Multilevel block factorization preconditioners: matrix-based analysis and algorithms for solving finite element equations

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. Topics covered include the classical incomplete block-factorization preconditioners and the most efficient methods such as the multigrid, algebraic multigrid, and domain decomposition. Additionally, the author discusses preconditioning of saddle-point, nonsymmetric and indefinite problems, as well as preconditioning of certain nonlinear and quadratic constrained minimization problemsthat typically arise in contact mechanics. The book presents analytical as well as algorithmic aspects. This text can serve as an indispensable reference for researchers, graduate students, and practitioners. It can also be used as asupplementary text for a topics course in preconditioning and/or multigrid methods at the graduate level. Uses block-matrix factorization to represent important developments in the field such as the algebraic multi-grid and domain decomposition methods Rigorous and self-contained presentation Includes four useful appendices Excellent reference for practitioners and researchers INDICE: 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). Topicsin 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.

• ISBN: 978-0-387-71563-6
• Editorial: Springer
• Encuadernacion: Cartoné
• Páginas: 545
• Fecha Publicación: 01/06/2008
• Nº Volúmenes: 1
• Idioma: Inglés