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 …

This manual describes the use of PETSc for the numerical solution of partial differential
equations and related problems on high-performance computers. The Portable, Extensible …

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

In lattice quantum chromodynamics (QCD) computations a substantial amount of work is
spent in solving discretized versions of the Dirac equation. Conventional Krylov solvers …

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 …

Algebraic multigrid methods continue to grow in robustness as effective solvers for the large
and sparse linear systems of equations that arise in many applications. Unlike geometric …

We present a new multi-level preconditioning scheme for discrete Poisson equations that
arise in various computer graphics applications such as colorization, edge-preserving …

Existing multigrid methods for cloth simulation are based on geometric multigrid. While good
results have been reported, geometric methods are problematic for unstructured grids …

In statistical modelling with Gaussian process regression, it has been shown that combining
(few) high-fidelity data with (many) low-fidelity data can enhance prediction accuracy …

Many computer graphics applications boil down to solving sparse systems of linear
equations. While the current arsenal of numerical solvers available in various specialized …