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Séminaire d'équipe(s)
Multigrid methods for the Dirac equation in LQCD
James Brannick

02 July 2012, 10h30 - 02 July 2012, 11h30
Salle/Bat : 455/PCRI-N
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Résumé :
In this talk, I will give an overview of recent research on designing Multigrid methods for solving the Wilson discretization of the Dirac equation in Lattice Quantum Chromodynamics, a commonly used numerical model problem in algorithm development for solving the linear systems arising in lattice field theory computations.
Several variants of adaptive Multigrid have been developed for solving the Dirac equation, dating back to works in the early 1980's by Brower and Rebbi from Boston University. While these earlier efforts resulted in significant progress, both in lattice QCD computations and in MG algorithm development, they failed to provide speed ups over single level Krylov methods for actual simulations of that day. Recent progress on the design of robust adaptive MG methods has, however, led to new techniques that are now capable of delivering up to 25-fold speed ups. One such approach, which I review in detail, is an integrated bootstrap-adaptive method that combines a multilevel singular-value solver with an adaptive Multigrid setup. Results of the method applied to the 2D and the full 4D Wilson Dirac systems are presented, demonstrating that the proposed method handles both efficiently. It is also shown that the solver resulting from the bootstrap-adaptive setup can be applied to the Wilson Dirac system for mass shifts that yield indefinite problems. As such, the solver is also expected to perform well for the chiral Domain Wall formulation of the Dirac equation.

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