A parallel SSOR preconditioner for lattice QCD

Computer Physics Communications

Volumn 98, Issue 1-2, 1996, Pages 20-34

  Fischer, S ^a   Frommer, A ^a   Glassner U ^a   Lippert, Th ^b,c   Ritzenhofer G ^b,c   Schilling, K ^a,b,c  

^a UNIVERSITY OF WUPPERTAL   (Germany)

^b c o KFA Jülich   (Germany)

^c DESY   (Germany)

Author keywords

Krylov subspace; Lattice gauge theory; Preconditioning; SSOR

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; ITERATIVE METHODS; MONTE CARLO METHODS; ORDER DISORDER TRANSITIONS; PARALLEL PROCESSING SYSTEMS; QUANTUM THEORY;

EISENSTAT TRICK; HYBRID MONTE CARLO (HMC) ALGORITHM; KRYLOV SUBSPACE ITERATIVE SOLVERS; LATTICE GAUGE THEORY; LATTICE QUANTUM CHROMODYNAMICS APPLICATIONS; PARALLELIZABLE PRECONDITIONING SCHEME; WILSON FERMIONS;

CRYSTAL LATTICES;

EID: 0030270329     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/0010-4655(96)00089-6     Document Type: Article

References (24)

1. K.G. Wilson, in: New Phenomena in Subnuclear Physics, A. Zichichi, ed. (Plenum, New York, 1975).
2. M. Lüscher, A new approach to the problem of dynamical quarks in the numerical simulation of lattice QCD, Nucl. Phys. B 418 (1994) 637-648.
3. C. Alexandrou, A. Borrelli, Ph. de Forcrand, A. Galli, and F. Jegerlehner, Full QCD with the Lüscher local bosonic action, preprint PSI-PR-95-09, IPS Report 95-14, UCY-PHY-95/5.
4. B. Jegerlehner, Improvements of L̈scher local bosonic fermion algorithm, preprint MPI-PhT/95-119, HEP-LAT 9512001.
5. H. van der Vorst, BiCGstab: A fast and smoothly converging variant of bi-CG for the solution of non-symmetric linear systems, SIAM J. Sc. Stat. Comput. 13 (1992) 631-644.
6. A. Frommer, V. Hannemann, B. Nöckel, Th. Lippert and K. Schilling, Accelerating Wilson fermion matrix inversions by means of the stabilized bi-conjugate gradient algorithm, Int. J. Mod. Phys. C 5 (1994) 1073-1088.
7. A. Borici and P. de Forcrand, Fast Krylov space methods for calculation of quark propagators, IPS Research Report No. 94-03, ETH Zürich (1994).
8. K. Schilling, A. Frommer, V. Hannemann, Th. Lippert and B. Nöckel, Tuning up an oldtimer: Hybrid Monte Carlo with Wilson fermions, Nucl. Phys. B (Proc. Suppl.) 42 (1995) 894-896.
9. P. de Forcrand, Review talk given at Lattice '95, Melbourne, 1995, to appear.
10. A. Frommer, Talk given at Workshop 'Grosse Gleichungssysteme auf Parallelrechnern', University of Wuppertal, 6 October 1994.
11. G. Katz, G. Batrouni, C. Davies, A. Kronfeld, P. Lepage, B. Svetitsky and K. Wilson, Phys. Rev. D 37 (1988) 1589.
12. T. DeGrand and P. Rossi, Comput. Phys. Comm. 60 (1990) 211.
13. R. Gupta et al., QCD with dynamical Wilson fermions, Phys. Rev. D 40 (1989) 2072.
14. Y. Oyanagi, An incomplete LDU decomposition of lattice fermions and its application to conjugate residual methods, Comput. Phys. Comm. 42 (1986) 333.
15. G. Hockney, Nuclear Physics B (Proc. Suppl.) 17 (1990) 301.
16. P. Bacilieri et al., The APE Collaboration, Nucl. Phys. B 317 (1989) 509.
17. G. Hockney, private communications.
18. S. Fischer, Parallele SOR/SSOR-Präkonditionierer für die Inversion der vollen Wilson-Fermion-Matrix durch das BiCGstab-Verfahren auf der Quadrics, Master's thesis (Department of Mathematics, University of Wuppertal, 1996).
19. U. Block, A. Frommer and G. Mayer, Block Coloring Schemes for the SOR Method on Local Memory Parallel Computers, Parallel Computing 14 (1990) 61.
20. S. Eisenstat, Efficient implementation of a class of preconditioned conjugate gradient methods, SIAM J. Sci. Stat. Comput. 2 (1981) 1.
21. J. Ortega, Introduction to Vector and Parallel Solution of Linear Systems (Plenum Press, New York, 1990).
22. For a discussion of the physical parameters as chosen in the SESAM project, see U. Glässner, S. Güsken, H. Hoeber, Th. Lippert, X. Luo, G. Ritzenhöfer, K. Schilling and G. Siegert, SESAM collaboration, QCD with dynamical Wilson fermions - first results from SESAM, talk given at lattice '95, Nucl. Phys. B (Proc. Suppl.), to appear.
23. R.C. Brower, T. Ivanenko, A.R. Levi and K.N. Orginos, Chronological inversion method for the Dirac matrix in Hybrid Monte Carlo, preprint BU-CCS-950601, HEP-LAT/9509012.
24. U. Glässner, S. Güsken, H. Hoeber, Th. Lippert, G. Ritzenhöfer, K. Schilling and G. Siegert, SESAM collaboration, Toolkit for HMC practitioners, technical report, HLRZ Jülich, in preparation.