Adaptive-Multilevel BDDC: a scalable and robust version - Softcover

Sousedik, Bedrich

Softcover

ISBN 10: 3639316975 ISBN 13: 9783639316971

Publisher: VDM Verlag Dr. Müller, 2010

Synopsis

The Balancing Domain Decomposition by Constraints (BDDC) method by Dohrmann (2003) is one of the the most advanced method from the Balancing family of iterative substructuring methods by Mandel (1993). In the first part we formulate a new family of abstract Multispace BDDC methods and give condition number bound from the abstract additive Schwarz preconditioning theory. The Multilevel BDDC is then treated as a special case of the Multispace BDDC. In the second part we propose a method for adaptive selection of the coarse space for the original two-level BDDC method. The method works by adding coarse degrees of freedom constructed from eigenvectors associated with intersections of selected pairs of adjacent substructures. In the third part we combine the advantages of both approaches to propose a new method called Adaptive -- Multilevel BDDC that preserves both, parallel scalability with increasing number of subdomains and also very good convergence properties. Performance of the method is illustrated by several numerical examples in two and three spatial dimensions.

About this title

About the Author

Bedrich Sousedik obtained his PhD at the Czech Technical University in Prague and also at the University of Colorado Denver.

Edition details

• Publisher: VDM Verlag Dr. Müller
• Publication date: 2010
• Language: English
• ISBN 10: 3639316975
• ISBN 13: 9783639316971
• Binding: Paperback
• Number of pages: 132