Skip to main content

The Primal Alternatives of the FETI Methods Equipped with the Lumped Preconditioner

  • Conference paper
Domain Decomposition Methods in Science and Engineering XVI

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 55))

Abstract

In the past few years, Domain Decomposition Methods (DDM) have emerged as advanced solvers in several areas of computational mechanics. In particular, during the last decade, in the area of solid and structural mechanics, they reached a considerable level of advancement and have been shown to be more efficient than popular solvers, like advanced sparse direct solvers. The present contribution follows the lines of a series of recent publications by the authors on DDM. In these papers, the authors developed a unified theory of primal and dual methods and presented a family of DDM that were shown to be more efficient than previous methods. The present paper extends this work, presenting a new family of related DDM, thus enriching the theory of the relations between primal and dual methods.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Bhardwaj, D. Day, C. Farhat, M. Lesoinne, K. Pierson, and D. Rixen, Application of the FETI method to ASCI problems - scalability results on 1000 processors and discussion of highly heterogeneous problems, Internat. J. Numer. Methods Engrg., 47 (2000), pp. 513–536.

    Article  MATH  Google Scholar 

  2. Y. Fragakis and M. Papadrakakis, The mosaic of high performance domain decomposition methods for structural mechanics: Formulation, interrelation and numerical effciency of primal and dual methods, Comput. Methods Appl. Mech. Engrg, 192 (2003), pp. 3799–3830.

    Article  MATH  Google Scholar 

  3. Y. Fragakis and M. Papadrakakis, The mosaic of high performance domain decomposition methods for structural mechanics - part II: Formulation enhancements, multiple right-hand sides and implicit dynamics, Comput. Methods Appl. Mech. Engrg., 193 (2004), pp. 4611–4662.

    Article  MATH  Google Scholar 

  4. Y. Fragakis and M. Papadrakakis, Derivation of the primal alternatives of the lumped preconditioned FETI methods, tech. rep., Institute of Structural Analysis and Seismic Research, National Technical University of Athens, Athens, Greece, 2005. Available from http://users.ntua.gr/fragayan/publications.htm.

    Google Scholar 

  5. A. Klawonn and O. B. Widlund, FETI and Neumann-Neumann iterative substructuring methods: Connections and new results, Comm. Pure Appl. Math., 54 (2001), pp. 57–90.

    Article  MATH  Google Scholar 

  6. J. Mandel, Balancing domain decomposition, Comm. Numer. Meth. Engrg., 9 (1993), pp. 233–241.

    Article  MATH  Google Scholar 

  7. J. Mandel, C. R. Dohrmann, and R. Tezaur, An algebraic theory for primal and dual substructuring methods by constraints, Appl. Numer. Math., 54 (2005), pp. 167–193.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer

About this paper

Cite this paper

Fragakis, Y., Papadrakakis, M. (2007). The Primal Alternatives of the FETI Methods Equipped with the Lumped Preconditioner. In: Widlund, O.B., Keyes, D.E. (eds) Domain Decomposition Methods in Science and Engineering XVI. Lecture Notes in Computational Science and Engineering, vol 55. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34469-8_45

Download citation

Publish with us

Policies and ethics