40 research outputs found
Fermions as Global Correction: the QCD Case
It is widely believed that the fermion determinant cannot be treated in
global acceptance-rejection steps of gauge link configurations that differ in a
large fraction of the links. However, for exact factorizations of the
determinant that separate the ultraviolet from the infrared modes of the Dirac
operator it is known that the latter show less variation under changes of the
gauge field compared to the former. Using a factorization based on recursive
domain decomposition allows for a hierarchical algorithm that starts with pure
gauge updates of the links within the domains and ends after a number of
filters with a global acceptance-rejection step. Ratios of determinants have to
be treated stochastically and we construct techniques to reduce the noise. We
find that the global acceptance rate is high on moderate lattice sizes and
demonstrate the effectiveness of the hierarchical filter.Comment: 36 pages, 9 figures; improved version to be published in
Comput.Phys.Commun., new results for the topological charge presented in
Figure
Adaptive Aggregation Based Domain Decomposition Multigrid for the Lattice Wilson Dirac Operator
In lattice QCD computations a substantial amount of work is spent in solving
discretized versions of the Dirac equation. Conventional Krylov solvers show
critical slowing down for large system sizes and physically interesting
parameter regions. We present a domain decomposition adaptive algebraic
multigrid method used as a precondtioner to solve the "clover improved" Wilson
discretization of the Dirac equation. This approach combines and improves two
approaches, namely domain decomposition and adaptive algebraic multigrid, that
have been used seperately in lattice QCD before. We show in extensive numerical
test conducted with a parallel production code implementation that considerable
speed-up over conventional Krylov subspace methods, domain decomposition
methods and other hierarchical approaches for realistic system sizes can be
achieved.Comment: Additional comparison to method of arXiv:1011.2775 and to
mixed-precision odd-even preconditioned BiCGStab. Results of numerical
experiments changed slightly due to more systematic use of odd-even
preconditionin
Aggregation-based Multilevel Methods for Lattice QCD
In Lattice QCD computations a substantial amount of work is spent in solving
the Dirac equation. In the recent past it has been observed that conventional
Krylov solvers tend to critically slow down for large lattices and small quark
masses. We present a Schwarz alternating procedure (SAP) multilevel method as a
solver for the Clover improved Wilson discretization of the Dirac equation.
This approach combines two components (SAP and algebraic multigrid) that have
separately been used in lattice QCD before. In combination with a bootstrap
setup procedure we show that considerable speed-up over conventional Krylov
subspace methods for realistic configurations can be achieved.Comment: Talk presented at the XXIX International Symposium on Lattice Field
Theory, July 10-16, 2011, Lake Tahoe, Californi
Perturbative versus non-perturbative decoupling of heavy quarks
We simulate a theory with heavy quarks of mass . At energies much
smaller than the heavy quarks decouple and the theory can be described by
an effective theory which is a pure gauge theory to leading order in . We
present results for the mass dependence of ratios such as . We
compute these ratios from simulations and compare them to the perturbative
prediction. The latter relies on a factorisation formula for the ratios which
is valid to leading order in .Comment: 7 pages, 3 figures, Proceedings of the 33rd International Symposium
on Lattice Field Theory, 14-18 July 2015, Kobe, Japa