Speaker
Attilio Cucchieri
(University of São Paulo)
Description
The study of Green's functions in Yang-Mills theory in
minimal Landau gauge (MLG) may offer crucial insights
for the understanding of quark confinement in quantum
chromodynamics. In MLG, the functional integral over
gauge-field configurations is restricted to the set of
transverse configurations for which the so-called
Faddeev-Popov (FP) matrix is positive definite. Thus,
this matrix should encode all the relevant (non-perturbative)
aspects of the theory, related to the color-confinement
mechanism. In particular, the inverse of the FP matrix
enters into the evaluation of several fundamental
Green's functions of the theory, such as the ghost
propagator, the ghost-gluon vertex, the Bose-ghost
propagator, etc. These Green's functions can be computed
through Monte Carlo simulations using the lattice formulation
of gauge theories. However, the numerical inversion of the
FP matrix is rather time consuming, since it is a huge (sparse)
matrix with an extremely small eigenvalue, thus requiring
the use of a parallel preconditioned conjugate-gradient (CG)
algorithm. Moreover, for each lattice configuration, this
inversion has to be done for hundreds of different kinematic
combinations. In fact, this matrix inversion is the
performance bottleneck for these numerical studies. In this
poster we present several preconditioned CG algorithms and
their implementation (through CUDA) in double and mixed
precisions using multiple GPUs. In particular, we report on
the performance of the code for Tesla and Kepler GPUs, as
well as on its weak and strong scaling for up to 32 GPUs
interconnected by InfiniBand.
Primary author
Attilio Cucchieri
(University of São Paulo)
Co-author
Tereza Mendes
(University of Sao Paulo)
