Download or read book Constraint Preconditioning of Saddle Point Problems written by Scott Aaron Ladenheim and published by . This book was released on 2015 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is concerned with the fast iterative solution of linear systems of equations of saddle point form. Saddle point problems are a ubiquitous class of matrices that arise in a host of computational science and engineering applications. The focus here is on improving the convergence of iterative methods for these problems by preconditioning. Preconditioning is a way to transform a given linear system into a different problem for which iterative methods converge faster. Saddle point matrices have a very specific block structure and many preconditioning strategies for these problems exploit this structure. The preconditioners considered in this thesis are constraint preconditioners. This class of preconditioner mimics the structure of the original saddle point problem. In this thesis, we prove norm- and field-of-values-equivalence for constraint preconditioners associated to saddle point matrices with a particular structure. As a result of these equivalences, the number of iterations needed for convergence of a constraint preconditioned minimal residual Krylov subspace method is bounded, independent of the size of the matrix. In particular, for saddle point systems that arise from the finite element discretization of partial differential equations (p.d.e.s), the number of iterations it takes for GMRES to converge for theses constraint preconditioned systems is bounded (asymptotically), independent of the size of the mesh width. Moreover, we extend these results when appropriate inexact versions of the constraint preconditioner are used. We illustrate this theory by presenting numerical experiments on saddle point matrices that arise from the finite element solution of coupled Stokes-Darcy flow. This is a system of p.d.e.s that models the coupling of a free flow to a porous media flow by conditions across the interface of the two flow regions. We present experiments in both two and three dimensions, using different types of elements (triangular, quadrilateral), different finite element schemes (continuous, discontinuous Galerkin methods), and different geometries. In all cases, the effectiveness of the constraint preconditioner is demonstrated.

Download or read book Saddle Point Problems and Their Iterative Solution written by Miroslav Rozložník and published by Springer. This book was released on 2018-11-19 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Model Order Reduction Theory Research Aspects and Applications written by Wilhelmus H. Schilders and published by Springer Science & Business Media. This book was released on 2008-08-27 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book A Note on Preconditioning Nonsymmetric Saddle Point Problems written by Piotr Krzyżanowski and published by . This book was released on 1997 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Efficient Preconditioned Solution Methods for Elliptic Partial Differential Equations written by Owe Axelsson and published by Bentham Science Publishers. This book was released on 2011 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book A Note on Preconditioning Nonsymmetric Saddle Point Problems written by Piotr Krzyżanowski (matematyk) and published by . This book was released on 1997 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Studies in Linear and Non Linear Programming written by Leonid Hurwicz and published by . This book was released on 2012-07-01 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Additional Contributing Authors Include Thomas Marschak, Robert Solow, Samuel Karlin, And Others.

Download or read book Preconditioning of Saddle Point Problems Using Hierarchical Matrices written by Deepti Jakkula and published by . This book was released on 2006 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Constraint preconditioned Krylov Solvers for Regularized Saddle point Systems written by Daniela Di Sarafino and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Finite Elements and Fast Iterative Solvers written by Howard Elman and published by OUP Oxford. This book was released on 2014-06-19 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a description of why and how to do Scientific Computing for fundamental models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is closely tied to freely available MATLAB codes that implement the methods described. The focus is on finite element approximation methods and fast iterative solution methods for the consequent linear(ized) systems arising in important problems that model incompressible fluid flow. The problems addressed are the Poisson equation, Convection-Diffusion problem, Stokes problem and Navier-Stokes problem, including new material on time-dependent problems and models of multi-physics. The corresponding iterative algebra based on preconditioned Krylov subspace and multigrid techniques is for symmetric and positive definite, nonsymmetric positive definite, symmetric indefinite and nonsymmetric indefinite matrix systems respectively. For each problem and associated solvers there is a description of how to compute together with theoretical analysis that guides the choice of approaches and describes what happens in practice in the many illustrative numerical results throughout the book (computed with the freely downloadable IFISS software). All of the numerical results should be reproducible by readers who have access to MATLAB and there is considerable scope for experimentation in the "computational laboratory " provided by the software. Developments in the field since the first edition was published have been represented in three new chapters covering optimization with PDE constraints (Chapter 5); solution of unsteady Navier-Stokes equations (Chapter 10); solution of models of buoyancy-driven flow (Chapter 11). Each chapter has many theoretical problems and practical computer exercises that involve the use of the IFISS software. This book is suitable as an introduction to iterative linear solvers or more generally as a model of Scientific Computing at an advanced undergraduate or beginning graduate level.

Download or read book Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications written by Daniele Bertaccini and published by CRC Press. This book was released on 2018-02-19 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Iterative Methods for Solving Linear Systems written by Anne Greenbaum and published by SIAM. This book was released on 1997-01-01 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.

Download or read book Domain Decomposition Methods in Science and Engineering XVI written by Olof Widlund and published by Springer Science & Business Media. This book was released on 2007-07-30 with total page 783 pages. Available in PDF, EPUB and Kindle. Book excerpt: Domain decomposition is an active research area concerned with the development, analysis, and implementation of coupling and decoupling strategies in mathematical and computational models of natural and engineered systems. The present volume sets forth new contributions in areas of numerical analysis, computer science, scientific and industrial applications, and software development.

Download or read book High Performance Scientific Computing written by Michael W. Berry and published by Springer Science & Business Media. This book was released on 2012-01-18 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the state of the art in parallel numerical algorithms, applications, architectures, and system software. The book examines various solutions for issues of concurrency, scale, energy efficiency, and programmability, which are discussed in the context of a diverse range of applications. Features: includes contributions from an international selection of world-class authorities; examines parallel algorithm-architecture interaction through issues of computational capacity-based codesign and automatic restructuring of programs using compilation techniques; reviews emerging applications of numerical methods in information retrieval and data mining; discusses the latest issues in dense and sparse matrix computations for modern high-performance systems, multicores, manycores and GPUs, and several perspectives on the Spike family of algorithms for solving linear systems; presents outstanding challenges and developing technologies, and puts these in their historical context.

Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.

Download or read book Numerical Mathematics and Advanced Applications written by F. Brezzi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 981 pages. Available in PDF, EPUB and Kindle. Book excerpt: An invaluable instrument for gaining a wide-ranging perspective on the latest developments in mathematical aspects of scientific computing, discovering new applications and the most recent developments in long-standing applications. Provides an insight into the state of the art of Numerical Mathematics and, more generally, into the field of Advanced Applications.

Download or read book Issues in Logic Operations and Computational Mathematics and Geometry 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 1187 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Logic, Operations, and Computational Mathematics and Geometry: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Random Structures and Algorithms. The editors have built Issues in Logic, Operations, and Computational Mathematics and Geometry: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Random Structures and Algorithms in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Operations, and Computational Mathematics and Geometry: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.