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The role of multigrid algorithms for LQCD

Ronald Babich, James Brannick, Richard C. Brower, Michael A. Clark, Saul D. Cohen, James C. Osborn, Claudio Rebbi
Center for Computational Science, Boston University, Boston, MA 02215
arXiv:0912.2186 [hep-lat] (11 Dec 2009)

@article{babich2009role,

   title={The role of multigrid algorithms for LQCD},

   author={Babich, R. and Brannick, J. and Brower, R.C. and Clark, M.A. and Cohen, S.D. and Osborn, J.C. and Rebbi, C.},

   journal={Arxiv preprint arXiv:0912.2186},

   year={2009}

}

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We report on the first successful QCD multigrid algorithm which demonstrates constant convergence rates independent of quark mass and lattice volume for the Wilson Dirac operator. The new ingredient is the adaptive method for constructing the near null space on which the coarse grid multigrid Dirac operator acts. In addition we speculate on future prospects for extending this algorithm to the Domain Wall and Staggered discretizations, its exceptional suitability for high performance GPU code and its potential impact on simulations at the physical pion mass.
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