Verwandte Artikel zu Domain Decomposition Algorithms for Indefinite Elliptic...
Inhaltsangabe
Excerpt from Domain Decomposition Algorithms for Indefinite Elliptic Problems
Domain decomposition techniques are powerful iterative methods for solving lin ear systems oi equations that arise from finite element problems. In each iteration step, a coarse mesh finite element problem and a number of smaller linear sys tems, which correspond to the restriction of the original problem to subregions, are solved instead of the large original system. These algorithms can be regarded as divide and conquer methods. The number of subproblems can be large and these methods are therefore promising for parallel computation. The central mathematical question is to obtain estimates on the rate of convergence of the iteration by deriving bounds on the spectrum of the iteration operator. We are able to establish quite satisfactory bounds if the coarse mesh is fine enough.
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.
Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.
Reseña del editor
Excerpt from Domain Decomposition Algorithms for Indefinite Elliptic Problems
Domain decomposition techniques are powerful iterative methods for solving lin ear systems oi equations that arise from finite element problems. In each iteration step, a coarse mesh finite element problem and a number of smaller linear sys tems, which correspond to the restriction of the original problem to subregions, are solved instead of the large original system. These algorithms can be regarded as divide and conquer methods. The number of subproblems can be large and these methods are therefore promising for parallel computation. The central mathematical question is to obtain estimates on the rate of convergence of the iteration by deriving bounds on the spectrum of the iteration operator. We are able to establish quite satisfactory bounds if the coarse mesh is fine enough.
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.
Reseña del editor
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.
„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.
Neu kaufen
Diesen Artikel anzeigen
EUR 17,39
Gratis für den Versand innerhalb von/der Deutschland
Versandziele, Kosten & DauerWeitere beliebte Ausgaben desselben Titels
Suchergebnisse für Domain Decomposition Algorithms for Indefinite Elliptic...
Foto des Verkäufers
DOMAIN DECOMPOSITION ALGORITHM
Anbieter: moluna, Greven, Deutschland
Verkäuferbewertung 5 von 5 Sternen
Zustand: New. KlappentextrnrnExcerpt from Domain Decomposition Algorithms for Indefinite Elliptic ProblemsDomain decomposition techniques are powerful iterative methods for solving lin ear systems oi equations that arise from finite element problems. . Bestandsnummer des Verkäufers 2147923058
Anzahl: Mehr als 20 verfügbar
Beispielbild für diese ISBN
Domain Decomposition Algorithms for Indefinite Elliptic Problems Classic Reprint
Anbieter: PBShop.store US, Wood Dale, IL, USA
Verkäuferbewertung 5 von 5 Sternen
PAP. Zustand: New. New Book. Shipped from UK. Established seller since 2000. Bestandsnummer des Verkäufers LW-9781332088577
Anzahl: 15 verfügbar
Beispielbild für diese ISBN
Domain Decomposition Algorithms for Indefinite Elliptic Problems Classic Reprint
Anbieter: PBShop.store UK, Fairford, GLOS, Vereinigtes Königreich
Verkäuferbewertung 5 von 5 Sternen
PAP. Zustand: New. New Book. Shipped from UK. Established seller since 2000. Bestandsnummer des Verkäufers LW-9781332088577
Anzahl: 15 verfügbar
Beispielbild für diese ISBN
Domain Decomposition Algorithms for Indefinite Elliptic Problems
Print-on-DemandAnbieter: Forgotten Books, London, Vereinigtes Königreich
Verkäuferbewertung 5 von 5 Sternen
Paperback. Zustand: New. Print on Demand. In this book, the author presents an iterative method that solves linear systems of algebraic equations that arise from finite element problems of elliptic nature. These issues are common in computational mechanics and the finite element method is a modern technique for finding approximate solutions to partial differential equations. The text focuses on problems with symmetric or non-symmetric and indefinite properties. The indefinite case includes some eigenvalues in the left half plane, which is a situation that can lead to difficulties with convergence. The author was able to find an alternative linear system that has the same solution as the original problem, thus allowing a solution via GMRES, a generalized conjugate residual method. In each iteration step, local problems are solved on small overlapping subregions of the original area, and a coarse mesh finite element problem is also solved, yielding a method that provides a way to construct preconditioners for many problems in terms of partitioning a certain finite element space into subspaces. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Bestandsnummer des Verkäufers 9781332088577_0
Anzahl: Mehr als 20 verfügbar