Skip to main content
U.S. Department of Energy
Office of Scientific and Technical Information

Least-squares finite element methods for quantum chromodynamics

Journal Article · · SIAM Journal on Scientific Computing
OSTI ID:957738

A significant amount of the computational time in large Monte Carlo simulations of lattice quantum chromodynamics (QCD) is spent inverting the discrete Dirac operator. Unfortunately, traditional covariant finite difference discretizations of the Dirac operator present serious challenges for standard iterative methods. For interesting physical parameters, the discretized operator is large and ill-conditioned, and has random coefficients. More recently, adaptive algebraic multigrid (AMG) methods have been shown to be effective preconditioners for Wilson's discretization of the Dirac equation. This paper presents an alternate discretization of the Dirac operator based on least-squares finite elements. The discretization is systematically developed and physical properties of the resulting matrix system are discussed. Finally, numerical experiments are presented that demonstrate the effectiveness of adaptive smoothed aggregation ({alpha}SA ) multigrid as a preconditioner for the discrete field equations resulting from applying the proposed least-squares FE formulation to a simplified test problem, the 2d Schwinger model of quantum electrodynamics.

Research Organization:
Los Alamos National Laboratory (LANL)
Sponsoring Organization:
DOE
DOE Contract Number:
AC52-06NA25396
OSTI ID:
957738
Report Number(s):
LA-UR-08-04368; LA-UR-08-4368
Journal Information:
SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing; ISSN 1064-8275; ISSN SJOCE3
Country of Publication:
United States
Language:
English