Multilevel Block Factorization Preconditioners: Matrix-based Analysis and Algorithms for Solving Finite Element Equations by Panayot S. VassilevskiMultilevel Block Factorization Preconditioners: Matrix-based Analysis and Algorithms for Solving Finite Element Equations by Panayot S. Vassilevski

Multilevel Block Factorization Preconditioners: Matrix-based Analysis and Algorithms for Solving…

byPanayot S. Vassilevski

Paperback | October 15, 2010

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This monograph is the first to provide a comprehensive, self-contained and rigorous presentation of some of the most powerful preconditioning methods for solving finite element equations in a common block-matrix factorization framework.The book covers both algorithms and analysis using a common block-matrix factorization approach which emphasizes its unique feature. Topics covered include the classical incomplete block-factorization preconditioners, the most efficient methods such as the multigrid, algebraic multigrid, and domain decomposition.This text can serve as an indispensable reference for researchers, graduate students, and practitioners. It can also be used as a supplementary text for a topics course in preconditioning and/or multigrid methods at the graduate level.
Title:Multilevel Block Factorization Preconditioners: Matrix-based Analysis and Algorithms for Solving…Format:PaperbackDimensions:544 pagesPublished:October 15, 2010Publisher:Springer New YorkLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:1441924485

ISBN - 13:9781441924483

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Table of Contents

Part I: Motivation for preconditioning. A finite element tutorial. The main goal.- Part II: Block factorization preconditioners. Two-by-two block matrices. Classical examlpes of block factorizations. Multigrid (MG). Topics in algebraic multigrid (AMG). Domain Decomposition (DD) Methods. Preconditioning nonsymmetric and indefinite matrices. Preconditioning saddle-point matrices. Variable-step iterative methods. Preconditioning nonlinear problems. Quadratic constrained minimization problems.- Part III: Appendices. GCG Methods. Properties of finite element matrices. Further details. Computable scales of Sobolev norms. Multilevel algorithms for boundary extension mappings. H01-norm characterization. MG convergence results for finite element problems.- Some auxiliary inequalities.

Editorial Reviews

From the reviews:"This book by Panayot Vassilevski is the first comprehensive text in the literature on multilevel preconditioners in the formulation of approximate block factorizations. . The presentation is comprehensive and detailed, and the theory is illustrated by classical examples of block factorizations like the block-ILU factorization. . valuable addition to the collection of research books for any researcher working in the field of multilevel methods who is interested in getting a different view on methods he or she knows and has helped to develop and shape." (Martin J. Gander, Mathematical Reviews, Issue 2010 b)"This well-written and timely book fills a great need in the literature. It provides a thorough and yet readable treatment of cotemporary theory . . book will be readily accessible to graduate students past introductory analysis and linear algebra. . The book will be a important reference for anyone interested in practical or theoretical aspects of iterative solvers for finite elements, from students to established researchers. Early chapters could serve well as a textbook on the topic." (Jan Mandel, Zentralblatt MATH, Vol. 1170, 2009)"The presentation sets out with a tutorial on finite elements, where already properties of matrices which turn out essential later on are exhibited. . this presentation will be of major interest to researchers and advanced students in that field." (H. Muthsam, Monatshefte für Mathematik, Vol. 157 (1), May, 2009)