is then solved by using GMRES, an iterative method of conjugate gradient type. In each iteration step, a coarse mesh finite element problem and a number of local problems are solved on small, overlapping subregions into which the original region is subdivided. We show that the rate of convergence is independent of the number of degrees of freedom and the number of local problems if the coarse mesh is fine enough. The performance of the method is illustrated by results of several numerical experiments. We also consider two other iterative method for solving the same class of elliptic problems in two dimensions. Using an observation of Dryja and Widlund, we show that the rate of convergence of certain iterative substructuring methods deteriorates only quite slowly when the local problems increase in size. A similar result is established for Yserentant shierarchical basis method. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Author : Andrea Toselli
Publisher : Springer Science & Business Media
Page : 454 pages
File Size : 40,97 MB
Release : 2006-06-20
Category : Mathematics
ISBN : 3540266623

GET BOOK

This book offers a comprehensive presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. It places strong emphasis on both algorithmic and mathematical aspects. It covers in detail important methods such as FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods.