Related papers: Multigrid Solver on Fugaku
Multigrid preconditioners and solvers for the indefinite Helmholtz equation suffer from non-stability of the stationary smoothers due to the indefinite spectrum of the operator. In this paper we explore GMRES as a replacement for the…
We present results of the implementation of one MILC lattice QCD application-simulation with dynamical clover fermions using the hybrid-molecular dynamics R algorithm-on the Cell Broadband Engine processor. Fifty-four individual…
As integrated circuits become increasingly complex, the demand for efficient and accurate simulation solvers continues to rise. Traditional solvers often struggle with large-scale sparse systems, leading to prolonged simulation times and…
A multigrid scheme is proposed for the pressure equation of the incompressible unsteady fluid flow equations, allowing efficient implementation on clusters of modern CPUs, many integrated core devices (MICs), and graphics processing units…
In this work, we benchmark and discuss the performance of the scalable methods for the Poisson problem which are used widely in practice: the fast Fourier transform (FFT), the fast multipole method (FMM), the geometric multigrid (GMG), and…
Lattice QCD calculations require significant computational effort, with the dominant fraction of resources typically spent in the numerical inversion of the Dirac operator. One of the simplest methods to solve such large and sparse linear…
Many subsurface engineering applications involve tight-coupling between fluid flow, solid deformation, fracturing, and similar processes. To better understand the complex interplay of different governing equations, and therefore design…
The paper proposes a combination of the subdomain deflation method and local algebraic multigrid as a scalable distributed memory preconditioner that is able to solve large linear systems of equations. The implementation of the algorithm is…
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…
The development of the A64FX processor by Fujitsu has been a massive innovation in vectorized processors and led to Fugaku: the current world's fastest supercomputer. We use a variety of tools to analyze the behavior and performance of…
In the present paper we concentrate on an important issue in constructing a good multigrid solver: the choice of an efficient smoother. We will introduce all-at-once multigrid solvers for optimal control problems which show robust…
This paper introduces a novel geometric multigrid solver for unstructured curved surfaces. Multigrid methods are highly efficient iterative methods for solving systems of linear equations. Despite the success in solving problems defined on…
This article presents updates to lifex [Africa, SoftwareX (2022)], a C++ library for high-performance finite element simulations of multiphysics, multiscale and multidomain problems. In this release, we introduce an additional intergrid…
We demonstrate that gauge-equivariant pooling and unpooling layers can perform as well as traditional restriction and prolongation layers in multigrid preconditioner models for lattice QCD. These layers introduce a gauge degree of freedom…
Ookami is a computer technology testbed supported by the United States National Science Foundation. It provides researchers with access to the A64FX processor developed by Fujitsu in collaboration with RIK{\Xi}N for the Japanese path to…
Here we present the cuLGT code for gauge fixing in lattice gauge field theories with graphic processing units (GPUs). Implementations for SU(3) Coulomb, Landau and maximally Abelian gauge fixing are available and the overrelaxation,…
The QCDSP machine at Columbia University has grown to 2,048 nodes achieving a peak speed of 100 Gigaflops. Software for quenched and Hybrid Monte Carlo (HMC) evolution schemes has been developed for staggered fermions, with support for…
Immersed boundary methods (IBMs) facilitate the simulation of flows around stationary, moving, and deforming bodies on Cartesian grids. However, extending these simulations to the large grid sizes required for realistic flow problems…
This paper presents the design, implementation, and performance analysis of a parallel and GPU-accelerated Poisson solver based on the Preconditioned Bi-Conjugate Gradient Stabilized (Bi-CGSTAB) method. The implementation utilizes the MPI…
In this work, we present the GPU implementation of the overrelaxation and steepest descent method with Fourier acceleration methods for Laudau and Coulomb gauge fixing using CUDA for SU(N) with N>2. A multi-GPU implementation of the…