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Title: Spectral Element Agglomerate AMGe

Conference ·

The purpose of this note is to describe an algorithm resulting from the uniting of two ideas introduced and applied elsewhere. For many problems, AMG has always been difficult due to complexities whose natures are difficult to discern from the entries of matrix A alone. Element-based interpolation has been shown to be an effective method for some of these problems, but it requires access to the element matrices on all levels. One way to obtain these has been to perform element agglomeration to form coarse elements, but in complicated situations defining the coarse degrees of freedom (dofs) is not easy. The spectral approach to coarse dof selection is very attractive due to its elegance and simplicity. The algorithm presented here combines the robustness of element interpolation, the ease of coarsening by element agglomeration, and the simplicity of defining coarse dofs through the spectral approach. As demonstrated in the numerical results, the method does yield a reasonable solver for the problems described. It can, however, be an expensive method due to the number and cost of the local, small dense linear algebra problems; making it a generally competitive method remains an area for further research.

Research Organization:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Organization:
US Department of Energy (US)
DOE Contract Number:
W-7405-ENG-48
OSTI ID:
15016350
Report Number(s):
UCRL-PROC-212439; TRN: US200513%%247
Resource Relation:
Journal Volume: 55; Conference: Presented at: 16th International Conference on Domain Decomposition Methods, New York, NY (US), 01/12/2005--01/15/2005; Other Information: PBD: 20 May 2005
Country of Publication:
United States
Language:
English

References (8)

Convergence of algebraic multigrid based on smoothed aggregation journal May 2001
Sparse matrix element topology with application to AMG(e) and preconditioning journal January 2002
AMGE Based on Element Agglomeration journal January 2001
Adaptive Smoothed Aggregation ($\alpha$SA) journal January 2004
Spectral AMGe ($\rho$AMGe) journal January 2003
Generalized Aggregation Multilevel solver journal December 1997
Algebraic Multigrid Based on Element Interpolation (AMGe) journal January 2001
Adaptive Algebraic Multigrid journal January 2006

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