Algebraic multigrid theory: The symmetric case
Applied Mathematics and Computation - Second Copper Mountain conference on Multigrid methods Copper Mountain, Colorado
Robustness and Scalability of Algebraic Multigrid
SIAM Journal on Scientific Computing
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
Symbolic methods for the element preconditioning technique
SNSC'01 Proceedings of the 2nd international conference on Symbolic and numerical scientific computation
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We are interested in the design of efficient algebraic multigrid (AMG) methods for the solution of large sparse systems of linear equations arising from finite element (FE) discretization of second-order elliptic partial differential equations (PDEs). In particular, we introduce the concept of so-called “edge matrices”, which–in the present context–are extracted from the individual element matrices. This allows for the construction of spectrally equivalent approximations of the original stiffness matrix that can be utilized in the framework of AMG. The edge matrices give rise to modify the definition of “strong” and “weak” connections (edges), which provides a basis for selecting the coarse-grid nodes in algebraic multigrid methods. Moreover, a reproduction of edge matrices on coarse levels offers the opportunity to combine classical coarsening algorithms with effective (energy minimizing) interpolation principles involving small-sized “computational molecules” (small collections of edge matrices). This yields a flexible and robust new variant of AMG, which we refer to as AMGm.