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Three-level BDDC in three dimensions
Tu, Xuemin
Tu, Xuemin
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Abstract
Balancing domain decomposition by constraints (BDDC) methods are nonoverlapping iterative substructuring domain decomposition methods for the solution of large sparse linear algebraic systems arising from the discretization of elliptic boundary value problems. Their coarse problems are given in terms of a small number of continuity constraints for each subdomain, which are enforced across the interface. The coarse problem matrix is generated and factored by a direct solver at the beginning of the computation and it can ultimately become a bottleneck if the number of subdomains is very large. In this paper, two three-level BDDC methods are introduced for solving the coarse problem approximately for problems in three dimensions. This is an extension of previous work for the two-dimensional case. Edge constraints are considered in this work since vertex constraints alone, which work well in two dimensions, result in a noncompetitive algorithm in three dimensions. Some new technical tools are then needed in the analysis and this makes the three-dimensional case more complicated. Estimates of the condition numbers are provided for two three-level BDDC methods, and numerical experiments are also discussed.
Description
This is the published version, also available here: http://dx.doi.org/10.1137/050629902.
Date
2007-10-05
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Society for Industrial and Applied Mathematics
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Keywords
BDDC, three-level, three dimensions, domain decomposition, coarse problem, condition number, Chebyshev iteration
Citation
Tu, Xuemin. "Three-level BDDC in three dimensions." (2007) SIAM J. Sci. Comput., 29(4), 1759–1780. (22 pages). http://dx.doi.org/10.1137/050629902.