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Title: Multigrid algorithm for staggered lattice fermions

Abstract

Critical slowing down in Krylov methods for the Dirac operator presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. Here we formulate a multigrid algorithm for the Kogut-Susskind (or staggered) fermion discretization which has proven difficult relative to Wilson multigrid due to its first-order anti-Hermitian structure. The solution is to introduce a novel spectral transformation by the Kähler-Dirac spin structure prior to the Galerkin projection. As a result, we present numerical results for the two-dimensional, two-flavor Schwinger model; however, the general formalism is agnostic to dimension and is directly applicable to four-dimensional lattice QCD.

Authors:
 [1];  [1];  [2];  [3]
  1. Boston Univ., Boston, MA (United States)
  2. NVIDIA Corp., Santa Clara, CA (United States)
  3. Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Publication Date:
Research Org.:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1457586
Alternate Identifier(s):
OSTI ID: 1437400
Report Number(s):
FERMILAB-PUB-18-073-CD; arXiv:1801.07823
Journal ID: ISSN 2470-0010; PRVDAQ; 1650136
Grant/Contract Number:  
AC02-07CH11359; SC0015845
Resource Type:
Journal Article: Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 97; Journal Issue: 11; 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

Citation Formats

Brower, Richard C., Weinberg, Evan, Clark, M. A., and Strelchenko, Alexei. Multigrid algorithm for staggered lattice fermions. United States: N. p., 2018. Web. doi:10.1103/PhysRevD.97.114513.
Brower, Richard C., Weinberg, Evan, Clark, M. A., & Strelchenko, Alexei. Multigrid algorithm for staggered lattice fermions. United States. doi:10.1103/PhysRevD.97.114513.
Brower, Richard C., Weinberg, Evan, Clark, M. A., and Strelchenko, Alexei. Thu . "Multigrid algorithm for staggered lattice fermions". United States. doi:10.1103/PhysRevD.97.114513.
@article{osti_1457586,
title = {Multigrid algorithm for staggered lattice fermions},
author = {Brower, Richard C. and Weinberg, Evan and Clark, M. A. and Strelchenko, Alexei},
abstractNote = {Critical slowing down in Krylov methods for the Dirac operator presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. Here we formulate a multigrid algorithm for the Kogut-Susskind (or staggered) fermion discretization which has proven difficult relative to Wilson multigrid due to its first-order anti-Hermitian structure. The solution is to introduce a novel spectral transformation by the Kähler-Dirac spin structure prior to the Galerkin projection. As a result, we present numerical results for the two-dimensional, two-flavor Schwinger model; however, the general formalism is agnostic to dimension and is directly applicable to four-dimensional lattice QCD.},
doi = {10.1103/PhysRevD.97.114513},
journal = {Physical Review D},
number = 11,
volume = 97,
place = {United States},
year = {Thu Jun 28 00:00:00 EDT 2018},
month = {Thu Jun 28 00:00:00 EDT 2018}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1103/PhysRevD.97.114513

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