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Local Fourier analysis is a commonly used tool for the analysis of multigridand other multilevel algorithms, providing both insight into observedconvergence rates and predictive analysis of the performance of manyalgorithms. In this paper, for the first time, we adapt local Fourier analysisto examine variants of two- and three-level balancing domain decomposition byconstraints (BDDC) algorithms, to better understand the eigenvaluedistributions and condition number bounds on these preconditioned operators.This adaptation is based on a modified choice of basis for the space of Fourierharmonics that greatly simplifies the application of local Fourier analysis inthis setting. The local Fourier analysis is validated by considering the twodimensional Laplacian and predicting the condition numbers of thepreconditioned operators with different sizes of subdomains. Several variantsare analyzed, showing the two- and three-level performance of the "lumped"variant can be greatly improved when used in multiplicative combination with aweighted diagonal scaling preconditioner, with weight optimized through the useof LFA.

Local Fourier analysis of Balancing Domain Decomposition by Constraints algorithms