Algebraic multigrid theory: The symmetric case
Applied Mathematics and Computation - Second Copper Mountain conference on Multigrid methods Copper Mountain, Colorado
Iterative solution methods
An energy-minimizing interpolation for robust multigrid methods
SIAM Journal on Scientific Computing
A multigrid tutorial: second edition
A multigrid tutorial: second edition
Robustness and Scalability of Algebraic Multigrid
SIAM Journal on Scientific Computing
Parallel smoothed aggregation multigrid: aggregation strategies on massively parallel machines
Proceedings of the 2000 ACM/IEEE conference on Supercomputing
Element-Free AMGe: General Algorithms for Computing Interpolation Weights in AMG
SIAM Journal on Scientific Computing
AMGE Based on Element Agglomeration
SIAM Journal on Scientific Computing
Algebraic Multigrid Based on Element Interpolation (AMGe)
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
On Generalizing the Algebraic Multigrid Framework
SIAM Journal on Numerical Analysis
On the utilization of edge matrices in algebraic multigrid
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Large-Scale Scientific Computing
On the utilization of edge matrices in algebraic multigrid
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
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We consider the problem of splitting a symmetric positive definite (SPD) stiffness matrix A arising from finite element discretization into a sum of edge matrices thereby assuming that A is given as the sum of symmetric positive semidefinite (SPSD) element matrices. We give necessary and sufficient conditions for the existence of an exact splitting into SPSD edge matrices and address the problem of best positive (nonnegative) approximation.Based on this disassembling process we present a new concept of ``strong'' and ``weak'' connections (edges), which provides a basis for selecting the coarse-grid nodes in algebraic multigrid methods. Furthermore, we examine the utilization of computational molecules (small collections of edge matrices) for deriving interpolation rules. The reproduction of edge matrices on coarse levels offers the opportunity to combine classical coarsening algorithms with effective (energy minimizing) interpolation principles yielding a flexible and robust new variant of AMG.