Spectral Element Agglomerate AMGe
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
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