Multilevel Block Factorization Preconditioners Matrix-based Analysis and Algorithms for Solving Finite Element Equations /

• Main Author: Vassilevski, Panayot S. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2008.
• Subjects: Mathematics.; Partial differential equations.; Computer mathematics.; Computational Mathematics and Numerical Analysis.; Partial Differential 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-factoriza...

Table of Contents:

• Motivation for Preconditioning
• A Finite Element Tutorial
• A Main Goal
• Block Factorization Preconditioners
• Two-by-Two Block Matrices and Their Factorization
• Classical Examples of Block-Factorizations
• Multigrid (MG)
• Topics on 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.