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An Overview of Scalable FETI—DP Algorithms for Variational Inequalities

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Domain Decomposition Methods in Science and Engineering XVI

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

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Abstract

We review our recent results concerning optimal algorithms for the numerical solution of both coercive and semi-coercive variational inequalities by combining dual-primal FETI algorithms with recent results for bound and equality constrained quadratic programming problems. The convergence bounds that guarantee the scalability of the algorithms are presented. These results are confirmed by numerical experiments.

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References

  1. P. Avery, G. Rebel, M. Lesoinne, and C. Farhat, A numerically scalable dual-primal substructuring method for the solution of contact problems -part I: the frictionless case, Comput. Methods Appl. Mech. Engrg., 193 (2004), pp. 2403–2426.

    Article  MATH  Google Scholar 

  2. D. P. Bertsekas, Nonlinear Programming, Athena Scientific, New Hampshire, second ed., 1999.

    MATH  Google Scholar 

  3. Z. Dostál, Box constrained quadratic programming with proportioning and projections, SIAM J. Optim., 7 (1997), pp. 871–887.

    Article  MATH  MathSciNet  Google Scholar 

  4. Z. Dostál, A proportioning based algorithm for bound constrained quadratic programming with the rate of convergence, Numer. Algorithms, 34 (2003), pp. 293–302.

    Article  MATH  MathSciNet  Google Scholar 

  5. Z. Dostál, Inexact semimonotonic augmented Lagrangians with optimal feasibility convergence for convex bound and equality constrained quadratic programming, SIAM J. Num. Anal., 43 (2006), pp. 96–115.

    Article  Google Scholar 

  6. Z. Dostál, An optimal algorithm for bound and equality constrained quadratic programming problems with bounded spectrum. Submitted to Computing, 2006.

    Google Scholar 

  7. Z. Dostál, A. Friedlander, and S. A. Santos, Solution of contact problems of elasticity by FETI domain decomposition, Contemporary Mathematics, 218 (1998), pp. 82–93.

    Google Scholar 

  8. Z. Dostál, D. Horák, and D. Stefanica, A scalable FETI-DP algorithm with non-penetration mortar conditions on contact interface. Submitted, 2004.

    Google Scholar 

  9. Z. Dostál, D. Horák, and D. Stefanica, A scalable FETI-DP algorithm for a coercive variational inequality, J. Appl. Numer. Math., 54 (2005), pp. 378–390.

    Article  MATH  Google Scholar 

  10. Z. Dostál, D. Horák, and D. Stefanica, A scalable FETI-DP algorithm for a semi-coercive variational inequality. Submitted, 2005.

    Google Scholar 

  11. Z. Dostál and J. Schöberl, Minimizing quadratic functions over non-negative cone with the rate of convergence and finite termination, Comput. Optim. Appl., 30 (2005), pp. 23–43.

    Article  MATH  MathSciNet  Google Scholar 

  12. C. Farhat, M. Lesoinne, P. LeTallec, K. Pierson, and D. Rixen, FETIDP: A Dual-Primal unified FETI method - part I: A faster alternative to the two-level FETI method, Internat. J. Numer. Methods Engrg., 50 (2001), pp. 1523–1544.

    Article  MATH  MathSciNet  Google Scholar 

  13. C. Farhat, J. Mandel, and F.-X. Roux, Optimal convergence properties of the FETI domain decomposition method, Comput. Methods Appl.Mech. Engrg., 115 (1994), pp. 365–385.

    Article  MathSciNet  Google Scholar 

  14. C. Farhat and F.-X. Roux, An unconventional domain decomposition method for an eficient parallel solution of large-scale finite element systems, SIAM J. Sc. Stat. Comput., 13 (1992), pp. 379–396.

    Article  MATH  MathSciNet  Google Scholar 

  15. 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 (2002), pp. 159–179.

    Article  MATH  MathSciNet  Google Scholar 

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Dostál, Z., Horák, D., Stefanica, D. (2007). An Overview of Scalable FETI—DP Algorithms for Variational Inequalities. 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_24

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