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Download or read book Experiments Using Incomplete Cholesky Factorization Preconditioners for Saddle-point Systems Arising in Interior-point Methods written by and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Scott Aaron Ladenheim
Publisher :
ISBN 13 :
Total Pages : 88 pages
Book Rating : 4.:/5 (128 download)
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.
Author : Yousef Saad
Publisher : SIAM
ISBN 13 : 0898715342
Total Pages : 537 pages
Book Rating : 4.8/5 (987 download)
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.
Author : Justin Solomon
Publisher : CRC Press
ISBN 13 : 1482251892
Total Pages : 400 pages
Book Rating : 4.4/5 (822 download)
Download or read book Numerical Algorithms written by Justin Solomon and published by CRC Press. This book was released on 2015-06-24 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig
Author : Dominique Orban
Publisher : SIAM
ISBN 13 : 1611974739
Total Pages : 101 pages
Book Rating : 4.6/5 (119 download)
Download or read book Iterative Solution of Symmetric Quasi-definite Linear Systems written by Dominique Orban and published by SIAM. This book was released on 2017-04-07 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerous applications, including computational optimization and fluid dynamics, give rise to block linear systems of equations said to have the quasi-definite structure. In practical situations, the size or density of those systems can preclude a factorization approach, leaving only iterative methods as the solution technique. Known iterative methods, however, are not specifically designed to take advantage of the quasi-definite structure.? This book discusses the connection between quasi-definite systems and linear least-squares problems, the most common and best understood problems in applied mathematics, and explains how quasi-definite systems can be solved using tailored iterative methods for linear least squares (with half as much work!). To encourage researchers and students to use the software, it is provided in MATLAB, Python, and Julia.? The authors provide a concise account of the most well-known methods for symmetric systems and least-squares problems, research-level advances in the solution of problems with specific illustrations in optimization and fluid dynamics, and a website that hosts software in three languages.?
Author : Loyce M. Adams
Publisher : SIAM
ISBN 13 : 9780898713763
Total Pages : 186 pages
Book Rating : 4.7/5 (137 download)
Download or read book Linear and Nonlinear Conjugate Gradient-related Methods written by Loyce M. Adams and published by SIAM. This book was released on 1996-01-01 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the AMS-IMS-SIAM Summer Research Conference held at the University of Washington, July 1995.
Author : Josef Malek
Publisher : SIAM
ISBN 13 : 161197383X
Total Pages : 106 pages
Book Rating : 4.6/5 (119 download)
Download or read book Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs written by Josef Malek and published by SIAM. This book was released on 2014-12-22 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs?is about the interplay between modeling, analysis, discretization, matrix computation, and model reduction. The authors link PDE analysis, functional analysis, and calculus of variations with matrix iterative computation using Krylov subspace methods and address the challenges that arise during formulation of the mathematical model through to efficient numerical solution of the algebraic problem. The book?s central concept, preconditioning of the conjugate gradient method, is traditionally developed algebraically using the preconditioned finite-dimensional algebraic system. In this text, however, preconditioning is connected to the PDE analysis, and the infinite-dimensional formulation of the conjugate gradient method and its discretization and preconditioning are linked together. This text challenges commonly held views, addresses widespread misunderstandings, and formulates thought-provoking open questions for further research.?
Author : Hans Petter Langtangen
Publisher : Springer
ISBN 13 : 3319524623
Total Pages : 152 pages
Book Rating : 4.3/5 (195 download)
Download or read book Solving PDEs in Python written by Hans Petter Langtangen and published by Springer. This book was released on 2017-03-21 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, including the Poisson equation, the equations of linear elasticity, the incompressible Navier–Stokes equations, and systems of nonlinear advection–diffusion–reaction equations, it guides readers through the essential steps to quickly solving a PDE in FEniCS, such as how to define a finite variational problem, how to set boundary conditions, how to solve linear and nonlinear systems, and how to visualize solutions and structure finite element Python programs. This book is open access under a CC BY license.
Author : Mats G. Larson
Publisher : Springer Science & Business Media
ISBN 13 : 3642332870
Total Pages : 403 pages
Book Rating : 4.6/5 (423 download)
Download or read book The Finite Element Method: Theory, Implementation, and Applications written by Mats G. Larson and published by Springer Science & Business Media. This book was released on 2013-01-13 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.
Author : Jorge Nocedal
Publisher : Springer Science & Business Media
ISBN 13 : 0387400656
Total Pages : 686 pages
Book Rating : 4.3/5 (874 download)
Download or read book Numerical Optimization written by Jorge Nocedal and published by Springer Science & Business Media. This book was released on 2006-12-11 with total page 686 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.
Author : Anders Logg
Publisher : Springer Science & Business Media
ISBN 13 : 3642230997
Total Pages : 723 pages
Book Rating : 4.6/5 (422 download)
Download or read book Automated Solution of Differential Equations by the Finite Element Method written by Anders Logg and published by Springer Science & Business Media. This book was released on 2012-02-24 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.
Author : Leslie Hogben
Publisher : CRC Press
ISBN 13 : 1466507284
Total Pages : 1906 pages
Book Rating : 4.4/5 (665 download)
Download or read book Handbook of Linear Algebra, Second Edition written by Leslie Hogben and published by CRC Press. This book was released on 2013-11-26 with total page 1906 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters. New to the Second Edition Separate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of matrices, generalized inverses, matrices over finite fields, invariant subspaces, representations of quivers, and spectral sets New chapters on combinatorial matrix theory topics, such as tournaments, the minimum rank problem, and spectral graph theory, as well as numerical linear algebra topics, including algorithms for structured matrix computations, stability of structured matrix computations, and nonlinear eigenvalue problems More chapters on applications of linear algebra, including epidemiology and quantum error correction New chapter on using the free and open source software system Sage for linear algebra Additional sections in the chapters on sign pattern matrices and applications to geometry Conjectures and open problems in most chapters on advanced topics Highly praised as a valuable resource for anyone who uses linear algebra, the first edition covered virtually all aspects of linear algebra and its applications. This edition continues to encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, and applications of linear algebra to various disciplines while also covering up-to-date software packages for linear algebra computations.
Author : Wolfgang Hackbusch
Publisher : Lecture Notes in Mathematics
ISBN 13 :
Total Pages : 348 pages
Book Rating : 4.F/5 ( download)
Download or read book Multigrid Methods II written by Wolfgang Hackbusch and published by Lecture Notes in Mathematics. This book was released on 1986-12 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alfio Quarteroni
Publisher : Springer Science & Business
ISBN 13 : 8847055229
Total Pages : 668 pages
Book Rating : 4.8/5 (47 download)
Download or read book Numerical Models for Differential Problems written by Alfio Quarteroni and published by Springer Science & Business. This book was released on 2014-04-25 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.
Author : Åke Björck
Publisher : Springer
ISBN 13 : 3319050893
Total Pages : 812 pages
Book Rating : 4.3/5 (19 download)
Download or read book Numerical Methods in Matrix Computations written by Åke Björck and published by Springer. This book was released on 2014-10-07 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work.
Author : S. W. Sloan
Publisher :
ISBN 13 : 9780725906146
Total Pages : 46 pages
Book Rating : 4.9/5 (61 download)
Download or read book A FORTRAN Program for Profile and Wavefront Reduction written by S. W. Sloan and published by . This book was released on 1988 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gianni Pillo
Publisher : Springer Science & Business Media
ISBN 13 : 0387300651
Total Pages : 297 pages
Book Rating : 4.3/5 (873 download)
Download or read book Large-Scale Nonlinear Optimization written by Gianni Pillo and published by Springer Science & Business Media. This book was released on 2006-06-03 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews and discusses recent advances in the development of methods and algorithms for nonlinear optimization and its applications, focusing on the large-dimensional case, the current forefront of much research. Individual chapters, contributed by eminent authorities, provide an up-to-date overview of the field from different and complementary standpoints, including theoretical analysis, algorithmic development, implementation issues and applications.
