This paper provides an overview of AMG methods for solving large-scale systems of
equations, such as those from discretizations of partial differential equations. AMG is often …

Laplacian matrices of graphs arise in large-scale computational applications such as
semisupervised machine learning; spectral clustering of images, genetic data, and web …

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 …

Linear solvers for reservoir simulation applications are the objective of this review.
Specifically, we focus on techniques for Fully Implicit (FI) solution methods, in which the set …

This paper studies the optimality of the restriction and prolongation operators in the
geometric multigrid method (GMG). GMG is used in solving discretized partial differential …

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 …

This is the official user guide for MUELU multigrid library in Trilinos version 12.13 (Dev). This
guide provides an overview of MUELU, its capabilities, and instructions for new users who …

Algebraic multigrid (AMG) is often an effective solver for symmetric positive definite (SPD)
linear systems resulting from the discretization of general elliptic PDEs or the spatial …

This is the official user guide for MUELU multigrid library in Trilinos version 11.12. This guide
provides an overview of MUELU, its capabilities, and instructions for new users who want to …

This paper provides a unified and detailed presentation of root-node--style algebraic
multigrid (AMG). AMG is a popular and effective iterative method for solving large, sparse …