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We apply a recent proposal to speed up the Hybrid-Monte-Carlo simulation of systems with dynamical fermions to two flavour QCD with clover-improvement. The basic idea of our proposal is to split the fermion matrix into two factors with a…

High Energy Physics - Lattice · Physics 2009-11-07 M. Hasenbusch , K. Jansen

The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated…

Numerical Analysis · Mathematics 2019-06-26 Andrea Franceschini , Victor A. Paludetto Magri , Gianluca Mazzucco , Nicolò Spiezia , Carlo Janna

OpenQ$^\star$D code has been used by the RC$^\star$ collaboration for the generation of fully dynamical QCD+QED gauge configurations with C$^\star$ boundary conditions. In this talk, optimization of solvers provided with the openQ$^\star$D…

High Energy Physics - Lattice · Physics 2022-02-16 Roman Gruber , Anton Kozhevnikov , Marina Krstić Marinković , Thomas C. Schulthess , Raffaele Solcà

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)…

High Energy Physics - Lattice · Physics 2010-01-21 Ken-Ichi Ishikawa

The geometric multigrid method (GMG) is one of the most efficient solving techniques for discrete algebraic systems arising from elliptic partial differential equations. GMG utilizes a hierarchy of grids or discretizations and reduces the…

Numerical Analysis · Mathematics 2013-01-14 Chunsheng Feng , Shi Shu , Jinchao Xu , Chen-Song Zhang

We provide an alternative Fourier analysis for multigrid applied to the Poisson problem in 1D, based on explicit derivation of spectra of the iteration matrix. The new Fourier analysis has advantages over the existing one. It is easy to…

General Mathematics · Mathematics 2021-01-29 Adem Kaya

An existing hybrid MPI-OpenMP scheme is augmented with a CUDA-based fine grain parallelization approach for multidimensional distributed Fourier transforms, in a well-characterized pseudospectral fluid turbulence code. Basics of the hybrid…

Computational Physics · Physics 2018-08-07 Duane Rosenberg , Pablo D. Mininni , Raghu Reddy , Annick Pouquet

We report on our efforts to implement overlap fermions on NVIDIA GPUs using CUDA, commenting on the algorithms used, implemetation details, and the performance of our code.

High Energy Physics - Lattice · Physics 2015-11-16 Nigel Cundy , Weonjong Lee

Preconditioning is at the core of modern many-fermion Monte Carlo algorithms, such as Hybrid Monte Carlo, where the repeated solution of a linear problem involving an ill-conditioned matrix is needed. We report on a performance comparison…

High Energy Physics - Lattice · Physics 2010-08-24 Timour Ten , Joaquín E. Drut , Timo A. Lähde

We investigate implementation of lattice Quantum Chromodynamics (QCD) code on the Intel AVX-512 architecture. The most time consuming part of the numerical simulations of lattice QCD is a solver of linear equation for a large sparse matrix…

High Energy Physics - Lattice · Physics 2018-11-05 Issaku Kanamori , Hideo Matsufuru

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…

High Energy Physics - Lattice · Physics 2025-02-06 Travis Whyte , Andreas Stathopoulos , Eloy Romero

The openQ*D code for the simulation of QCD+QED with C$^\star$ boundary conditions is presented. This code is based on openQCD-1.6, from which it inherits the core features that ensure its efficiency: the locally-deflated SAP-preconditioned…

Markov Chain Monte Carlo simulations of lattice Quantum Chromodynamics (QCD) are the only known tool to investigate non-perturbatively the theory of the strong interaction and are required to perform precision tests of the Standard Model of…

A Dirac choice for the averaging kernel $C$ is implemented numerically. This improved kernel will be needed in gauge covariant multigrid computations for propagators of staggered fermions. Results for $C$ and the variational coarse grid…

High Energy Physics - Lattice · Physics 2016-08-31 Thomas Kalkreuter

Multigrid methods are well suited to large massively parallel computer architectures because they are mathematically optimal and display excellent parallelization properties. Since current architecture trends are favoring regular compute…

Numerical Analysis · Mathematics 2022-05-31 Victor A. Paludetto Magri , Robert D. Falgout , Ulrike M. Yang

We present a non-iterative solver based on the Schur complement method for sparse linear systems of special form which appear in Quantum Monte-Carlo (QMC) simulations of strongly interacting fermions on the lattice. While the number of…

Strongly Correlated Electrons · Physics 2019-01-30 Maksim Ulybyshev , Nils Kintscher , Karsten Kahl , Pavel Buividovich

We apply a recent proposal to speed up the Hybrid-Monte-Carlo simulation of systems with dynamical fermions to two flavor QCD with clover-improvement. For our smallest quark masses we see a speed-up of more than a factor of two compared…

High Energy Physics - Lattice · Physics 2009-11-07 M. Hasenbusch , K. Jansen

We develop a matrix-free Full Approximation Storage (FAS) multigrid solver based on staggered finite differences and implemented on GPU in MATLAB. To enhance performance, intermediate variables are reused, and an X-shape Multi-Color…

Numerical Analysis · Mathematics 2025-10-14 Jiale Meng , Shuqi Tang , Steven M. Wise , Zhenlin Guo

Multigrid solvers face multiple challenges on parallel computers. Two fundamental ones read as follows: Multiplicative solvers issue coarse grid solves which exhibit low concurrency and many multigrid implementations suffer from an…

Numerical Analysis · Mathematics 2020-07-02 Charles D. Murray , Tobias Weinzierl

Efficiently solving large-scale linear systems is a critical challenge in electromagnetic simulations, particularly when using the Crank-Nicolson Finite-Difference Time-Domain (CN-FDTD) method. Existing iterative solvers are commonly…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-10-24 Haoyuan Zhang , Yaqian Gao , Xinxin Zhang , Jialin Li , Runfeng Jin , Yidong Chen , Feng Zhang , Wu Yuan , Wenpeng Ma , Shan Liang , Jian Zhang , Zhonghua Lu