Related papers: Adaptive Multigrid Algorithm for Lattice QCD

We present an efficient MPI-parallel geometric multigrid library for quadtree (2D) or octree (3D) grids with adaptive refinement. Cartesian 2D/3D and cylindrical 2D geometries are supported, with second-order discretizations for the…

We propose a robust, adaptive coarse-grid correction scheme for matrix-free geometric multigrid targeting PDEs with strongly varying coefficients. The method combines uniform geometric coarsening of the underlying grid with heterogeneous…

With the ever-growing number of computing architectures, performance portability is an important aspect of (Lattice QCD) software. The Grid library provides a good framework for writing such code, as it thoroughly separates…

In QCD chiral symmetry is explicitly broken by quark masses, the effect of which can be described reliably by chiral perturbation theory. Effects of explicit chiral symmetry breaking by the lattice regularisation of the Dirac operator,…

A modification to the setup algorithm for the multigrid preconditioner of Wilson fermions in lattice QCD is presented. A larger basis of test vectors than that used in conventional multigrid is calculated by the smoother and truncated by…

We propose new techniques for the numerical implementation of the overlap-Dirac operator, which exploit the physical properties of the underlying theory to avoid nested algorithms. We test these procedures in the two-dimensional Schwinger…

We construct a hierarchy of lattice fermions, where the coarser lattice Dirac operator is the Schur complement of the block UL decomposition of the finer lattice operator. We show that the construction is an exact gauged renormalisation…

We present details of our implementation of the Wuppertal adaptive algebraic multigrid code DD-$\alpha$AMG on SIMD architectures, with particular emphasis on the Intel Xeon Phi processor (KNC) used in QPACE 2. As a smoother, the algorithm…

We propose new techniques to implement numerically the overlap-Dirac operator which exploit the physical properties of the underlying theory to avoid nested algorithms. We test these procedures in the two-dimensional Schwinger model and the…

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…

We present a numerical study of the properties of the Fixed Point lattice Dirac operator in the Schwinger model. We verify the theoretical bounds on the spectrum, the existence of exact zero modes with definite chirality, and the Index…

We present a modification to the setup algorithm for the multigrid preconditioner of Wilson fermions in lattice QCD. A larger number of test vectors than that used in conventional multigrid is generated by the smoother. This set of test…

Recently various new concepts for the construction of Dirac operators in lattice Quantum Chromodynamics (QCD) have been introduced. These operators satisfy the so-called Ginsparg-Wilson condition (GWC), thus obeying the Atiyah-Singer index…

Lattice QCD simulations at small lattice spacings and quark masses close to their physical values are technically challenging. In particular, the simulations can get trapped in the topological charge sectors of field space or may run into…

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…

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…

We present a multigrid based eigensolver for computing low-modes of the Hermitian Wilson Dirac operator. For the non-Hermitian case multigrid methods have already replaced conventional Krylov subspace solvers in many lattice QCD…

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…

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…

Gauge fixing is an essential step in lattice QCD calculations, particularly for studying gauge-dependent observables. Traditional iterative algorithms are computationally expensive and often suffer from critical slowing down and scaling…