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On Algebraic Multilevel Preconditioners in Lattice Gauge Theory

  • Björn Medeke
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 15)

Abstract

Based on a Schur complement approach we develop a parallelizable multi-level preconditioning method for computing quark propagators in lattice gauge theory.

Keywords

Coarse Grid Eigenvalue Distribution Lattice Gauge Theory Krylov Subspace Method Wilson Fermion 
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.

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References

  1. 1.
    O. Axelsson, P. Vassilevski: Algebraic multilevel preconditioning methods — Part I, Numer. Math. 56, 157–177 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    O. Axelsson, P. Vassilevski: Algebraic multilevel preconditioning methods — Part II, SIAM J. Num. Anal. 27, 1569–1590 (1990)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    R. Barrett, M. Berry, T. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H. van der Vorst: Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM, Philadelphia (1994)CrossRefGoogle Scholar
  4. 4.
    W. Bietenholz, N. Sicker, A. Frommer, Th. Lippert, B. Medeke, K. Schilling, G. Weuffen, Preconditioning of Improved and “Perfect” Fermion Actions, Comput.Phys.Commun. 119 (1999) 1–18zbMATHCrossRefGoogle Scholar
  5. 5.
    P. de Forcrand: Progress on lattice QCD algorithms, Nucl.Phys.Proc.Suppl. 47 (1996) 228–235CrossRefGoogle Scholar
  6. 6.
    N. Eicker, W. Bietenholz, A. Frommer, Th. Lippert, B. Medeke, K Schilling, A Preconditioner for Improved Fermion Actions, Nucl.Phys.Proc.Suppl. 73 (1999) 850–852zbMATHCrossRefGoogle Scholar
  7. 7.
    S. Fischer, A. Frommer, U. Glässner, Th. Lippert, K. Schilling: A Parallel SSOR Preconditioner for Lattice QCD, Comp. Phys. Comm. 98, 20–34 (1996)Google Scholar
  8. 8.
    R. Fletcher, Conjugate gradient methods for indefinite systems, in: Lecture Notes in Mathematics 506, Springer Verlag, 1976Google Scholar
  9. 9.
    R. Freund, N. Nachtigal: QMR: a quasi-minimal residual method for non-Hermitian linear systems, Numer. Math. 60, 315–339 (1991)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    A. Frommer: Linear systems solvers - recent developments and implications for lattice computations, Nuclear Physics B, 53 (Proc. Suppl.) 120–126 (1997)CrossRefGoogle Scholar
  11. 11.
    A. Frommer, Th. Lippert, B. Medeke, K. Schilling, (edts.). Numerical Challenges in Lattice Quantum Chromodynamics. Proceedings of the Interdisciplinary Workshop on Numerical Challenges in Lattice QCD, Wuppertal, August 22–24, 1999. Series Lecture Notes in Computational Science and Engineering (LNCSE). Springer Verlag, Heidelberg, 2000.Google Scholar
  12. 12.
    A. Frommer, B. Medeke: Exploiting Structure in Krylov Subspace Methods for the Wilson Fermion Matrix, in: 15th IMACS World Congress on Scientific Cornputation, Modelling and Applied Mathematics (A. Sydow, ed.), Wissenschaft & Technik Verlag, Berlin, 485–490 (1997)Google Scholar
  13. 13.
    Gutknecht, M. H.: Remarks on Lanczos-type methods for Wilson fermions, in [11]Google Scholar
  14. 14.
    W. Hackbusch: Multi-grid methods and applications, Springer, Heidelberg (1985)zbMATHGoogle Scholar
  15. 15.
    Notay, Y.: Optimal V-cycle algebraic multilevel preconditioning. (1997)Google Scholar
  16. 16.
    Notay, Y.: On Algebraic Multilevel Preconditioning, in [11]Google Scholar
  17. 17.
    Reusken, A.: An Algebraic Multilevel Preconditioner for Symmetric Positive Definite and Indefinite Systems, in [11]Google Scholar
  18. 18.
    Y. Saad, M. Schultz: GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comp. 7, 856–869 (1986)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    H. van der Vorst: Bi-CGStab: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Stat. Comp. 13, 631–644 (1992)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Björn Medeke
    • 1
  1. 1.Department of Mathematics Institute of Applied Computer ScienceUniversity of WuppertalWuppertalGermany

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