Multigrid preconditioning for the overlap operator in lattice QCD

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• 作者：James Brannick ; Andreas Frommer ; Karsten Kahl ; Björn Leder…
• 关键词：65F08 ; 65F10 ; 65Z05 ; 65Y05
• 刊名：Numerische Mathematik
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：132
• 期：3
• 页码：463-490
• 全文大小：1,094 KB
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• 作者单位：James Brannick (1)
  Andreas Frommer (2)
  Karsten Kahl (2)
  Björn Leder (2)
  Matthias Rottmann (2)
  Artur Strebel (2)
  
  1. Department of Mathematics, Pennsylvania State University, State College, USA
  2. Fachbereich Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Wuppertal, Germany
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Numerical Analysis
  Mathematics
  Mathematical and Computational Physics
  Mathematical Methods in Physics
  Numerical and Computational Methods
  Applied Mathematics and Computational Methods of Engineering
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：0945-3245

文摘

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. Mathematics Subject Classification 65F08 65F10 65Z05 65Y05