Built on

D. Richtmann, P. A. Boyle and T. Wettig, “Multigrid for Wilson Clover Fermions in Grid,” PoS LATTICE2018
Original
1904
Earlier work this paper cites.
Hestenes, Magnus R.; Stiefel, Eduard. “Methods of Conjugate Gradients for Solving Linear Systems”. Journal of Research of the National Bureau of Standards. 49 (6): 409. 1952
1952
Earlier work this paper cites.
S. C. Eisenstat, H. C. Elman, and H. C. Schultz. “Variational iterative methods for nonsymmetric systems of linear equations.” SIAM J. Numer. Anal., 20, 1983
1983
Earlier work this paper cites.
S. Duane, A. D. Kennedy, B. J. Pendleton and D. Roweth, “Hybrid Monte Carlo,” Phys. Lett. B 195
1987
Earlier work this paper cites.
D. B. Kaplan, “A Method for simulating chiral fermions on the lattice,” Phys. Lett. B 288
1992
Earlier work this paper cites.
Y. Shamir, “Chiral fermions from lattice boundaries,” Nucl. Phys. B 406
1993
Earlier work this paper cites.
S. Aoki and Y. Taniguchi, “One loop calculation in lattice QCD with domain wall quarks,” Phys. Rev. D 59
1999
Earlier work this paper cites.
R. C. Brower, M. A. Clark, D. Howarth and E. S. Weinberg, “Multigrid for Chiral Lattice Fermions: Domain Wall,” [arXiv:2004.07732 [hep-lat]]
Original
2004
Earlier work this paper cites.
M. Luscher, “Local coherence and deflation of the low quark modes in lattice QCD,” JHEP 0707
Original
2007
Earlier work this paper cites.

Similar

J. Brannick, R. C. Brower, M. A. Clark, J. C. Osborn and C. Rebbi, “Adaptive Multigrid Algorithm for the QCD Dirac-Wilson Operator,” PoS LAT 2007
Original
2007
Cited alongside, same era.
C. Allton et al
2007
Cited alongside, same era.
J. Brannick, R. C. Brower, M. A. Clark, J. C. Osborn and C. Rebbi, “Adaptive Multigrid Algorithm for Lattice QCD,” Phys. Rev. Lett. 100
Original
2008
Cited alongside, same era.
M. A. Clark, J. Brannick, R. C. Brower, S. F. McCormick, T. A. Manteuffel, J. C. Osborn and C. Rebbi, “The Removal of critical slowing down,” PoS LATTICE 2008
Original
2008
Cited alongside, same era.
R. Babich, J. Brannick, R. C. Brower, M. A. Clark, S. D. Cohen, J. C. Osborn and C. Rebbi, “The Role of multigrid algorithms for LQCD,” PoS LAT 2009
Original
2009

Then

S. D. Cohen, R. C. Brower, M. A. Clark and J. C. Osborn, “Multigrid Algorithms for Domain-Wall Fermions,” PoS LATTICE 2011
Original
2011
Later among the works it cites.
Rudy Arthur, PhD thesis, University of Edinburgh, 2012
2012
Later among the works it cites.
A. Frommer, K. Kahl, S. Krieg, B. Leder and M. Rottmann, “Adaptive Aggregation Based Domain Decomposition Multigrid for the Lattice Wilson Dirac Operator,” SIAM J. Sci. Comput. 36
Original
2014
Later among the works it cites.
A. Yamaguchi and P. Boyle, “Hierarchically deflated conjugate residual,” PoS LATTICE2016
Original
2016
Later among the works it cites.
P. A. Boyle, G. Cossu, A. Yamaguchi and A. Portelli, “Grid: A next generation data parallel C++ QCD library,” PoS LATTICE 2015
2016

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2021

Comparison of Domain Wall Fermion Multigrid Methods

Boyle, Peter, Yamaguchi, Azusa

Understand

We present a detailed comparison of several recent and new approaches to multigrid solver algorithms suitable for the solution of 5d chiral fermion actions such as Domain Wall fermions in the Shamir formulation, and also for the Partial Fraction and Continued Fraction overlap.

Our focus is on the acceleration of gauge configuration sampling, and a compact nearest neighbour stencil is required to limit the calculational cost of obtaining a coarse operator.
This necessitates the coarsening of a nearest neighbour operator to preserve sparsity in coarsened grids, unlike HDCG.
We compare the approaches of HDCR and the Multigrid algorithm and also several new hybrid schemes.

Built on

D. Richtmann, P. A. Boyle and T. Wettig, “Multigrid for Wilson Clover Fermions in Grid,” PoS LATTICE2018
Original
1904
Earlier work this paper cites.
Hestenes, Magnus R.; Stiefel, Eduard. “Methods of Conjugate Gradients for Solving Linear Systems”. Journal of Research of the National Bureau of Standards. 49 (6): 409. 1952
1952
Earlier work this paper cites.
S. C. Eisenstat, H. C. Elman, and H. C. Schultz. “Variational iterative methods for nonsymmetric systems of linear equations.” SIAM J. Numer. Anal., 20, 1983
1983
Earlier work this paper cites.
S. Duane, A. D. Kennedy, B. J. Pendleton and D. Roweth, “Hybrid Monte Carlo,” Phys. Lett. B 195
1987
Earlier work this paper cites.
D. B. Kaplan, “A Method for simulating chiral fermions on the lattice,” Phys. Lett. B 288
1992
Earlier work this paper cites.
Y. Shamir, “Chiral fermions from lattice boundaries,” Nucl. Phys. B 406
1993
Earlier work this paper cites.
S. Aoki and Y. Taniguchi, “One loop calculation in lattice QCD with domain wall quarks,” Phys. Rev. D 59
1999
Earlier work this paper cites.
R. C. Brower, M. A. Clark, D. Howarth and E. S. Weinberg, “Multigrid for Chiral Lattice Fermions: Domain Wall,” [arXiv:2004.07732 [hep-lat]]
Original
2004
Earlier work this paper cites.
M. Luscher, “Local coherence and deflation of the low quark modes in lattice QCD,” JHEP 0707
Original
2007
Earlier work this paper cites.

Similar

J. Brannick, R. C. Brower, M. A. Clark, J. C. Osborn and C. Rebbi, “Adaptive Multigrid Algorithm for the QCD Dirac-Wilson Operator,” PoS LAT 2007
Original
2007
Cited alongside, same era.
C. Allton et al
2007
Cited alongside, same era.
J. Brannick, R. C. Brower, M. A. Clark, J. C. Osborn and C. Rebbi, “Adaptive Multigrid Algorithm for Lattice QCD,” Phys. Rev. Lett. 100
Original
2008
Cited alongside, same era.
M. A. Clark, J. Brannick, R. C. Brower, S. F. McCormick, T. A. Manteuffel, J. C. Osborn and C. Rebbi, “The Removal of critical slowing down,” PoS LATTICE 2008
Original
2008
Cited alongside, same era.
R. Babich, J. Brannick, R. C. Brower, M. A. Clark, S. D. Cohen, J. C. Osborn and C. Rebbi, “The Role of multigrid algorithms for LQCD,” PoS LAT 2009
Original
2009

Then

S. D. Cohen, R. C. Brower, M. A. Clark and J. C. Osborn, “Multigrid Algorithms for Domain-Wall Fermions,” PoS LATTICE 2011
Original
2011
Later among the works it cites.
Rudy Arthur, PhD thesis, University of Edinburgh, 2012
2012
Later among the works it cites.
A. Frommer, K. Kahl, S. Krieg, B. Leder and M. Rottmann, “Adaptive Aggregation Based Domain Decomposition Multigrid for the Lattice Wilson Dirac Operator,” SIAM J. Sci. Comput. 36
Original
2014
Later among the works it cites.
A. Yamaguchi and P. Boyle, “Hierarchically deflated conjugate residual,” PoS LATTICE2016
Original
2016
Later among the works it cites.
P. A. Boyle, G. Cossu, A. Yamaguchi and A. Portelli, “Grid: A next generation data parallel C++ QCD library,” PoS LATTICE 2015
2016

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Cited alongside, same era.

J. C. Osborn, R. Babich, J. Brannick, R. C. Brower, M. A. Clark, S. D. Cohen and C. Rebbi, “Multigrid solver for clover fermions,” PoS LATTICE 2010

Original

2010

Cited alongside, same era.

R. Babich, J. Brannick, R. C. Brower, M. A. Clark, T. A. Manteuffel, S. F. McCormick, J. C. Osborn and C. Rebbi, “Adaptive multigrid algorithm for the lattice Wilson-Dirac operator,” Phys. Rev. Lett. 105

Original

2010

Cited alongside, same era.

A. Frommer, K. Kahl, S. Krieg, B. Leder and M. Rottmann, “Aggregation-based Multilevel Methods for Lattice QCD,” PoS LATTICE 2011

Original

2011

Cited alongside, same era.

P. A. Boyle, “Hierarchically deflated conjugate gradient,” arXiv:1402.2585 [hep-lat]

Original

Cited in the paper.

M. Brezina, R. Falgout, S. MacLachlan, T. Manteuffel, S. McCormick, and J. Ruge. Adaptive Smoothed Aggregation (aSA) - SIAM J.Sci.Statist.Comput.,25,1896

Cited in the paper.

A. Frommer, K. Kahl, S. Krieg, B. Leder and M. Rottmann, “An adaptive aggregation based domain decomposition multilevel method for the lattice wilson dirac operator: multilevel results,” arXiv:1307.6101 [hep-lat]

Original

Cited in the paper.

N. M. Nachtigal, S. C. Reddy, and L. N. Trefethen, ”How Fast are Nonsymmetric Matrix Iterations?” SIAM. J. Matrix Anal. Appl., 13(3), 778795

Cited in the paper.

Later among the works it cites.

E. S. Weinberg, R. C. Brower, K. Clark and A. Strelchenko, “Progress Report on Staggered Multigrid,” PoS LATTICE2016

2017

Later among the works it cites.

R. C. Brower, M. A. Clark, A. Strelchenko and E. Weinberg, “Multigrid algorithm for staggered lattice fermions,” Phys. Rev. D 97

Original

2018

Later among the works it cites.

M. A. Clark, C. Jung and C. Lehner, “Multi-Grid Lanczos,” EPJ Web Conf. 175

Original

2018

Later among the works it cites.