Advertisement

A FETI Method for a Class of Indefinite or Complex Second- or Fourth-Order Problems

  • Charbel Farhat
  • Jing Li
  • Michel Lesoinne
  • Philippe Avery
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 40)

Summary

The FETI-DP domain decomposition method is extended to address the iterative solution of a class of indefinite problems of the form (Kσ 2 M)x = b, and a class of complex problems of the form (Kσ 2 M + D)x = b, where K, M, and D are three real symmetric positive semi-definite matrices arising from the finite element discretization of either second-order elastodynamic problems or fourth-order plate and shell dynamic problems, i is the imaginary complex number, and σ is a positive real number.

Keywords

Preconditioned Conjugate Gradient Shell Problem Coarse Problem Preconditioned Conjugate Gradient Iteration Preconditioned Conjugate Gradient Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. X. C. Cai and O. Widlund. Domain decomposition algorithms for indefinite elliptic problems. SIAM J. Sci. Statist. Comput., 13:243–258, 1992.MathSciNetCrossRefMATHGoogle Scholar
  2. C. Farhat, M. Lesoinne, and K. Pierson. A scalable dual-primal domain decomposition method. Numer. Lin. Alg. Appl., 7:687–714, 2000.MathSciNetCrossRefMATHGoogle Scholar
  3. C. Farhat, M. Lesoinne, P. LeTallec, K. Pierson, and D. Rixen. FETI-DP: a dual-primal unified FETI method-part I: a faster alternative to the two-level FETI method. Internat. J. Numer. Meths. Engrg., 50:1523–1544, 2001.MathSciNetCrossRefMATHGoogle Scholar
  4. C. Farhat. A Lagrange multiplier based divide and conquer finite element algorithm. J. Comput. Sys. Engrg., 2:149–156, 1991.CrossRefGoogle Scholar
  5. C. Farhat and F. X. Roux. A method of finite element tearing and interconnecting and its parallel solution algorithm, Internat. J. Numer. Meths. Engrg., 32:1205–1227, 1991.CrossRefMATHGoogle Scholar
  6. C. Farhat, J. Mandel and F. X. Roux. Optimal convergence properties of the FETI domain decomposition method. Comput. Meths. Appl. Mech. Engrg., 115:367–388, 1994.MathSciNetCrossRefGoogle Scholar
  7. J. Mandel and R. Tezaur, On the convergence of a dual-primal substructuring method. Numer. Math., 88:543–558, 2001.MathSciNetCrossRefMATHGoogle Scholar
  8. A. Klawonn, O. B. Widlund and M. Dryja. Dual-primal FETI methods for three-dimensional elliptic problems with heterogeneous coefficients. SIAM J. Numer. Anal., 40:159–179, 2002.MathSciNetCrossRefMATHGoogle Scholar
  9. C. Farhat, P. S. Chen, F. Risler and F. X. Roux. A unified framework for accelerating the convergence of iterative substructuring methods with Lagrange multipliers. Internat. J. Numer. Meths. Engrg., 42:257–288, 1998.MathSciNetCrossRefMATHGoogle Scholar
  10. D. Rixen and C. Farhat. A simple and efficient extension of a class of substructure based preconditioners to heterogeneous structural mechanics problems. Internat. J. Numer. Meths. Engrg., 44:489–516, 1999.MathSciNetCrossRefMATHGoogle Scholar
  11. C. Farhat, A. Macedo and M. Lesoinne. A two-level domain decomposition method for the iterative solution of high frequency exterior Helmholtz problems. Numer.Math., 85:283–308, 2000.MathSciNetCrossRefMATHGoogle Scholar
  12. A. Klawonn. Preconditioners for Indefinite Problems. Ph. D. Thesis, Westfalische, Wilhelms-Universitat, Munster, 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Charbel Farhat
    • 1
  • Jing Li
    • 2
  • Michel Lesoinne
    • 1
  • Philippe Avery
    • 1
  1. 1.Department of Aerospace Engineering SciencesUniversity of Colorado at BoulderBoulder
  2. 2.Department of Mathematical SciencesKent State UniversityKent

Personalised recommendations