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2012

Aggregation-based Multilevel Methods for Lattice QCD

Frommer, Andreas, Kahl, Karsten, Krieg, Stefan et al.

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In Lattice QCD computations a substantial amount of work is spent in solving the Dirac equation.

In the recent past it has been observed that conventional Krylov solvers tend to critically slow down for large lattices and small quark masses.
We present a Schwarz alternating procedure (SAP) multilevel method as a solver for the Clover improved Wilson discretization of the Dirac equation.
This approach combines two components (SAP and algebraic multigrid) that have separately been used in lattice QCD before.

Aggregation-based Multilevel Methods for Lattice QCD · Around

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M. Luscher, “Solution of the Dirac equation in lattice QCD using a domain decomposition method,” Comput.Phys.Commun. 156 (2004) 209–220 , arXiv:hep-lat/0310048 [hep-lat]
2004
Earlier work this paper cites.
M. Brezina, R. Falgout, S. MacLachlan, T. Manteuffel, S. McCormick, and J. Ruge, “Adaptive smoothed aggregation ( α \alpha SA) multigrid,” SIAM Review 47, No. 2
2005
Earlier work this paper cites.
M. Luscher, “Local coherence and deflation of the low quark modes in lattice QCD,” JHEP 0707 (2007) 081 , arXiv:0706.2298 [hep-lat]
Original
2007
Earlier work this paper cites.
L. Del Debbio, L. Giusti, M. Lüscher, R. Petronzio, and N. Tantalo, “QCD with light Wilson quarks on fine lattices (I): First experiences and physics results,” JHEP 0702 (2007) 056 , arXiv:hep-lat/0610059 [hep-lat]
2007
Earlier work this paper cites.

Similar

J. Brannick, R. Brower, M. Clark, J. Osborn, and C. Rebbi, “Adaptive Multigrid Algorithm for Lattice QCD,” Phys.Rev.Lett. 100 (2008) 041601 , arXiv:0707.4018 [hep-lat]
Original
2008
Cited alongside, same era.
J. Osborn, R. Babich, J. Brannick, R. Brower, M. Clark, et al
Original
2010
Cited alongside, same era.
R. Babich, J. Brannick, R. Brower, M. Clark, T. Manteuffel, et al
Original
2010
Cited alongside, same era.
H. Schwarz, “Gesammelte mathematische Abhandlungen,” Vierteljahrschrift Naturforsch. Ges. Zürich
Cited in the paper.

Then

A. Brandt, J. Brannick, K. Kahl, and I. Livshits, “Bootstrap AMG.,” SIAM J. Sci. Comput. 33 no.~2, (2011) 612–632
2011
Later among the works it cites.
S. Durr, Z. Fodor, C. Hoelbling, S. Katz, S. Krieg, et al
Original
2011
Later among the works it cites.
S. Durr, Z. Fodor, C. Hoelbling, S. Katz, S. Krieg, et al
Original
2011
Later among the works it cites.

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