Related papers: A Parallel SSOR Preconditioner for Lattice QCD
We propose an efficient numerical algorithm for the solution of diffeomorphic image registration problems. We use a variational formulation constrained by a partial differential equation (PDE), where the constraints are a scalar transport…
Compatible finite element discretisations for the atmospheric equations of motion have recently attracted considerable interest. Semi-implicit timestepping methods require the repeated solution of a large saddle-point system of linear…
For several classes of mathematical models that yield linear systems, the splitting of the matrix into its Hermitian and skew Hermitian parts is naturally related to properties of the underlying model. This is particularly so for…
In this paper, we present a preconditioned variant of the generalized successive overrelaxation (GSOR) iterative method for solving a broad class of complex symmetric linear systems. We study conditions under which the spectral radius of…
Cost estimates for simulations of full QCD with n_f=2 Wilson fermions by hybrid Monte Carlo are presented. The extrapolations are based on the average number of iterations of the iterative solver within the fermionic part of the HMC…
This paper presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits the domain…
We investigate the use of half-precision floating-point numbers (FP16) in mixed-precision linear solvers for lattice QCD simulations. Since the emergence of GPUs for general-purpose, mixed-precision algorithms that combine single-precision…
Performing Bayesian inference on large spatio-temporal models requires extracting inverse elements of large sparse precision matrices for marginal variances, as well as estimating model hyperparameters. Although direct matrix factorizations…
The chromoelectric and chromomagnetic fields, created by a static gluon-quark-antiquark system, are computed in quenched SU(3) lattice QCD, in a $24^3\times 48$ lattice at $\beta=6.2$ and $a=0.07261(85) fm$. We compute the hybrid Wilson…
I review recent machine trends and algorithmic developments for dynamical lattice QCD simulations with the HMC algorithm for Wilson-type fermions. The topics include the trend toward multi-core processors and general purpose GPU (GPGPU)…
In the last few years it has been proposed a one-dimensional factorization of the fermion determinant in lattice QCD with Wilson-type fermions that leads to a block-local action of the auxiliary bosonic fields. Here we propose a…
We introduce a preconditioner for a hybridizable discontinuous Galerkin discretization of the linearized Navier-Stokes equations at high Reynolds number. The preconditioner is based on an augmented Lagrangian approach of the full…
We introduce a parallel algorithm to construct a preconditioner for solving a large, sparse linear system where the coefficient matrix is a Laplacian matrix (a.k.a., graph Laplacian). Such a linear system arises from applications such as…
We develop an implementation for a recently proposed Noisy Monte Carlo approach to the simulation of lattice QCD with dynamical fermions by incorporating the full fermion determinant directly. Our algorithm uses a quenched gauge field…
At fine lattice spacings, Markov chain Monte Carlo simulations of QCD and other gauge theories with or without fermions are plagued by slow modes that give rise to large autocorrelation times. This can lead to simulation runs that are…
We experiment with a massively parallel implementation of an algorithm for simulating the dynamics of metastable decay in kinetic Ising models. The parallel scheme is directly applicable to a wide range of stochastic cellular automata where…
We present an adaptive multigrid Dirac solver developed for Wilson clover fermions which offers order-of-magnitude reductions in solution time compared to conventional Krylov solvers. The solver incorporates even-odd preconditioning and…
The lattice Boltzmann method exhibits excellent scalability on current supercomputing systems and has thus increasingly become an alternative method for large-scale non-stationary flow simulations, reaching up to a trillion grid nodes.…
Lattice simulations of Quantum Chromodynamics (QCD) enable one to calculate the low-energy properties of the strong interaction among quarks and gluons based on the first principle. The most time-consuming part of the numerical simulations…
This paper introduces the localized sparsifying preconditioner for the pseudospectral approximations of indefinite systems on periodic structures. The work is built on top of the recently proposed sparsifying preconditioner with two major…