Multigrid for chiral lattice fermions: Domain wall

Brower, Richard C.; Clark, M. A.; Weinberg, Evan; Howarth, Dean

doi:10.1103/PhysRevD.102.094517

Title: Multigrid for chiral lattice fermions: Domain wall

Abstract

Critical slowing down for the Krylov Dirac solver presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. We propose a new multi-grid approach for chiral fermions, applicable to both the 5-d domain wall or 4-d Overlap operator. The central idea is to directly coarsen the 4-d Wilson kernel, giving an effective domain wall or overlap operator on each level. We provide here an explicit construction for the Shamir domain wall formulation with numerical tests for the 2-d Schwinger prototype, demonstrating near ideal multi-grid scaling. The framework is designed for a natural extension to 4-d lattice QCD chiral fermions, such as the Möbius, Zolotarev or Borici domain wall discretizations or directly to a rational expansion of the 4-d Overlap operator. For the Shamir operator, the effective overlap operator is isolated by the use of a Pauli-Villars preconditioner in the spirit of the Kähler-Dirac spectral map used in a recent staggered MG algorithm [1].

Authors:

Brower, Richard C.; Clark, M. A.;

; Howarth, Dean

Publication Date:: Tue Nov 24 00:00:00 EST 2020

Research Org.:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); Boston Univ., MA (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC)

OSTI Identifier:: 1724236

Alternate Identifier(s):: OSTI ID: 1763665; OSTI ID: 1833400

Grant/Contract Number:: SC0015845; 17-SC-20-SC; AC02-05CH11231

Resource Type:: Published Article

Journal Name:: Physical Review. D.

Additional Journal Information:: Journal Name: Physical Review. D. Journal Volume: 102 Journal Issue: 9; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Lattice field theory; lattice gauge theory; lower-dimensional field theories; hybrid Monte Carlo algorithm; lattice QCD

Citation Formats


                    Brower, Richard C., Clark, M. A., Weinberg, Evan, and Howarth, Dean. Multigrid for chiral lattice fermions: Domain wall.  United States: N. p., 2020. 
Web.  doi:10.1103/PhysRevD.102.094517.

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                    Brower, Richard C., Clark, M. A., Weinberg, Evan, & Howarth, Dean. Multigrid for chiral lattice fermions: Domain wall.  United States.  https://doi.org/10.1103/PhysRevD.102.094517

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                    Brower, Richard C., Clark, M. A., Weinberg, Evan, and Howarth, Dean. Tue .  
"Multigrid for chiral lattice fermions: Domain wall".  United States.  https://doi.org/10.1103/PhysRevD.102.094517.

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@article{osti_1724236,

  title        = {Multigrid for chiral lattice fermions: Domain wall},

  author       = {Brower, Richard C. and Clark, M. A. and Weinberg, Evan and Howarth, Dean},

  abstractNote = {Critical slowing down for the Krylov Dirac solver presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. We propose a new multi-grid approach for chiral fermions, applicable to both the 5-d domain wall or 4-d Overlap operator. The central idea is to directly coarsen the 4-d Wilson kernel, giving an effective domain wall or overlap operator on each level. We provide here an explicit construction for the Shamir domain wall formulation with numerical tests for the 2-d Schwinger prototype, demonstrating near ideal multi-grid scaling. The framework is designed for a natural extension to 4-d lattice QCD chiral fermions, such as the Möbius, Zolotarev or Borici domain wall discretizations or directly to a rational expansion of the 4-d Overlap operator. For the Shamir operator, the effective overlap operator is isolated by the use of a Pauli-Villars preconditioner in the spirit of the Kähler-Dirac spectral map used in a recent staggered MG algorithm [1].},

  doi          = {10.1103/PhysRevD.102.094517},

  journal      = {Physical Review. D.},

  number       = 9,

  volume       = 102,

  place        = {United States},

  year         = {Tue Nov 24 00:00:00 EST 2020},

  month        = {Tue Nov 24 00:00:00 EST 2020}

}

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Title: Multigrid for chiral lattice fermions: Domain wall

Abstract

Citation Formats

Multigrid preconditioning for the overlap operator in lattice QCD journal, May 2015

Critical amplitudes in two-dimensional theories journal, January 1997

Möbius Fermions: Improved Domain Wall Chiral Fermions journal, March 2005

Anomalies and fermion zero modes on strings and domain walls journal, January 1985

Multigrid algorithm for staggered lattice fermions journal, June 2018

The renormalization group: Critical phenomena and the Kondo problem journal, October 1975

Optimal Lattice Domain-Wall Fermions journal, February 2003

Matrix Computations book, February 2013

Confinement of quarks journal, October 1974

Projective multigrid for Wilson fermions journal, December 1991

Adaptive Multigrid Algorithm for the Lattice Wilson-Dirac Operator journal, November 2010

Adaptive Multigrid Algorithm for Lattice QCD journal, January 2008

The Dirac-Kähler equation and fermions on the lattice journal, December 1982

New domain-wall fermion actions journal, August 2000

Reducing Complexity in Parallel Algebraic Multigrid Preconditioners journal, January 2006

Truncated overlap fermions journal, April 2000

Multigrid Algorithms for Domain-Wall Fermions conference, July 2012

Equivalence of Dirac-Kähler and staggered lattice fermions in two dimensions journal, August 1988

A method for simulating chiral fermions on the lattice journal, August 1992

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Parallel Implementation and Practical Use of Sparse Approximate Inverse Preconditioners with a Priori Sparsity Patterns journal, February 2001

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A remnant of chiral symmetry on the lattice journal, May 1982

Hamiltonian formulation of Wilson's lattice gauge theories journal, January 1975

Low energy effective action of domain-wall fermion and the Ginsparg-Wilson relation journal, April 2000

Hierarchically deflated conjugate residua conference, March 2017

Gauge Invariance and Mass. II journal, December 1962

Möbius Fermions journal, March 2006

Theoretical Foundation for the Index Theorem on the Lattice with Staggered Fermions journal, April 2010

Multigrid inversion of the staggered fermion matrix journal, May 1991

Chiral symmetry restoration in the Schwinger model with domain wall fermions journal, February 1998

Comparison of Chiral Fermion Methods conference, December 2005

Non-Abelian projective multigrid for lattice gauge theory journal, March 1991

Locality of optimal lattice domain-wall fermions journal, January 2003

Vectorlike gauge theories with almost massless fermions on the lattice journal, May 1998

Convergence analysis of Krylov subspace methods: Convergence analysis of Krylov subspace methods journal, December 2004

Exact chiral symmetry for domain wall fermions with finite Ls journal, March 2001

Multigrid preconditioning for the overlap operator in lattice QCD
journal, May 2015

Critical amplitudes in two-dimensional theories
journal, January 1997

Möbius Fermions: Improved Domain Wall Chiral Fermions
journal, March 2005

Anomalies and fermion zero modes on strings and domain walls
journal, January 1985

Multigrid algorithm for staggered lattice fermions
journal, June 2018

The renormalization group: Critical phenomena and the Kondo problem
journal, October 1975

Optimal Lattice Domain-Wall Fermions
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Matrix Computations
book, February 2013

Confinement of quarks
journal, October 1974

Projective multigrid for Wilson fermions
journal, December 1991

Adaptive Multigrid Algorithm for the Lattice Wilson-Dirac Operator
journal, November 2010

Adaptive Multigrid Algorithm for Lattice QCD
journal, January 2008

The Dirac-Kähler equation and fermions on the lattice
journal, December 1982

New domain-wall fermion actions
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Reducing Complexity in Parallel Algebraic Multigrid Preconditioners
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Truncated overlap fermions
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Multigrid Algorithms for Domain-Wall Fermions
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A method for simulating chiral fermions on the lattice
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