Abstract
The linear systems arising in lattice quantum chromodynamics (QCD) pose significant challenges for traditional iterative solvers. The Dirac operator associated with these systems is nearly singular, indicating the need for efficient preconditioners. Multilevel preconditioners cannot, however, be easily constructed for these systems becasue the Dirac operator has multiple locally distinct near-kernel components (the so-called slow-to-converge error components of relaxation) that are generally both oscillatory and not known a priori.
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References
A. Brandt, Multigrid methods in lattice field computations, Nuclear Phys. B Proc. Suppl., 26 (1992), pp. 137–180.
M. Brezina, R. Falgout, S. MacLachlan, T. Manteuffel, S. McCormick, and J. Ruge, Adaptive smoothed aggregation (αSA), SIAM J. Sci. Comput., 25 (2004), pp. 1896–1920.
R. C. Brower, R. G. Edwards, C. Rebbi, and E. Vicari, Projective multigrid for Wilson fermions, Nucl. Phys., B366 (1991), pp. 689–709.
M. Creutz, Quarks, Gluons and Lattices, Cambridge Univ. Press, Cambridge, 1982.
V. Faber, T. A. Manteuffel, and S. V. Parter, On the theory of equivalent operators and application to the numerical solution of uniformly elliptic partial differential operators, Adv. in Appl. Math., 11 (1989), pp. 109–163.
M. Lüscher, Lattice QCD and the Schwarz alternating procedure, tech. rep., CERN, Theory Division, 2004.
C. Rebbi, hwilson2d, Code description, tech. rep., Boston University, 2003.
P. Vanêk, J. Mandel, and M. Brezina, Algebraic multigrid by smooth aggregation for second and fourth order elliptic problems, Computing, 56 (1996), pp. 179–196.
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Brannick, J. et al. (2007). Adaptive Smoothed Aggregation in Lattice QCD. 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_63
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DOI: https://doi.org/10.1007/978-3-540-34469-8_63
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