TY - JOUR
T1 - Multigrid preconditioning for the overlap operator in lattice QCD
AU - Brannick, James
AU - Frommer, Andreas
AU - Kahl, Karsten
AU - Leder, Björn
AU - Rottmann, Matthias
AU - Strebel, Artur
N1 - Funding Information:
This work was partially funded by the Deutsche Forschungsgemeinschaft (DFG) Transregional Collaborative Research Centre 55 (SFB/TRR55) and by the National Science Foundation under grant DMS:1320608.
Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.
PY - 2016/3/1
Y1 - 2016/3/1
N2 - The overlap operator is a lattice discretization of the Dirac operator of quantum chromodynamics (QCD), the fundamental physical theory of the strong interaction between the quarks. As opposed to other discretizations, it preserves the important physical property of chiral symmetry, at the expense of requiring much more effort when solving systems posed with this operator. We present a preconditioning technique based on another lattice discretization, the Wilson-Dirac operator. The mathematical analysis precisely describes the effect of this preconditioning strategy in the case that the Wilson-Dirac operator is normal. Although this is not exactly the case in realistic settings, we show that current smearing techniques indeed drive the Wilson-Dirac operator towards normality, thus providing motivation for why our preconditioner works well in practice. Results of numerical experiments in physically relevant settings show that our preconditioning yields accelerations of more than an order of magnitude compared to unpreconditioned solvers.
AB - The overlap operator is a lattice discretization of the Dirac operator of quantum chromodynamics (QCD), the fundamental physical theory of the strong interaction between the quarks. As opposed to other discretizations, it preserves the important physical property of chiral symmetry, at the expense of requiring much more effort when solving systems posed with this operator. We present a preconditioning technique based on another lattice discretization, the Wilson-Dirac operator. The mathematical analysis precisely describes the effect of this preconditioning strategy in the case that the Wilson-Dirac operator is normal. Although this is not exactly the case in realistic settings, we show that current smearing techniques indeed drive the Wilson-Dirac operator towards normality, thus providing motivation for why our preconditioner works well in practice. Results of numerical experiments in physically relevant settings show that our preconditioning yields accelerations of more than an order of magnitude compared to unpreconditioned solvers.
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U2 - 10.1007/s00211-015-0725-6
DO - 10.1007/s00211-015-0725-6
M3 - Article
AN - SCOPUS:84957849338
SN - 0029-599X
VL - 132
SP - 463
EP - 490
JO - Numerische Mathematik
JF - Numerische Mathematik
IS - 3
ER -