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Title: Multigrid for chiral lattice fermions: Domain wall

Abstract

The phenomena of critical slowing down in the iterative solution of the Dirac equation presents a major challenge to further applications of lattice field theory in the approach to the continuum solution. We propose a new multigrid approach for chiral fermions, applicable to both the 5D domain wall or 4D overlap operator. The central idea is to directly coarsen the 4D 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 2D Schwinger prototype, demonstrating near ideal multigrid scaling. The framework is designed for a natural extension to 4D lattice QCD chiral fermions, such as the Möbius, Zolotarev or Borici domain wall discretizations or directly to a rational expansion of the 4D 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 multigrid algorithm [R. C. Brower, E. Weinberg, M. A. Clark, and A. Strelchenko, Phys. Rev. D 97, 114513 (2018)].

Authors:
; ; ORCiD logo;
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC)
OSTI Identifier:
1724236
Alternate Identifier(s):
OSTI ID: 1763665
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. https://doi.org/10.1103/PhysRevD.102.094517.
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
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.
@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 = {The phenomena of critical slowing down in the iterative solution of the Dirac equation presents a major challenge to further applications of lattice field theory in the approach to the continuum solution. We propose a new multigrid approach for chiral fermions, applicable to both the 5D domain wall or 4D overlap operator. The central idea is to directly coarsen the 4D 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 2D Schwinger prototype, demonstrating near ideal multigrid scaling. The framework is designed for a natural extension to 4D lattice QCD chiral fermions, such as the Möbius, Zolotarev or Borici domain wall discretizations or directly to a rational expansion of the 4D 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 multigrid algorithm [R. C. Brower, E. Weinberg, M. A. Clark, and A. Strelchenko, Phys. Rev. D 97, 114513 (2018)].},
doi = {10.1103/PhysRevD.102.094517},
journal = {Physical Review D},
number = 9,
volume = 102,
place = {United States},
year = {2020},
month = {11}
}

Journal Article:
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https://doi.org/10.1103/PhysRevD.102.094517

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