Preconditioning for sparse linear systems at the dawn of the 21st century: History, current developments, and future perspectives
M Ferronato - International Scholarly Research Notices, 2012 - Wiley Online Library
Iterative methods are currently the solvers of choice for large sparse linear systems of
equations. However, it is well known that the key factor for accelerating, or even allowing for …
equations. However, it is well known that the key factor for accelerating, or even allowing for …
Exposing fine-grained parallelism in algebraic multigrid methods
Algebraic multigrid methods for large, sparse linear systems are a necessity in many
computational simulations, yet parallel algorithms for such solvers are generally …
computational simulations, yet parallel algorithms for such solvers are generally …
Spectral coarsening of geometric operators
We introduce a novel approach to measure the behavior of a geometric operator before and
after coarsening. By comparing eigenvectors of the input operator and its coarsened …
after coarsening. By comparing eigenvectors of the input operator and its coarsened …
Reducing parallel communication in algebraic multigrid through sparsification
Algebraic multigrid (AMG) is an O(n) solution process for many large sparse linear systems.
A hierarchy of progressively coarser grids which utilize complementary relaxation and …
A hierarchy of progressively coarser grids which utilize complementary relaxation and …
A root-node--based algebraic multigrid method
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 …
multigrid (AMG). AMG is a popular and effective iterative method for solving large, sparse …
A general interpolation strategy for algebraic multigrid using energy minimization
Algebraic multigrid methods solve sparse linear systems Ax=b by automatic construction of a
multilevel hierarchy. This hierarchy is defined by grid transfer operators that must accurately …
multilevel hierarchy. This hierarchy is defined by grid transfer operators that must accurately …
A matrix dependent/algebraic multigrid approach for extruded meshes with applications to ice sheet modeling
A multigrid method is proposed that combines ideas from matrix dependent multigrid for
structured grids and algebraic multigrid for unstructured grids. It targets problems where a …
structured grids and algebraic multigrid for unstructured grids. It targets problems where a …
Coarse-grid selection using simulated annealing
Multilevel techniques are efficient approaches for solving the large linear systems that arise
from discretized partial differential equations and other problems. While geometric multigrid …
from discretized partial differential equations and other problems. While geometric multigrid …
Smoothed aggregation multigrid solvers for high-order discontinuous Galerkin methods for elliptic problems
LN Olson, JB Schroder - Journal of Computational Physics, 2011 - Elsevier
We develop a smoothed aggregation-based algebraic multigrid solver for high-order
discontinuous Galerkin discretizations of the Poisson problem. Algebraic multigrid is a …
discontinuous Galerkin discretizations of the Poisson problem. Algebraic multigrid is a …
Smoothed aggregation solvers for anisotropic diffusion
JB Schroder - Numerical Linear Algebra with Applications, 2012 - Wiley Online Library
SUMMARY A smoothed aggregation‐based algebraic multigrid solver for anisotropic
diffusion problems is presented. Algebraic multigrid is a popular and effective method for …
diffusion problems is presented. Algebraic multigrid is a popular and effective method for …