Related papers: Implementation of the conjugate gradient algorithm…
The Preconditioned Conjugate Gradient (PCG) method is widely used for solving linear systems of equations with sparse matrices. A recent version of PCG, Pipelined PCG, eliminates the dependencies in the computations of the PCG algorithm so…
Structured Cartesian grids are a fundamental component in numerical simulations. Although these grids facilitate straightforward discretization schemes, their na\"{i}ve use in sparse domains leads to excessive memory overhead and…
Programming modern high-performance computing systems is challenging due to the need to efficiently program GPUs and accelerators and to handle data movement between nodes. The C++ language has been continuously enhanced in recent years…
The pervasive adoption of Deep Learning (DL) and Graph Processing (GP) makes it a de facto requirement to build large-scale clusters of heterogeneous accelerators including GPUs and FPGAs. The OpenCL programming framework can be used on the…
The rise of exascale supercomputers has fueled competition among GPU vendors, driving lattice QCD developers to write code that supports multiple APIs. Moreover, new developments in algorithms and physics research require frequent updates…
Heterogeneous systems are becoming more common on High Performance Computing (HPC) systems. Even using tools like CUDA and OpenCL it is a non-trivial task to obtain optimal performance on the GPU. Approaches to simplifying this task include…
One of the great triumphs in the history of numerical methods was the discovery of the Conjugate Gradient (CG) algorithm. It could solve a symmetric positive-definite system of linear equations of dimension N in exactly N steps. As many…
Current PC processors are equipped with vector processing units and have other advanced features that can be used to accelerate lattice QCD programs. Clusters of PCs with a high-bandwidth network thus become powerful and cost-effective…
A portable implementation of elaborated algorithm is important to use variety of architectures in HPC applications. In this work we implement and benchmark an algebraic multi-grid solver for Lattice QCD on three different architectures,…
Spectral clustering is one of the most popular graph clustering algorithms, which achieves the best performance for many scientific and engineering applications. However, existing implementations in commonly used software platforms such as…
In recent years the computational capacity of single Field Programmable Gate Arrays (FPGA) devices as well as their versatility has increased significantly. Adding to that the High Level Synthesis frameworks allowing to program such…
We review the architecture of massively parallel machines used for lattice QCD simulations and present benchmarks for the performance of popular algorithms on these platforms. We cover commercial supercomputers, PC clusters, and…
We analyze the convergence of the Conjugate Gradient (CG) method in exact arithmetic, when the coefficient matrix $A$ is symmetric positive semidefinite and the system is consistent. To do so, we diagonalize $A$ and decompose the algorithm…
The presence of GPU from different vendors demands the Lattice QCD codes to support multiple architectures. To this end, Open Computing Language (OpenCL) is one of the viable frameworks for writing a portable code. It is of interest to find…
An efficient method, preconditioned conjugate gradient method with a filtering function (PCG-F), is proposed for solving iteratively the Dirac equation in 3D lattice space for nuclear systems. The filtering function is adopted to avoid the…
Solving discretized versions of the Dirac equation represents a large share of execution time in lattice Quantum Chromodynamics (QCD) simulations. Many high-performance computing (HPC) clusters use graphics processing units (GPUs) to offer…
This paper presents distributed adaptive algorithms based on the conjugate gradient (CG) method for distributed networks. Both incremental and diffusion adaptive solutions are all considered. The distributed conventional (CG) and modified…
We describe the GPU implementation of shifted or multimass iterative solvers for sparse linear systems of the sort encountered in lattice gauge theory. We provide a generic tool that can be used by those without GPU programming experience…
We consider three mathematically equivalent variants of the conjugate gradient (CG) algorithm and how they perform in finite precision arithmetic. It was shown in [{\em Behavior of slightly perturbed Lanczos and conjugate-gradient…
The paper presents AMGCL -- an opensource C++ library implementing the algebraic multigrid method (AMG) for solution of large sparse linear systems of equations, usually arising from discretization of partial differential equations on an…