Efficient Iterative Methods for Saddle Point Problems PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Efficient Iterative Methods for Saddle Point Problems PDF full book. Access full book title Efficient Iterative Methods for Saddle Point Problems by Vivek Sarin. Download full books in PDF and EPUB format.
Author: Vivek Sarin Publisher: ISBN: Category : Approximation theory Languages : en Pages : 86
Book Description
Abstract: "This thesis investigates efficient iterative methods for a type of saddle-point problem, namely the generalized Stokes problem, which arises frequently in the simulation of time-dependent Navier-Stokes equations for incompressible fluid flow. These systems are indefinite due to a set of linear constraints on the velocity, causing difficulty for most preconditioners and iterative methods. A multilevel algorithm is proposed for the solution of such systems, which uses a novel technique for the construction of a basis for the space satisfying the constraints. The proposed algorithm achieves faster convergence on account of implicit preconditioning of the linear system, and can be implemented efficiently on parallel processors. Along with a scalable parallel implementation described in the thesis, the multilevel algorithm yields a competitive parallel preconditioned iterative method for the solution of these problems."
Author: Vivek Sarin Publisher: ISBN: Category : Approximation theory Languages : en Pages : 86
Book Description
Abstract: "This thesis investigates efficient iterative methods for a type of saddle-point problem, namely the generalized Stokes problem, which arises frequently in the simulation of time-dependent Navier-Stokes equations for incompressible fluid flow. These systems are indefinite due to a set of linear constraints on the velocity, causing difficulty for most preconditioners and iterative methods. A multilevel algorithm is proposed for the solution of such systems, which uses a novel technique for the construction of a basis for the space satisfying the constraints. The proposed algorithm achieves faster convergence on account of implicit preconditioning of the linear system, and can be implemented efficiently on parallel processors. Along with a scalable parallel implementation described in the thesis, the multilevel algorithm yields a competitive parallel preconditioned iterative method for the solution of these problems."
Author: Daniele Bertaccini Publisher: CRC Press ISBN: 1351649612 Category : Mathematics Languages : en Pages : 321
Book Description
This book describes, in a basic way, the most useful and effective iterative solvers and appropriate preconditioning techniques for some of the most important classes of large and sparse linear systems. The solution of large and sparse linear systems is the most time-consuming part for most of the scientific computing simulations. Indeed, mathematical models become more and more accurate by including a greater volume of data, but this requires the solution of larger and harder algebraic systems. In recent years, research has focused on the efficient solution of large sparse and/or structured systems generated by the discretization of numerical models by using iterative solvers.
Author: Owe Axelsson Publisher: Bentham Science Publishers ISBN: 1608052915 Category : Mathematics Languages : en Pages : 153
Book Description
This e-book presents several research areas of elliptical problems solved by differential equations. The mathematical models explained in this e-book have been contributed by experts in the field and can be applied to a wide range of real life examples. M
Author: Miroslav Rozložník Publisher: Springer ISBN: 3030014312 Category : Mathematics Languages : en Pages : 147
Book Description
This book provides essential lecture notes on solving large linear saddle-point systems, which arise in a wide range of applications and often pose computational challenges in science and engineering. The focus is on discussing the particular properties of such linear systems, and a large selection of algebraic methods for solving them, with an emphasis on iterative methods and preconditioning. The theoretical results presented here are complemented by a case study on potential fluid flow problem in a real world-application. This book is mainly intended for students of applied mathematics and scientific computing, but also of interest for researchers and engineers working on various applications. It is assumed that the reader has completed a basic course on linear algebra and numerical mathematics.
Author: Arieh Iserles Publisher: Cambridge University Press ISBN: 9780521858076 Category : Mathematics Languages : en Pages : 584
Book Description
A high-impact factor, prestigious annual publication containing invited surveys by subject leaders: essential reading for all practitioners and researchers.
Author: Wilhelmus H. Schilders Publisher: Springer Science & Business Media ISBN: 3540788417 Category : Mathematics Languages : en Pages : 471
Book Description
The idea for this book originated during the workshop “Model order reduction, coupled problems and optimization” held at the Lorentz Center in Leiden from S- tember 19–23, 2005. During one of the discussion sessions, it became clear that a book describing the state of the art in model order reduction, starting from the very basics and containing an overview of all relevant techniques, would be of great use for students, young researchers starting in the ?eld, and experienced researchers. The observation that most of the theory on model order reduction is scattered over many good papers, making it dif?cult to ?nd a good starting point, was supported by most of the participants. Moreover, most of the speakers at the workshop were willing to contribute to the book that is now in front of you. The goal of this book, as de?ned during the discussion sessions at the workshop, is three-fold: ?rst, it should describe the basics of model order reduction. Second, both general and more specialized model order reduction techniques for linear and nonlinear systems should be covered, including the use of several related numerical techniques. Third, the use of model order reduction techniques in practical appli- tions and current research aspects should be discussed. We have organized the book according to these goals. In Part I, the rationale behind model order reduction is explained, and an overview of the most common methods is described.
Author: Daniele Bertaccini Publisher: CRC Press ISBN: 1498764177 Category : Mathematics Languages : en Pages : 375
Book Description
This book describes, in a basic way, the most useful and effective iterative solvers and appropriate preconditioning techniques for some of the most important classes of large and sparse linear systems. The solution of large and sparse linear systems is the most time-consuming part for most of the scientific computing simulations. Indeed, mathematical models become more and more accurate by including a greater volume of data, but this requires the solution of larger and harder algebraic systems. In recent years, research has focused on the efficient solution of large sparse and/or structured systems generated by the discretization of numerical models by using iterative solvers.
Author: Anne Greenbaum Publisher: SIAM ISBN: 9781611970937 Category : Mathematics Languages : en Pages : 235
Book Description
Much recent research has concentrated on the efficient solution of large sparse or structured linear systems using iterative methods. A language loaded with acronyms for a thousand different algorithms has developed, and it is often difficult even for specialists to identify the basic principles involved. Here is a book that focuses on the analysis of iterative methods. The author includes the most useful algorithms from a practical point of view and discusses the mathematical principles behind their derivation and analysis. Several questions are emphasized throughout: Does the method converge? If so, how fast? Is it optimal, among a certain class? If not, can it be shown to be near-optimal? The answers are presented clearly, when they are known, and remaining important open questions are laid out for further study. Greenbaum includes important material on the effect of rounding errors on iterative methods that has not appeared in other books on this subject. Additional important topics include a discussion of the open problem of finding a provably near-optimal short recurrence for non-Hermitian linear systems; the relation of matrix properties such as the field of values and the pseudospectrum to the convergence rate of iterative methods; comparison theorems for preconditioners and discussion of optimal preconditioners of specified forms; introductory material on the analysis of incomplete Cholesky, multigrid, and domain decomposition preconditioners, using the diffusion equation and the neutron transport equation as example problems. A small set of recommended algorithms and implementations is included.
Author: Vivek Sarin
Author: Vivek Sarin
Author: Yousef Saad
Author: Daniele Bertaccini
Author: Owe Axelsson
Author: Miroslav Rozložník
Author: Walter Zulehner
Author: Arieh Iserles
Author: Wilhelmus H. Schilders
Author: Daniele Bertaccini
Author: Anne Greenbaum