Adaptive Multigrid Algorithm for the Lattice Wilson-Dirac Operator

Journal Article · Fri Nov 12 04:00:00 EST 2010 · Physical Review Letters

DOI:https://doi.org/10.1103/PHYSREVLETT.105.201602· OSTI ID:21541691

Babich, R; Brower, R C; Rebbi, C ^[1]; Brannick, J ^[2]; Clark, M A ^[3]; Manteuffel, T A; McCormick, S F ^[4]; Osborn, J C ^[5]

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1. Center for Computational Science, Boston University, 3 Cummington Street, Boston, Massachusetts 02215 (United States)
2. Department of Mathematics, The Pennsylvania State University, 230 McAllister Building, University Park, Pennsylvania 16802 (United States)
3. Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138 (United States)
4. Department of Applied Mathematics, Campus Box 526, University of Colorado at Boulder, Boulder, Colorado 80309 (United States)
5. Argonne Leadership Computing Facility, Argonne National Laboratory, Argonne, Illinois 60439 (United States)

We present an adaptive multigrid solver for application to the non-Hermitian Wilson-Dirac system of QCD. The key components leading to the success of our proposed algorithm are the use of an adaptive projection onto coarse grids that preserves the near null space of the system matrix together with a simplified form of the correction based on the so-called {gamma}{sub 5}-Hermitian symmetry of the Dirac operator. We demonstrate that the algorithm nearly eliminates critical slowing down in the chiral limit and that it has weak dependence on the lattice volume.

• OSTI ID: 21541691
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 20 Vol. 105; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGORITHMS
CHIRALITY
CORRECTIONS
DIRAC OPERATORS
FIELD THEORIES
HERMITIAN MATRIX
MATHEMATICAL LOGIC
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATRICES
PARTICLE PROPERTIES
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
SLOWING-DOWN
SPACE
SYMMETRY