Numerical methods for the QCD overlap operator: III. Nested iterations

Cundy, Nigel; Eshof, Jasper van den; Frommer, Andreas; Krieg, Stefan; Lippert, Thomas; Schäfer, Katrin

doi:10.1016/j.cpc.2004.10.005

Cited by 49 publications

(68 citation statements)

References 55 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It was observed on small lattices [73] that this relaxation leads to roughly a factor of 2 reduction in the computational cost.…”

Section: Overlap Solvermentioning

confidence: 98%

“…We employ the relaxed stopping condition outlined in Ref. [73]. This is based on the idea that, as the outer solver proceeds, the correction to the solution vector |x i −x i−1 | becomes smaller and we do not have to evaluate D(m) with too much accuracy.…”

Section: Overlap Solvermentioning

confidence: 99%

“…where i is the iteration count for the outer solver [72,73]. We employ the relaxed stopping condition outlined in Ref.…”

Section: Overlap Solvermentioning

confidence: 99%

See 2 more Smart Citations

Two-flavor QCD simulation with exact chiral symmetry

et al. 2008

View full text Add to dashboard Cite

We perform numerical simulations of lattice QCD with two flavors of dynamical overlap quarks, which have exact chiral symmetry on the lattice. While this fermion discretization is computationally demanding, we demonstrate the feasibility to simulate reasonably large and fine lattices by a careful choice of the lattice action and algorithmic improvements. Our production runs are carried out on a 16 3 × 32 lattice at a single lattice spacing around 0.12 fm. We explore the sea quark mass region down to m s /6, where m s is the physical strange quark mass, for a good control of the chiral extrapolation in future calculations of physical observables. We describe in detail our setup and algorithmic properties of the production simulations and present results for the static quark potential to fix the lattice scale and the locality of the overlap operator.

show abstract

“…It was observed on small lattices [73] that this relaxation leads to roughly a factor of 2 reduction in the computational cost.…”

Section: Overlap Solvermentioning

confidence: 98%

Section: Overlap Solvermentioning

confidence: 99%

See 1 more Smart Citation

Two-flavor QCD simulation with exact chiral symmetry

et al. 2008

View full text Add to dashboard Cite

show abstract

“…Thus arises the need of building an inversion algorithm for chiral fermions that avoids critical slowing. One method to reduce the critical slowing down is to use the preconditioned algorithms [7].In [8] the preconditioned is built upon an inaccurate approximation to the sign function, while we use as the preconditioned part the approximation of the overlap operator with the truncated overlap operator with finite N 3 dimension. Thus, in order to develop fast algorithms, we use the truncated overlap variant of domain wall fermions in 2 + 1 dimensions with the extra finite dimension N 3 .…”

Section: Development Of Algorithms In 2 Dimensionsmentioning

confidence: 99%

Fast algorithms for chiral fermions in 2 dimensions

Hyka

Osmanaj

2018

EPJ Web Conf.

View full text Add to dashboard Cite

Abstract. In lattice QCD simulations the formulation of the theory in lattice should be chiral in order that symmetry breaking happens dynamically from interactions. In order to guarantee this symmetry on the lattice one uses overlap and domain wall fermions. On the other hand high computational cost of lattice QCD simulations with overlap or domain wall fermions remains a major obstacle of research in the field of elementary particles. We have developed the preconditioned GMRESR algorithm as fast inverting algorithm for chiral fermions in U(1) lattice gauge theory. In this algorithm we used the geometric multigrid idea along the extra dimension.The main result of this work is that the preconditioned GMRESR is capable to accelerate the convergence 2 to 12 times faster than the other optimal algorithms (SHUMR) for different coupling constant and lattice 32x32. Also, in this paper we tested it for larger lattice size 64x64. From the results of simulations we can see that our algorithm is faster than SHUMR. This is a very promising result that this algorithm can be adapted also in 4 dimension.

show abstract

“…Each such product is computed through another, inner iteration using matrix-vector multiplications with Q. In this context, it is very important to be able to assess the accuracy of the computed approximation to sign(Q)b from the inner method, since one can steer the outer method so as to require less and less accurate computations of sign(Q)b, resulting in substantial savings in computational work, see [1].…”

Section: Introductionmentioning

confidence: 99%

Accurate error bounds and estimates for the sign function

Frommer¹,

Kahl²,

Lippert³

et al. 2012

Proceedings of XXIX International Symposium on Lattice Field Theory — PoS(Lattice 2011)

View full text Add to dashboard Cite

The Overlap operator fulfills the Ginsparg-Wilson relation exactly and therefore represents an optimal discretization of the QCD Dirac operator with respect to chiral symmetry. When computing propagators or in HMC simulations, where one has to invert the overlap operator using some iterative solver, one has to approxomate the action of the sign function of the (symmetrized) Wilson fermion matrix Q on a vector b in each iteration. This is usually done iteratively using a 'primary' Lanczos iteration. In this process, it is very important to have good stopping criteria which allow to reliably assess the quality of the approximation to the action of the sign function computed so far. In this work we show how to cheaply recover a secondary Lanczos process, starting at an arbitrary Lanczos vector of the primary process and how to use this secondary process to efficiently obtain computable error estimates and error bounds for the Lanczos approximations to sign(Q)b, where the sign function is approximated by the Zolotarev rational approximation.

show abstract

Numerical methods for the QCD overlap operator: III. Nested iterations

Cited by 49 publications

References 55 publications

Two-flavor QCD simulation with exact chiral symmetry

Two-flavor QCD simulation with exact chiral symmetry

Fast algorithms for chiral fermions in 2 dimensions

Accurate error bounds and estimates for the sign function

Contact Info

Product

Resources

About