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Adaptive multigrid algorithm for lattice QCD.

J Brannick1, R C Brower, M A Clark

  • 1Department of Mathematics, The Pennsylvania State University, 230 McAllister Building, University Park, Pennsylvania 16802, USA.

Physical Review Letters
|March 21, 2008
PubMed
Summary
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We developed a new multigrid solver for disordered gauge fields, crucial for quantum chromodynamics simulations. This adaptive projection method minimizes critical slowing down, improving computational efficiency.

Area of Science:

  • Computational physics
  • Quantum field theory
  • Numerical analysis

Background:

  • Simulating quantum field theories requires efficient solvers for large, sparse matrices.
  • The Dirac operator in disordered gauge fields presents significant computational challenges.
  • Existing multigrid methods often struggle with the near null space of these operators.

Purpose of the Study:

  • To introduce a novel multigrid solver optimized for the Dirac operator with disordered gauge fields.
  • To address the limitations of current solvers in preserving the near null space.
  • To enhance the computational efficiency of lattice quantum chromodynamics (LQCD) calculations.

Main Methods:

  • Development of a multigrid solver incorporating adaptive projection onto coarse grids.

Related Experiment Videos

  • Preservation of the near null space of the Dirac operator during the coarse-graining process.
  • Application to the Wilson-Dirac operator in the 2D U(1) Schwinger model.

    • Main Results:

    • The new multigrid solver demonstrates suitability for disordered gauge fields.
    • Adaptive projection effectively preserves the near null space.
    • The algorithm shows weak dependence on gauge coupling and minimal critical slowing down in the chiral limit.

    Conclusions:

    • The proposed multigrid solver offers a significant improvement for lattice gauge theory simulations.
    • Adaptive projection is a key technique for handling the near null space problem.
    • This method provides a more efficient path towards unquenched LQCD calculations.