BoomerAMG: a parallel algebraic multigrid solver and preconditioner
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
hypre: A Library of High Performance Preconditioners
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Flow Field Clustering via Algebraic Multigrid
VIS '04 Proceedings of the conference on Visualization '04
Variations on algebraic recursive multilevel solvers (ARMS) for the solution of CFD problems
Applied Numerical Mathematics
Conceptual interfaces in hypre
Future Generation Computer Systems
An Introduction to Algebraic Multigrid
Computing in Science and Engineering
Journal of Computational and Applied Mathematics
Compatible coarsening in the multigraph algorithm
Advances in Engineering Software
Relaxed RS0 or CLJP coarsening strategy for parallel AMG
Parallel Computing
Precursor simulations in spreading using a multi-mesh adaptive finite element method
Journal of Computational Physics
Applied Numerical Mathematics
Large-Scale Scientific Computing
Journal of Scientific Computing
Conceptual interfaces in hypre
Future Generation Computer Systems
Estimating the Laplace-Beltrami operator by restricting 3D functions
SGP '09 Proceedings of the Symposium on Geometry Processing
Convergence analysis of multigrid methods with residual scaling techniques
Journal of Computational and Applied Mathematics
A Comparison of Two-Level Preconditioners Based on Multigrid and Deflation
SIAM Journal on Matrix Analysis and Applications
Algebraic Multigrid for Linear Systems Obtained by Explicit Element Reduction
SIAM Journal on Scientific Computing
On the utilization of edge matrices in algebraic multigrid
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Algebraic multigrid solver on clusters of CPUs and GPUs
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2
Semi-automatic sparse preconditioners for high-order finite element methods on non-uniform meshes
Journal of Computational Physics
An Algebraic Multigrid Method with Guaranteed Convergence Rate
SIAM Journal on Scientific Computing
Hi-index | 0.01 |
We introduce AMGe, an algebraic multigrid method for solving the discrete equations that arise in Ritz-type finite element methods for partial differential equations. Assuming access to the element stiffness matrices, we have that AMGe is based on the use of two local measures, which are derived from global measures that appear in existing multigrid theory. These new measures are used to determine local representations of algebraically "smooth" error components that provide the basis for constructing effective interpolation and, hence, the coarsening process for AMG. Here, we focus on the interpolation process; choice of the coarse "grids" based on these measures is the subject of current research. We develop a theoretical foundation for AMGe and present numerical results that demonstrate the efficacy of the method.