769 research outputs found
A Parallel SSOR Preconditioner for Lattice QCD
A parallelizable SSOR preconditioning scheme for Krylov subspace iterative
solvers in lattice QCD applications involving Wilson fermions is presented. In
actual Hybrid Monte Carlo and quark propagator calculations it helps to reduce
the number of iterations by a factor of 2 compared to conventional odd-even
preconditioning. This corresponds to a gain in cpu-time of 30\% - 70\% over
odd-even preconditioning.Comment: Talk presented at LATTICE96(algorithms), 3 pages, LaTeX file, 3
epsf-files include
How to compute Green's Functions for entire Mass Trajectories within Krylov Solvers
The availability of efficient Krylov subspace solvers play a vital role for
the solution of a variety of numerical problems in computational science. Here
we consider lattice field theory. We present a new general numerical method to
compute many Green's functions for complex non-singular matrices within one
iteration process. Our procedure applies to matrices of structure , with
proportional to the unit matrix, and can be integrated within any Krylov
subspace solver. We can compute the derivatives of the solution
vector with respect to the parameter and construct the Taylor expansion
of around . We demonstrate the advantages of our method using a minimal
residual solver. Here the procedure requires intermediate vector for each
Green's function to compute. As real life example, we determine a mass
trajectory of the Wilson fermion matrix for lattice QCD. Here we find that we
can obtain Green's functions at all masses at the price of one
inversion at mass .Comment: 11 pages, 2 eps-figures, needs epsf.st
Preconditioning of Improved and ``Perfect'' Fermion Actions
We construct a locally-lexicographic SSOR preconditioner to accelerate the
parallel iterative solution of linear systems of equations for two improved
discretizations of lattice fermions: the Sheikholeslami-Wohlert scheme where a
non-constant block-diagonal term is added to the Wilson fermion matrix and
renormalization group improved actions which incorporate couplings beyond
nearest neighbors of the lattice fermion fields. In case (i) we find the block
llssor-scheme to be more effective by a factor about 2 than odd-even
preconditioned solvers in terms of convergence rates, at beta=6.0. For type
(ii) actions, we show that our preconditioner accelerates the iterative
solution of a linear system of hypercube fermions by a factor of 3 to 4.Comment: 27 pages, Latex, 17 Figures include
SESAM and TXL Results for Wilson Action--A Status Report
Results from two studies of full QCD with two flavours of dynamical Wilson
fermions are presented. At beta=5.6, the region 0.83 > m_pi/m_rho > 0.56 at
m_pia > 0.23 L^{-1} is explored. The SESAM collaboration has generated
ensembles of about 200 statistically independent configurations on a 16^3 x
32-lattice at three different kappa-values and is entering the final phase of
data analysis. The TXL simulation on a 24^3 x 40-lattice at two kappa-values
has reached half statistics and data analysis has started recently, hence most
results presented here are preliminary. The focus of this report is fourfold:
we demonstrate that algorithmic improvements like fast Krylov solvers and
parallel preconditioning recently introduced can be put into practise in full
QCD simulations, we present encouraging observations as to the critical
dynamics of the Hybrid Monte Carlo algorithm in the approach to the chiral
limit, we mention signal improvements of noisy estimator techniques for
disconnected diagrams to the pi-N sigma term, and we report on SESAM's results
for light hadron spectrum, light quark masses, and heavy quarkonia.Comment: 24 pages, tex + postscript figures, to appear in Proceedings of Int.
Workshop "Lattice QCD on Parallel Computers", University of Tsukuba, Japa
A Study of Practical Implementations of the Overlap-Dirac Operator in Four Dimensions
We study three practical implementations of the Overlap-Dirac operator in four dimensions. Two implementations are
based on different representations of as a sum over poles. One
of them is a polar decomposition and the other is an optimal fit to a ratio of
polynomials. The third one is obtained by representing using
Gegenbauer polynomials and is referred to as the fractional inverse method.
After presenting some spectral properties of the Hermitian operator
, we study its spectrum in a smooth SU(2) instanton
background with the aim of comparing the three implementations of . We
also present some results in SU(2) gauge field backgrounds generated at
on an lattice. Chiral properties have been numerically
verified.Comment: 23 pages latex with 9 postscript figures included by epsf. Some
change in referencing and one figure modifie
Dynamical overlap fermions, results with hybrid Monte-Carlo algorithm
We present first, exploratory results of a hybrid Monte-Carlo algorithm for
dynamical, n_f=2, four-dimensional QCD with overlap fermions. As expected, the
computational requirements are typically two orders of magnitude larger for the
dynamical overlap formalism than for the more conventional (Wilson or
staggered) formulations.Comment: 13 pages, 2 figure
Critical Dynamics of the Hybrid Monte Carlo Algorithm
We investigate the critical dynamics of the Hybrid Monte Carlo algorithm
approaching the chiral limit of standard Wilson fermions. Our observations are
based on time series of lengths O(5000) for a variety of observables. The
lattice sizes are 16^3 x 32 and 24^3 x 40. We work at beta=5.6, and
kappa=0.156, 0.157, 0.1575, 0.158, with 0.83 > m_pi/m_rho > 0.55. We find
surprisingly small integrated autocorrelation times for local and extended
observables. The dynamical critical exponent of the exponential
autocorrelation time is compatible with 2. We estimate the total computational
effort to scale between V^2 and V^2.25 towards the chiral limit.Comment: 3 pages, Latex with espcrc2.sty and postscript figures, Talk given at
Lattice 9
A study of chiral symmetry in quenched QCD using the Overlap-Dirac operator
We compute fermionic observables relevant to the study of chiral symmetry in
quenched QCD using the Overlap-Dirac operator for a wide range of the fermion
mass. We use analytical results to disentangle the contribution from exact zero
modes and simplify our numerical computations. Details concerning the numerical
implementation of the Overlap-Dirac operator are presented.Comment: 24 pages revtex with 5 postscript figures included by eps
Improved Quenched QCD on Large Lattices - First Results
Continuing our investigations of quenched QCD with improved fermions we have
started simulations for lattice size 32^3 x 64 at beta=6.2. We present first
results for light hadron masses at kappa=0.13520, 0.13540, and 0.13555.
Moreover we compare our initial experiences on the T3E with those for
APE/Quadrics systems.Comment: 3 pages, Latex2e, 4 figures, espcrc2, epsfig and latexsym require
Domain Wall Fermions with Exact Chiral Symmetry
We show how the standard domain wall action can be simply modified to allow
arbitrarily exact chiral symmetry at finite fifth dimensional extent. We note
that the method can be used for both quenched and dynamical calculations. We
test the method using smooth and thermalized gauge field configurations. We
also make comparisons of the performance (cost) of the domain wall operator for
spectroscopy compared to other methods such as the overlap-Dirac operator and
find both methods are comparable in cost.Comment: revtex, 37 pages, 11 color postscript figure
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