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Related papers: The role of multigrid algorithms for LQCD

200 papers

I review the lattice formulations of vector-like gauge theories (e.g. QCD) with domain-wall/overlap fermions, and discuss how to optimize the chiral symmetry for any finite $ N_s $ (sites in the fifth dimension). In this formulation, quark…

High Energy Physics - Lattice · Physics 2011-02-16 Ting-Wai Chiu

Similarly to the interaction lagrangian, the possible boundary conditions in quantum field theories on space-time manifolds with boundaries are strongly constrained by the symmetry and scaling properties of the theory. Based on this general…

High Energy Physics - Lattice · Physics 2009-11-11 Martin Lüscher

The simulation of lattice QCD on massively parallel computers stimulated the development of scalable algorithms for the solution of sparse linear systems. We tackle the problem of the Wilson-Dirac operator inversion by combining a Schwarz…

High Energy Physics - Lattice · Physics 2012-04-25 Andreas Frommer , Andrea Nobile , Paul Zingler

New exact upper and lower bounds are derived on the spectrum of the square of the hermitian Wilson Dirac operator. It is hoped that the derivations and the results will be of help in the search for ways to reduce the cost of simulations…

High Energy Physics - Lattice · Physics 2009-07-09 H. Neuberger

In lattice QCD it is possible, in principle, to determine the parameters in the effective chiral lagrangian (including weak interaction couplings) by performing numerical simulations in the $\epsilon$--regime, i.e. at quark masses where the…

High Energy Physics - Lattice · Physics 2011-07-19 L. Giusti , C. Hoelbling , M. Lüscher , H. Wittig

The Adaptive Aggregation-based Domain Decomposition Multigrid method (arXiv:1303.1377) is extended for two degenerate flavors of twisted mass fermions. By fine-tuning the parameters we achieve a speed-up of the order of hundred times…

High Energy Physics - Lattice · Physics 2016-12-21 Constantia Alexandrou , Simone Bacchio , Jacob Finkenrath , Andreas Frommer , Karsten Kahl , Matthias Rottmann

The past decade has witnessed a dramatic acceleration of lattice quantum chromodynamics calculations in nuclear and particle physics. This has been due to both significant progress in accelerating the iterative linear solvers using…

High Energy Physics - Lattice · Physics 2016-12-26 M. A. Clark , Bálint Joó , Alexei Strelchenko , Michael Cheng , Arjun Gambhir , Richard Brower

Numerical simulations of quantum chromodynamics (QCD) on a lattice require the frequent solution of linear systems of equations with large, sparse and typically ill-conditioned matrices. Algebraic multigrid methods are meanwhile the…

Numerical Analysis · Mathematics 2023-03-28 Jesus Espinoza-Valverde , Andreas Frommer , Gustavo Ramirez-Hidalgo , Matthias Rottmann

As computing resources are limited, choosing the parameters for a full Lattice QCD simulation always amounts to a compromise between the competing objectives of a lattice spacing as small, quarks as light, and a volume as large as possible.…

High Energy Physics - Lattice · Physics 2009-11-11 B. Orth , Th. Lippert , K. Schilling

Critical slowing down in Krylov methods for the Dirac operator presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. Here we formulate a multi-grid algorithm for the Kogut-Susskind…

High Energy Physics - Lattice · Physics 2018-07-04 Richard C. Brower , M. A. Clark , Alexei Strelchenko , Evan Weinberg

Application of multigrid solvers in shifted linear systems is studied. We focus on accelerating the rational approximation needed for simulating single flavor operators. This is particularly useful, in the case of twisted mass fermions for…

High Energy Physics - Lattice · Physics 2019-02-20 Constantia Alexandrou , Simone Bacchio , Jacob Finkenrath

The Overlap-Dirac operator provides a lattice regularization of massless vector gauge theories with an exact chiral symmetry. Practical implementations of this operator and recent results in quenched QCD using this Overlap-Dirac operator…

High Energy Physics - Lattice · Physics 2007-05-23 Robert G. Edwards , Urs M. Heller , Rajamani Narayanan

The spectral properties of the Wilson-Dirac operator in 2-dimensional QED responsible for the appearance of exceptional configurations in quenched simulations are studied in detail. The mass singularity structure of the quenched functional…

High Energy Physics - Lattice · Physics 2009-10-30 W. Bardeen , A. Duncan , E. Eichten , H. Thacker

We discuss a Lattice QCD mixed action investigation employing Wilson maximally twisted mass sea and overlap valence fermions. Using four values of the lattice spacing, we demonstrate that the overlap Dirac operator assumes a point-like…

High Energy Physics - Lattice · Physics 2013-01-15 Krzysztof Cichy , Vincent Drach , Elena Garcia-Ramos , Gregorio Herdoiza , Karl Jansen

Eigenvalues of the Hermitian Wilson-Dirac operator are of special interest in several lattice QCD simulations, e.g., for noise reduction when evaluating all-to-all propagators. In this paper we present a Davidson-type eigensolver that…

High Energy Physics - Lattice · Physics 2020-10-28 Andreas Frommer , Karsten Kahl , Francesco Knechtli , Matthias Rottmann , Artur Strebel , Ian Zwaan

We perform hybrid Monte Carlo simulation of (2+1+1)-flavors lattice QCD with the optimal domain-wall fermion (which has the effective 4D Dirac operator exactly equal to the Zolotarev optimal rational approximation of the overlap Dirac…

High Energy Physics - Lattice · Physics 2017-02-09 Yu-Chih Chen , Ting-Wai Chiu

I review the theoretical foundations, properties as well as the simulation results obtained so far of a variant of the Wilson lattice QCD formulation: Wilson twisted mass lattice QCD. Emphasis is put on the discretization errors and on the…

High Energy Physics - Lattice · Physics 2008-05-19 A. Shindler

We discuss how the peculiar properties of maximally twisted Wilson fermions can be exploited to set up a consistent LQCD computational scheme in which the CP-conserving matrix elements of the $\Delta S =1,2$ effective weak Hamiltonian can…

High Energy Physics - Lattice · Physics 2016-09-01 Roberto Frezzotti , Giancarlo Rossi

We simulate Quantum Chromodynamics (QCD) in four Euclidean dimensions with two (degenerate mass) flavors of dynamical quarks. The Dirac operator we use is the so-called chirally improved Dirac operator. We discuss the algorithm used for the…

High Energy Physics - Lattice · Physics 2007-05-23 C. B. Lang , Pushan Majumdar , Wolfgang Ortner

In this paper we discuss how the peculiar properties of twisted lattice QCD at maximal twist can be employed to set up a consistent computational scheme in which, despite the explicit breaking of chiral symmetry induced by the presence of…

High Energy Physics - Lattice · Physics 2010-02-03 R. Frezzotti , G. C. Rossi