ISI Report

Algebraic Multigrid (AMG) is a widely used technique for solving large, sparse linear systems arising in various scientific and engineering applications. While AMG has shown great promise in terms of its ability to accelerate iterative solvers and handle complex geometries, its performance and scalability can be limited in certain cases. This article reviews recent developments in AMG algorithms that aim to improve its performance and scalability. We focus on two main areas: parallelization strategies and preconditioning techniques. Through the literature review and experiments, we demonstrate the effectiveness of these developments in improving the performance and scalability of AMG. Algebraic Multigrid (AMG) is a widely-used numerical technique for solving large sparse linear systems arising from many scientific and engineering applications. However, its performance and scalability can be limited due to the increasing size and complexity of modern datasets. This paper aims to explore recent developments in improving the performance and scalability of AMG, with a focus on parallel and distributed computing techniques. The research methodology includes a literature review of recent advancements in this area and a performance analysis of parallel AMG solvers. The results demonstrate the effectiveness of these techniques in improving the performance and scalability of AMG on modern datasets. Algebraic Multigrid (AMG) is a popular technique for solving linear systems arising from a wide range of applications. However, its performance and scalability can be limited when applied to large-scale problems with complex structures. In this article, we review recent advances in improving the performance and scalability of AMG methods. Specifically, we focus on parallelization techniques, adaptive algorithms, and preconditioning strategies that have been developed to enhance the efficiency and robustness of AMG solvers. We also highlight future research directions and challenges in this field. Algebraic Multigrid (AMG) is a widely used method in solving large scale linear systems. However, when it comes to high performance computing, the performance and scalability of AMG become crucial factors. In this paper, we investigate different approaches to improving the performance and scalability of AMG, including parallel computing, coarse grid selection, and preconditioning techniques. We also present experimental results that demonstrate the effectiveness of these approaches on different types of problems.