Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

A framework of parallel algebraic multilevel preconditioning iterations

A framework of parallel algebraic multilevel preconditioning iterations A framework for parallel algebraic multilevel preconditioning methods is presented for solving large sparse systems of linear equations with symmetric positive definite coefficient matrices, which arise in suitable finite element discretizations of many second-order self-adjoint elliptic boundary value problems. This framework not only covers all known parallel algebraic multilevel preconditioning methods, but also yields new ones. It is shown that all preconditioners within this framework have optimal orders of complexities for problems in two-dimensional (2-D) and three-dimensional (3-D) problem domains, and their relative condition numbers are bounded uniformly with respect to the numbers of both levels and nodes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

A framework of parallel algebraic multilevel preconditioning iterations

Acta Mathematicae Applicatae Sinica , Volume 15 (4) – Jul 4, 2007

Loading next page...
 
/lp/springer-journals/a-framework-of-parallel-algebraic-multilevel-preconditioning-0wlSif4lxJ

References (10)

Publisher
Springer Journals
Copyright
Copyright © 1999 by Science Press
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02684039
Publisher site
See Article on Publisher Site

Abstract

A framework for parallel algebraic multilevel preconditioning methods is presented for solving large sparse systems of linear equations with symmetric positive definite coefficient matrices, which arise in suitable finite element discretizations of many second-order self-adjoint elliptic boundary value problems. This framework not only covers all known parallel algebraic multilevel preconditioning methods, but also yields new ones. It is shown that all preconditioners within this framework have optimal orders of complexities for problems in two-dimensional (2-D) and three-dimensional (3-D) problem domains, and their relative condition numbers are bounded uniformly with respect to the numbers of both levels and nodes.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 4, 2007

There are no references for this article.