Related papers: Parallel Performance of Algebraic Multigrid Domain…

In distributed optimization and federated learning, asynchronous alternating direction method of multipliers (ADMM) serves as an attractive option for large-scale optimization, data privacy, straggler nodes and variety of objective…

Laplacian matrices of graphs arise in large-scale computational applications such as machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits; and elliptic…

Isogeometric analysis (IgA) offers enhanced approximation capabilities for the discretization of elliptic boundary-value problems, yet it results in large, sparse, and increasingly ill-conditioned linear systems due to higher…

The implementation of a vast majority of machine learning (ML) algorithms boils down to solving a numerical optimization problem. In this context, Stochastic Gradient Descent (SGD) methods have long proven to provide good results, both in…

Efficient numerical solvers for sparse linear systems are crucial in science and engineering. One of the fastest methods for solving large-scale sparse linear systems is algebraic multigrid (AMG). The main challenge in the construction of…

In this work, a new parallel dual-grid multiscale approach for CFD-DEM couplings is investigated. Dual- grid multiscale CFD-DEM couplings have been recently developed and successfully adopted in different applications still, an efficient…

We describe main issues and design principles of an efficient implementation, tailored to recent generations of Nvidia Graphics Processing Units (GPUs), of an Algebraic Multigrid (AMG) preconditioner previously proposed by one of the…

Topology optimization for large scale problems continues to be a computational challenge. Several works exist in the literature to address this topic, and all make use of iterative solvers to handle the linear system arising from the Finite…

Algebraic multigrid (AMG) solvers and preconditioners are some of the fastest numerical methods to solve linear systems, particularly in a parallel environment, scaling to hundreds of thousands of cores. Most AMG methods and theory assume a…

With the increase in the amount of data and the expansion of model scale, distributed parallel training becomes an important and successful technique to address the optimization challenges. Nevertheless, although distributed stochastic…

We design and implement a parallel algebraic multigrid method for isotropic graph Laplacian problems on multicore Graphical Processing Units (GPUs). The proposed AMG method is based on the aggregation framework. The setup phase of the…

Stochastic Gradient Descent (SGD) is the standard numerical method used to solve the core optimization problem for the vast majority of machine learning (ML) algorithms. In the context of large scale learning, as utilized by many Big Data…

This paper proposes a mode multigrid (MMG) method, and applies it to accelerate the convergence of the steady state flow on unstructured grids. The dynamic mode decomposition (DMD) technique is used to analyze the convergence process of…

Algebraic multigrid (AMG) methods are powerful solvers with linear or near-linear computational complexity for certain classes of linear systems, Ax=b. Broadening the scope of problems that AMG can effectively solve requires the development…

Distributed-memory implementations of numerical optimization algorithm, such as stochastic gradient descent (SGD), require interprocessor communication at every iteration of the algorithm. On modern distributed-memory clusters where…

In this paper, we propose a novel distributed alternating direction method of multipliers (ADMM) algorithm with synergetic communication and computation, called SCCD-ADMM, to reduce the total communication and computation cost of the…

The efficient solution of sparse, linear systems resulting from the discretization of partial differential equations is crucial to the performance of many physics-based simulations. The algorithmic optimality of multilevel approaches for…

Laplacian matrices of graphs arise in large-scale computational applications such as semi-supervised machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits;…

Distributed computing has been widely applied in distributed edge networks for reducing the processing burden of high-dimensional data centralization, where a high-dimensional computational task is decomposed into multiple low-dimensional…

Stochastic Gradient Descent (SGD) is the key learning algorithm for many machine learning tasks. Because of its computational costs, there is a growing interest in accelerating SGD on HPC resources like GPU clusters. However, the…