LOCAL FOURIER ANALYSIS OF BDDC-LIKE ALGORITHMS∗

Local Fourier analysis is a commonly used tool for the analysis of multigrid and other multilevel algorithms, providing both insight into observed convergence rates and predictive analysis of the performance of many algorithms. In this paper, we adapt local Fourier analysis to examine variants of twoand three-level BDDC algorithms, to better understand the eigenvalue distributions and condition number bounds on these preconditioned operators. This adaptation is based on a new choice of basis for the space of Fourier harmonics that greatly simplifies the application of local Fourier analysis in this setting. The local Fourier analysis is validated by considering the two dimensional Laplacian and predicting the condition numbers of the preconditioned operators with different sizes of subdomains. Several variants are analyzed, showing the twoand three-level performance of the “lumped” variant can be greatly improved when used in multiplicative combination with a weighted diagonal scaling preconditioner, with weight optimized through the use of LFA.

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